Atlas Format

Atlas files contain a collection of map assignments or redistrictings. The format is a specialization of the JSONL format. Each line in an Atlas file is a JSON object. The first three lines describe the particular Atlas. Starting with the fourth line, each line is a JSON object that describes a map assignment. In addition to the map assignment, each line can also contain statistics and other information about the map assignment. These can be specified by the user.

AtlasIO code

The primary code is written in the Julia programming language, but it can be used in Python as well. The Julia AtlasIO library is an official Julia package and can be loaded using the Julia Package Manager.

The Python libraries, as well as the Julia source code, can be found in the AtlasIO Git repository. This repository contains a number of tools to read in and manipulate Atlas files. The Python library can only read Atlas files, it cannot write them. The Julia library can read and write Atlas files.

The Atlas File Format

The Atlas format is a JSONL (JSON Lines) format adapted to hold district maps from redistricting efforts. The Atlas format is a simple extension of the JSONL format that allows for the storage of maps and their associated data in a single file. The AtlasIO.jl Julia library provides the ability to read and write Atlas files. The AtlasIO.py Python library, from the same git repository, provides the ability to read but not the ability to write files. This format was developed by the Duke Quantifying Gerrymandering Group.

Structure of an Atlas File

Each individual line of an Atlas file is JSON object. As such they can be read line by line unlike a single JSON.

  • This first line is a comment that identifies the file as an Atlas of maps and describes the Atlas format.
  • The second line is a JSON object that describes the basic information of the collection of maps saved in this Atlas.
  • The third line is a JSON object that describes the extra data assigned to each map. It can be adapted to the particular setting. In particular, it gives that data times and key names associated to the additional data.
  • Each of the following lines, starting with the 4th line, is a JSON object that describes a map and its associated data.

Example Atlas file

This is a simple example of Atlas file. It is for splitting a 4x4 rectangular grid into two districts. It was generated using the cycle walk algorithm. The file can be down loaded here cycleWalk_grid4x4__gamma0.0_kappa0.1.jsonl.

"This is an Atlas for Redistricting Maps. See 'https://git.math.duke.edu/gitlab/jonm/atlasio.jl' for more information."
{"description":"","date":"2025-09-07T15:39:21.934","atlasParamType":"Dict{String, Any}","mapParamType":"Dict{String, Any}"}
{"energy weights":[],"population bounds":[8,8],"energies":[],"package.version":"CycleWalk v0.1.3","districts":2,"popdev":0.05}
{"name":"step1","weight":1,"data":{"get_log_spanning_forests":8.0507033814703,"get_log_spanning_trees":[4.02535169073515,4.02535169073515],"get_isoperimetric_scores":[18.0,18.0]},"districting":[{"[\"(3,0)\"]":2},{"[\"(0,1)\"]":1},{"[\"(2,0)\"]":2},{"[\"(0,2)\"]":1},{"[\"(3,1)\"]":2},{"[\"(1,1)\"]":1},{"[\"(3,2)\"]":2},{"[\"(3,3)\"]":2},{"[\"(0,3)\"]":1},{"[\"(0,0)\"]":1},{"[\"(1,0)\"]":1},{"[\"(2,1)\"]":2},{"[\"(1,2)\"]":1},{"[\"(2,2)\"]":2},{"[\"(2,3)\"]":2},{"[\"(1,3)\"]":1}]}
{"name":"step10","weight":1,"data":{"get_log_spanning_forests":8.0507033814703,"get_log_spanning_trees":[4.02535169073515,4.02535169073515],"get_isoperimetric_scores":[18.0,18.0]},"districting":[{"[\"(3,0)\"]":2},{"[\"(0,1)\"]":1},{"[\"(2,0)\"]":2},{"[\"(0,2)\"]":1},{"[\"(3,1)\"]":2},{"[\"(1,1)\"]":1},{"[\"(3,2)\"]":2},{"[\"(3,3)\"]":2},{"[\"(0,3)\"]":1},{"[\"(0,0)\"]":1},{"[\"(1,0)\"]":1},{"[\"(2,1)\"]":2},{"[\"(1,2)\"]":1},{"[\"(2,2)\"]":2},{"[\"(2,3)\"]":2},{"[\"(1,3)\"]":1}]}
{"name":"step20","weight":1,"data":{"get_log_spanning_forests":5.411646051855039,"get_log_spanning_trees":[4.025351690735149,1.3862943611198901],"get_isoperimetric_scores":[18.0,32.0]},"districting":[{"[\"(3,0)\"]":2},{"[\"(0,1)\"]":1},{"[\"(2,0)\"]":1},{"[\"(0,2)\"]":1},{"[\"(3,1)\"]":2},{"[\"(1,1)\"]":1},{"[\"(3,2)\"]":2},{"[\"(3,3)\"]":2},{"[\"(0,3)\"]":2},{"[\"(0,0)\"]":1},{"[\"(1,0)\"]":1},{"[\"(2,1)\"]":1},{"[\"(1,2)\"]":1},{"[\"(2,2)\"]":2},{"[\"(2,3)\"]":2},{"[\"(1,3)\"]":2}]}
{"name":"step30","weight":1,"data":{"get_log_spanning_forests":5.411646051855039,"get_log_spanning_trees":[4.025351690735149,1.3862943611198901],"get_isoperimetric_scores":[18.0,32.0]},"districting":[{"[\"(3,0)\"]":2},{"[\"(0,1)\"]":1},{"[\"(2,0)\"]":1},{"[\"(0,2)\"]":1},{"[\"(3,1)\"]":2},{"[\"(1,1)\"]":1},{"[\"(3,2)\"]":2},{"[\"(3,3)\"]":2},{"[\"(0,3)\"]":2},{"[\"(0,0)\"]":1},{"[\"(1,0)\"]":1},{"[\"(2,1)\"]":1},{"[\"(1,2)\"]":1},{"[\"(2,2)\"]":2},{"[\"(2,3)\"]":2},{"[\"(1,3)\"]":2}]}
{"name":"step40","weight":1,"data":{"get_log_spanning_forests":8.0507033814703,"get_log_spanning_trees":[4.02535169073515,4.02535169073515],"get_isoperimetric_scores":[18.0,18.0]},"districting":[{"[\"(3,0)\"]":1},{"[\"(0,1)\"]":1},{"[\"(2,0)\"]":1},{"[\"(0,2)\"]":2},{"[\"(3,1)\"]":1},{"[\"(1,1)\"]":1},{"[\"(3,2)\"]":2},{"[\"(3,3)\"]":2},{"[\"(0,3)\"]":2},{"[\"(0,0)\"]":1},{"[\"(1,0)\"]":1},{"[\"(2,1)\"]":1},{"[\"(1,2)\"]":2},{"[\"(2,2)\"]":2},{"[\"(2,3)\"]":2},{"[\"(1,3)\"]":2}]}
{"name":"step50","weight":1,"data":{"get_log_spanning_forests":8.0507033814703,"get_log_spanning_trees":[4.02535169073515,4.02535169073515],"get_isoperimetric_scores":[18.0,18.0]},"districting":[{"[\"(3,0)\"]":1},{"[\"(0,1)\"]":1},{"[\"(2,0)\"]":1},{"[\"(0,2)\"]":2},{"[\"(3,1)\"]":1},{"[\"(1,1)\"]":1},{"[\"(3,2)\"]":2},{"[\"(3,3)\"]":2},{"[\"(0,3)\"]":2},{"[\"(0,0)\"]":1},{"[\"(1,0)\"]":1},{"[\"(2,1)\"]":1},{"[\"(1,2)\"]":2},{"[\"(2,2)\"]":2},{"[\"(2,3)\"]":2},{"[\"(1,3)\"]":2}]}
{"name":"step60","weight":1,"data":{"get_log_spanning_forests":8.0507033814703,"get_log_spanning_trees":[4.02535169073515,4.02535169073515],"get_isoperimetric_scores":[18.0,18.0]},"districting":[{"[\"(3,0)\"]":1},{"[\"(0,1)\"]":1},{"[\"(2,0)\"]":1},{"[\"(0,2)\"]":2},{"[\"(3,1)\"]":1},{"[\"(1,1)\"]":1},{"[\"(3,2)\"]":2},{"[\"(3,3)\"]":2},{"[\"(0,3)\"]":2},{"[\"(0,0)\"]":1},{"[\"(1,0)\"]":1},{"[\"(2,1)\"]":1},{"[\"(1,2)\"]":2},{"[\"(2,2)\"]":2},{"[\"(2,3)\"]":2},{"[\"(1,3)\"]":2}]}
{"name":"step70","weight":1,"data":{"get_log_spanning_forests":8.0507033814703,"get_log_spanning_trees":[4.02535169073515,4.02535169073515],"get_isoperimetric_scores":[18.0,18.0]},"districting":[{"[\"(3,0)\"]":1},{"[\"(0,1)\"]":1},{"[\"(2,0)\"]":1},{"[\"(0,2)\"]":2},{"[\"(3,1)\"]":1},{"[\"(1,1)\"]":1},{"[\"(3,2)\"]":2},{"[\"(3,3)\"]":2},{"[\"(0,3)\"]":2},{"[\"(0,0)\"]":1},{"[\"(1,0)\"]":1},{"[\"(2,1)\"]":1},{"[\"(1,2)\"]":2},{"[\"(2,2)\"]":2},{"[\"(2,3)\"]":2},{"[\"(1,3)\"]":2}]}
{"name":"step80","weight":1,"data":{"get_log_spanning_forests":8.0507033814703,"get_log_spanning_trees":[4.02535169073515,4.02535169073515],"get_isoperimetric_scores":[18.0,18.0]},"districting":[{"[\"(3,0)\"]":1},{"[\"(0,1)\"]":1},{"[\"(2,0)\"]":1},{"[\"(0,2)\"]":2},{"[\"(3,1)\"]":1},{"[\"(1,1)\"]":1},{"[\"(3,2)\"]":2},{"[\"(3,3)\"]":2},{"[\"(0,3)\"]":2},{"[\"(0,0)\"]":1},{"[\"(1,0)\"]":1},{"[\"(2,1)\"]":1},{"[\"(1,2)\"]":2},{"[\"(2,2)\"]":2},{"[\"(2,3)\"]":2},{"[\"(1,3)\"]":2}]}
{"name":"step90","weight":1,"data":{"get_log_spanning_forests":8.0507033814703,"get_log_spanning_trees":[4.02535169073515,4.02535169073515],"get_isoperimetric_scores":[18.0,18.0]},"districting":[{"[\"(3,0)\"]":1},{"[\"(0,1)\"]":1},{"[\"(2,0)\"]":1},{"[\"(0,2)\"]":2},{"[\"(3,1)\"]":1},{"[\"(1,1)\"]":1},{"[\"(3,2)\"]":2},{"[\"(3,3)\"]":2},{"[\"(0,3)\"]":2},{"[\"(0,0)\"]":1},{"[\"(1,0)\"]":1},{"[\"(2,1)\"]":1},{"[\"(1,2)\"]":2},{"[\"(2,2)\"]":2},{"[\"(2,3)\"]":2},{"[\"(1,3)\"]":2}]}
{"name":"step100","weight":1,"data":{"get_log_spanning_forests":8.0507033814703,"get_log_spanning_trees":[4.02535169073515,4.02535169073515],"get_isoperimetric_scores":[18.0,18.0]},"districting":[{"[\"(3,0)\"]":1},{"[\"(0,1)\"]":1},{"[\"(2,0)\"]":1},{"[\"(0,2)\"]":2},{"[\"(3,1)\"]":1},{"[\"(1,1)\"]":1},{"[\"(3,2)\"]":2},{"[\"(3,3)\"]":2},{"[\"(0,3)\"]":2},{"[\"(0,0)\"]":1},{"[\"(1,0)\"]":1},{"[\"(2,1)\"]":1},{"[\"(1,2)\"]":2},{"[\"(2,2)\"]":2},{"[\"(2,3)\"]":2},{"[\"(1,3)\"]":2}]}
{"name":"step110","weight":1,"data":{"get_log_spanning_forests":5.416100402204422,"get_log_spanning_trees":[2.708050201102211,2.708050201102211],"get_isoperimetric_scores":[24.5,24.5]},"districting":[{"[\"(3,0)\"]":1},{"[\"(0,1)\"]":1},{"[\"(2,0)\"]":1},{"[\"(0,2)\"]":1},{"[\"(3,1)\"]":2},{"[\"(1,1)\"]":1},{"[\"(3,2)\"]":2},{"[\"(3,3)\"]":2},{"[\"(0,3)\"]":2},{"[\"(0,0)\"]":1},{"[\"(1,0)\"]":1},{"[\"(2,1)\"]":1},{"[\"(1,2)\"]":2},{"[\"(2,2)\"]":2},{"[\"(2,3)\"]":2},{"[\"(1,3)\"]":2}]}
{"name":"step120","weight":1,"data":{"get_log_spanning_forests":5.416100402204422,"get_log_spanning_trees":[2.708050201102211,2.708050201102211],"get_isoperimetric_scores":[24.5,24.5]},"districting":[{"[\"(3,0)\"]":1},{"[\"(0,1)\"]":1},{"[\"(2,0)\"]":1},{"[\"(0,2)\"]":1},{"[\"(3,1)\"]":2},{"[\"(1,1)\"]":1},{"[\"(3,2)\"]":2},{"[\"(3,3)\"]":2},{"[\"(0,3)\"]":2},{"[\"(0,0)\"]":1},{"[\"(1,0)\"]":1},{"[\"(2,1)\"]":1},{"[\"(1,2)\"]":2},{"[\"(2,2)\"]":2},{"[\"(2,3)\"]":2},{"[\"(1,3)\"]":2}]}
{"name":"step130","weight":1,"data":{"get_log_spanning_forests":5.416100402204422,"get_log_spanning_trees":[2.708050201102211,2.708050201102211],"get_isoperimetric_scores":[24.5,24.5]},"districting":[{"[\"(3,0)\"]":1},{"[\"(0,1)\"]":1},{"[\"(2,0)\"]":1},{"[\"(0,2)\"]":1},{"[\"(3,1)\"]":2},{"[\"(1,1)\"]":1},{"[\"(3,2)\"]":2},{"[\"(3,3)\"]":2},{"[\"(0,3)\"]":2},{"[\"(0,0)\"]":1},{"[\"(1,0)\"]":1},{"[\"(2,1)\"]":1},{"[\"(1,2)\"]":2},{"[\"(2,2)\"]":2},{"[\"(2,3)\"]":2},{"[\"(1,3)\"]":2}]}
{"name":"step140","weight":1,"data":{"get_log_spanning_forests":8.0507033814703,"get_log_spanning_trees":[4.02535169073515,4.02535169073515],"get_isoperimetric_scores":[18.0,18.0]},"districting":[{"[\"(3,0)\"]":1},{"[\"(0,1)\"]":1},{"[\"(2,0)\"]":1},{"[\"(0,2)\"]":2},{"[\"(3,1)\"]":1},{"[\"(1,1)\"]":1},{"[\"(3,2)\"]":2},{"[\"(3,3)\"]":2},{"[\"(0,3)\"]":2},{"[\"(0,0)\"]":1},{"[\"(1,0)\"]":1},{"[\"(2,1)\"]":1},{"[\"(1,2)\"]":2},{"[\"(2,2)\"]":2},{"[\"(2,3)\"]":2},{"[\"(1,3)\"]":2}]}
{"name":"step150","weight":1,"data":{"get_log_spanning_forests":8.0507033814703,"get_log_spanning_trees":[4.02535169073515,4.02535169073515],"get_isoperimetric_scores":[18.0,18.0]},"districting":[{"[\"(3,0)\"]":1},{"[\"(0,1)\"]":1},{"[\"(2,0)\"]":1},{"[\"(0,2)\"]":2},{"[\"(3,1)\"]":1},{"[\"(1,1)\"]":1},{"[\"(3,2)\"]":2},{"[\"(3,3)\"]":2},{"[\"(0,3)\"]":2},{"[\"(0,0)\"]":1},{"[\"(1,0)\"]":1},{"[\"(2,1)\"]":1},{"[\"(1,2)\"]":2},{"[\"(2,2)\"]":2},{"[\"(2,3)\"]":2},{"[\"(1,3)\"]":2}]}
{"name":"step160","weight":1,"data":{"get_log_spanning_forests":8.0507033814703,"get_log_spanning_trees":[4.02535169073515,4.02535169073515],"get_isoperimetric_scores":[18.0,18.0]},"districting":[{"[\"(3,0)\"]":1},{"[\"(0,1)\"]":1},{"[\"(2,0)\"]":1},{"[\"(0,2)\"]":2},{"[\"(3,1)\"]":1},{"[\"(1,1)\"]":1},{"[\"(3,2)\"]":2},{"[\"(3,3)\"]":2},{"[\"(0,3)\"]":2},{"[\"(0,0)\"]":1},{"[\"(1,0)\"]":1},{"[\"(2,1)\"]":1},{"[\"(1,2)\"]":2},{"[\"(2,2)\"]":2},{"[\"(2,3)\"]":2},{"[\"(1,3)\"]":2}]}
{"name":"step170","weight":1,"data":{"get_log_spanning_forests":8.0507033814703,"get_log_spanning_trees":[4.02535169073515,4.02535169073515],"get_isoperimetric_scores":[18.0,18.0]},"districting":[{"[\"(3,0)\"]":1},{"[\"(0,1)\"]":1},{"[\"(2,0)\"]":1},{"[\"(0,2)\"]":2},{"[\"(3,1)\"]":1},{"[\"(1,1)\"]":1},{"[\"(3,2)\"]":2},{"[\"(3,3)\"]":2},{"[\"(0,3)\"]":2},{"[\"(0,0)\"]":1},{"[\"(1,0)\"]":1},{"[\"(2,1)\"]":1},{"[\"(1,2)\"]":2},{"[\"(2,2)\"]":2},{"[\"(2,3)\"]":2},{"[\"(1,3)\"]":2}]}
{"name":"step180","weight":1,"data":{"get_log_spanning_forests":8.0507033814703,"get_log_spanning_trees":[4.02535169073515,4.02535169073515],"get_isoperimetric_scores":[18.0,18.0]},"districting":[{"[\"(3,0)\"]":1},{"[\"(0,1)\"]":1},{"[\"(2,0)\"]":1},{"[\"(0,2)\"]":2},{"[\"(3,1)\"]":1},{"[\"(1,1)\"]":1},{"[\"(3,2)\"]":2},{"[\"(3,3)\"]":2},{"[\"(0,3)\"]":2},{"[\"(0,0)\"]":1},{"[\"(1,0)\"]":1},{"[\"(2,1)\"]":1},{"[\"(1,2)\"]":2},{"[\"(2,2)\"]":2},{"[\"(2,3)\"]":2},{"[\"(1,3)\"]":2}]}
{"name":"step190","weight":1,"data":{"get_log_spanning_forests":8.0507033814703,"get_log_spanning_trees":[4.02535169073515,4.02535169073515],"get_isoperimetric_scores":[18.0,18.0]},"districting":[{"[\"(3,0)\"]":1},{"[\"(0,1)\"]":1},{"[\"(2,0)\"]":1},{"[\"(0,2)\"]":2},{"[\"(3,1)\"]":1},{"[\"(1,1)\"]":1},{"[\"(3,2)\"]":2},{"[\"(3,3)\"]":2},{"[\"(0,3)\"]":2},{"[\"(0,0)\"]":1},{"[\"(1,0)\"]":1},{"[\"(2,1)\"]":1},{"[\"(1,2)\"]":2},{"[\"(2,2)\"]":2},{"[\"(2,3)\"]":2},{"[\"(1,3)\"]":2}]}
{"name":"step200","weight":1,"data":{"get_log_spanning_forests":8.0507033814703,"get_log_spanning_trees":[4.02535169073515,4.02535169073515],"get_isoperimetric_scores":[18.0,18.0]},"districting":[{"[\"(3,0)\"]":1},{"[\"(0,1)\"]":1},{"[\"(2,0)\"]":1},{"[\"(0,2)\"]":2},{"[\"(3,1)\"]":1},{"[\"(1,1)\"]":1},{"[\"(3,2)\"]":2},{"[\"(3,3)\"]":2},{"[\"(0,3)\"]":2},{"[\"(0,0)\"]":1},{"[\"(1,0)\"]":1},{"[\"(2,1)\"]":1},{"[\"(1,2)\"]":2},{"[\"(2,2)\"]":2},{"[\"(2,3)\"]":2},{"[\"(1,3)\"]":2}]}
{"name":"step210","weight":1,"data":{"get_log_spanning_forests":8.0507033814703,"get_log_spanning_trees":[4.02535169073515,4.02535169073515],"get_isoperimetric_scores":[18.0,18.0]},"districting":[{"[\"(3,0)\"]":1},{"[\"(0,1)\"]":1},{"[\"(2,0)\"]":1},{"[\"(0,2)\"]":2},{"[\"(3,1)\"]":1},{"[\"(1,1)\"]":1},{"[\"(3,2)\"]":2},{"[\"(3,3)\"]":2},{"[\"(0,3)\"]":2},{"[\"(0,0)\"]":1},{"[\"(1,0)\"]":1},{"[\"(2,1)\"]":1},{"[\"(1,2)\"]":2},{"[\"(2,2)\"]":2},{"[\"(2,3)\"]":2},{"[\"(1,3)\"]":2}]}
{"name":"step220","weight":1,"data":{"get_log_spanning_forests":8.0507033814703,"get_log_spanning_trees":[4.02535169073515,4.02535169073515],"get_isoperimetric_scores":[18.0,18.0]},"districting":[{"[\"(3,0)\"]":1},{"[\"(0,1)\"]":1},{"[\"(2,0)\"]":1},{"[\"(0,2)\"]":2},{"[\"(3,1)\"]":1},{"[\"(1,1)\"]":1},{"[\"(3,2)\"]":2},{"[\"(3,3)\"]":2},{"[\"(0,3)\"]":2},{"[\"(0,0)\"]":1},{"[\"(1,0)\"]":1},{"[\"(2,1)\"]":1},{"[\"(1,2)\"]":2},{"[\"(2,2)\"]":2},{"[\"(2,3)\"]":2},{"[\"(1,3)\"]":2}]}
{"name":"step230","weight":1,"data":{"get_log_spanning_forests":8.0507033814703,"get_log_spanning_trees":[4.02535169073515,4.02535169073515],"get_isoperimetric_scores":[18.0,18.0]},"districting":[{"[\"(3,0)\"]":1},{"[\"(0,1)\"]":1},{"[\"(2,0)\"]":1},{"[\"(0,2)\"]":2},{"[\"(3,1)\"]":1},{"[\"(1,1)\"]":1},{"[\"(3,2)\"]":2},{"[\"(3,3)\"]":2},{"[\"(0,3)\"]":2},{"[\"(0,0)\"]":1},{"[\"(1,0)\"]":1},{"[\"(2,1)\"]":1},{"[\"(1,2)\"]":2},{"[\"(2,2)\"]":2},{"[\"(2,3)\"]":2},{"[\"(1,3)\"]":2}]}
{"name":"step240","weight":1,"data":{"get_log_spanning_forests":5.411646051855042,"get_log_spanning_trees":[1.3862943611198915,4.0253516907351505],"get_isoperimetric_scores":[32.0,18.0]},"districting":[{"[\"(3,0)\"]":1},{"[\"(0,1)\"]":1},{"[\"(2,0)\"]":1},{"[\"(0,2)\"]":1},{"[\"(3,1)\"]":2},{"[\"(1,1)\"]":1},{"[\"(3,2)\"]":2},{"[\"(3,3)\"]":2},{"[\"(0,3)\"]":1},{"[\"(0,0)\"]":1},{"[\"(1,0)\"]":1},{"[\"(2,1)\"]":2},{"[\"(1,2)\"]":2},{"[\"(2,2)\"]":2},{"[\"(2,3)\"]":2},{"[\"(1,3)\"]":2}]}
{"name":"step250","weight":1,"data":{"get_log_spanning_forests":4.02535169073515,"get_log_spanning_trees":[4.440892098500626e-16,4.025351690735149],"get_isoperimetric_scores":[40.5,18.0]},"districting":[{"[\"(3,0)\"]":1},{"[\"(0,1)\"]":1},{"[\"(2,0)\"]":1},{"[\"(0,2)\"]":1},{"[\"(3,1)\"]":2},{"[\"(1,1)\"]":2},{"[\"(3,2)\"]":2},{"[\"(3,3)\"]":2},{"[\"(0,3)\"]":1},{"[\"(0,0)\"]":1},{"[\"(1,0)\"]":1},{"[\"(2,1)\"]":2},{"[\"(1,2)\"]":2},{"[\"(2,2)\"]":2},{"[\"(2,3)\"]":2},{"[\"(1,3)\"]":1}]}
{"name":"step260","weight":1,"data":{"get_log_spanning_forests":8.0507033814703,"get_log_spanning_trees":[4.02535169073515,4.02535169073515],"get_isoperimetric_scores":[18.0,18.0]},"districting":[{"[\"(3,0)\"]":1},{"[\"(0,1)\"]":1},{"[\"(2,0)\"]":1},{"[\"(0,2)\"]":2},{"[\"(3,1)\"]":1},{"[\"(1,1)\"]":1},{"[\"(3,2)\"]":2},{"[\"(3,3)\"]":2},{"[\"(0,3)\"]":2},{"[\"(0,0)\"]":1},{"[\"(1,0)\"]":1},{"[\"(2,1)\"]":1},{"[\"(1,2)\"]":2},{"[\"(2,2)\"]":2},{"[\"(2,3)\"]":2},{"[\"(1,3)\"]":2}]}
{"name":"step270","weight":1,"data":{"get_log_spanning_forests":8.0507033814703,"get_log_spanning_trees":[4.02535169073515,4.02535169073515],"get_isoperimetric_scores":[18.0,18.0]},"districting":[{"[\"(3,0)\"]":1},{"[\"(0,1)\"]":1},{"[\"(2,0)\"]":1},{"[\"(0,2)\"]":2},{"[\"(3,1)\"]":1},{"[\"(1,1)\"]":1},{"[\"(3,2)\"]":2},{"[\"(3,3)\"]":2},{"[\"(0,3)\"]":2},{"[\"(0,0)\"]":1},{"[\"(1,0)\"]":1},{"[\"(2,1)\"]":1},{"[\"(1,2)\"]":2},{"[\"(2,2)\"]":2},{"[\"(2,3)\"]":2},{"[\"(1,3)\"]":2}]}
{"name":"step280","weight":1,"data":{"get_log_spanning_forests":8.0507033814703,"get_log_spanning_trees":[4.02535169073515,4.02535169073515],"get_isoperimetric_scores":[18.0,18.0]},"districting":[{"[\"(3,0)\"]":1},{"[\"(0,1)\"]":1},{"[\"(2,0)\"]":1},{"[\"(0,2)\"]":2},{"[\"(3,1)\"]":1},{"[\"(1,1)\"]":1},{"[\"(3,2)\"]":2},{"[\"(3,3)\"]":2},{"[\"(0,3)\"]":2},{"[\"(0,0)\"]":1},{"[\"(1,0)\"]":1},{"[\"(2,1)\"]":1},{"[\"(1,2)\"]":2},{"[\"(2,2)\"]":2},{"[\"(2,3)\"]":2},{"[\"(1,3)\"]":2}]}
{"name":"step290","weight":1,"data":{"get_log_spanning_forests":8.0507033814703,"get_log_spanning_trees":[4.02535169073515,4.02535169073515],"get_isoperimetric_scores":[18.0,18.0]},"districting":[{"[\"(3,0)\"]":1},{"[\"(0,1)\"]":1},{"[\"(2,0)\"]":1},{"[\"(0,2)\"]":2},{"[\"(3,1)\"]":1},{"[\"(1,1)\"]":1},{"[\"(3,2)\"]":2},{"[\"(3,3)\"]":2},{"[\"(0,3)\"]":2},{"[\"(0,0)\"]":1},{"[\"(1,0)\"]":1},{"[\"(2,1)\"]":1},{"[\"(1,2)\"]":2},{"[\"(2,2)\"]":2},{"[\"(2,3)\"]":2},{"[\"(1,3)\"]":2}]}
{"name":"step300","weight":1,"data":{"get_log_spanning_forests":8.0507033814703,"get_log_spanning_trees":[4.02535169073515,4.02535169073515],"get_isoperimetric_scores":[18.0,18.0]},"districting":[{"[\"(3,0)\"]":1},{"[\"(0,1)\"]":1},{"[\"(2,0)\"]":1},{"[\"(0,2)\"]":2},{"[\"(3,1)\"]":1},{"[\"(1,1)\"]":1},{"[\"(3,2)\"]":2},{"[\"(3,3)\"]":2},{"[\"(0,3)\"]":2},{"[\"(0,0)\"]":1},{"[\"(1,0)\"]":1},{"[\"(2,1)\"]":1},{"[\"(1,2)\"]":2},{"[\"(2,2)\"]":2},{"[\"(2,3)\"]":2},{"[\"(1,3)\"]":2}]}
{"name":"step310","weight":1,"data":{"get_log_spanning_forests":8.0507033814703,"get_log_spanning_trees":[4.02535169073515,4.02535169073515],"get_isoperimetric_scores":[18.0,18.0]},"districting":[{"[\"(3,0)\"]":1},{"[\"(0,1)\"]":1},{"[\"(2,0)\"]":1},{"[\"(0,2)\"]":2},{"[\"(3,1)\"]":1},{"[\"(1,1)\"]":1},{"[\"(3,2)\"]":2},{"[\"(3,3)\"]":2},{"[\"(0,3)\"]":2},{"[\"(0,0)\"]":1},{"[\"(1,0)\"]":1},{"[\"(2,1)\"]":1},{"[\"(1,2)\"]":2},{"[\"(2,2)\"]":2},{"[\"(2,3)\"]":2},{"[\"(1,3)\"]":2}]}
{"name":"step320","weight":1,"data":{"get_log_spanning_forests":8.0507033814703,"get_log_spanning_trees":[4.02535169073515,4.02535169073515],"get_isoperimetric_scores":[18.0,18.0]},"districting":[{"[\"(3,0)\"]":1},{"[\"(0,1)\"]":1},{"[\"(2,0)\"]":1},{"[\"(0,2)\"]":2},{"[\"(3,1)\"]":1},{"[\"(1,1)\"]":1},{"[\"(3,2)\"]":2},{"[\"(3,3)\"]":2},{"[\"(0,3)\"]":2},{"[\"(0,0)\"]":1},{"[\"(1,0)\"]":1},{"[\"(2,1)\"]":1},{"[\"(1,2)\"]":2},{"[\"(2,2)\"]":2},{"[\"(2,3)\"]":2},{"[\"(1,3)\"]":2}]}
{"name":"step330","weight":1,"data":{"get_log_spanning_forests":5.41610040220442,"get_log_spanning_trees":[2.7080502011022105,2.7080502011022096],"get_isoperimetric_scores":[24.5,24.5]},"districting":[{"[\"(3,0)\"]":2},{"[\"(0,1)\"]":1},{"[\"(2,0)\"]":1},{"[\"(0,2)\"]":1},{"[\"(3,1)\"]":2},{"[\"(1,1)\"]":1},{"[\"(3,2)\"]":2},{"[\"(3,3)\"]":2},{"[\"(0,3)\"]":1},{"[\"(0,0)\"]":1},{"[\"(1,0)\"]":1},{"[\"(2,1)\"]":2},{"[\"(1,2)\"]":1},{"[\"(2,2)\"]":2},{"[\"(2,3)\"]":2},{"[\"(1,3)\"]":2}]}
{"name":"step340","weight":1,"data":{"get_log_spanning_forests":5.41610040220442,"get_log_spanning_trees":[2.7080502011022105,2.7080502011022096],"get_isoperimetric_scores":[24.5,24.5]},"districting":[{"[\"(3,0)\"]":2},{"[\"(0,1)\"]":1},{"[\"(2,0)\"]":1},{"[\"(0,2)\"]":1},{"[\"(3,1)\"]":2},{"[\"(1,1)\"]":1},{"[\"(3,2)\"]":2},{"[\"(3,3)\"]":2},{"[\"(0,3)\"]":1},{"[\"(0,0)\"]":1},{"[\"(1,0)\"]":1},{"[\"(2,1)\"]":2},{"[\"(1,2)\"]":1},{"[\"(2,2)\"]":2},{"[\"(2,3)\"]":2},{"[\"(1,3)\"]":2}]}
{"name":"step350","weight":1,"data":{"get_log_spanning_forests":5.416100402204422,"get_log_spanning_trees":[2.7080502011022123,2.7080502011022096],"get_isoperimetric_scores":[24.5,24.5]},"districting":[{"[\"(3,0)\"]":2},{"[\"(0,1)\"]":1},{"[\"(2,0)\"]":2},{"[\"(0,2)\"]":1},{"[\"(3,1)\"]":2},{"[\"(1,1)\"]":2},{"[\"(3,2)\"]":2},{"[\"(3,3)\"]":2},{"[\"(0,3)\"]":1},{"[\"(0,0)\"]":1},{"[\"(1,0)\"]":2},{"[\"(2,1)\"]":2},{"[\"(1,2)\"]":1},{"[\"(2,2)\"]":1},{"[\"(2,3)\"]":1},{"[\"(1,3)\"]":1}]}
{"name":"step360","weight":1,"data":{"get_log_spanning_forests":5.416100402204422,"get_log_spanning_trees":[2.7080502011022123,2.7080502011022096],"get_isoperimetric_scores":[24.5,24.5]},"districting":[{"[\"(3,0)\"]":2},{"[\"(0,1)\"]":1},{"[\"(2,0)\"]":2},{"[\"(0,2)\"]":1},{"[\"(3,1)\"]":2},{"[\"(1,1)\"]":2},{"[\"(3,2)\"]":2},{"[\"(3,3)\"]":2},{"[\"(0,3)\"]":1},{"[\"(0,0)\"]":1},{"[\"(1,0)\"]":2},{"[\"(2,1)\"]":2},{"[\"(1,2)\"]":1},{"[\"(2,2)\"]":1},{"[\"(2,3)\"]":1},{"[\"(1,3)\"]":1}]}
{"name":"step370","weight":1,"data":{"get_log_spanning_forests":5.41610040220442,"get_log_spanning_trees":[2.7080502011022105,2.7080502011022096],"get_isoperimetric_scores":[24.5,24.5]},"districting":[{"[\"(3,0)\"]":2},{"[\"(0,1)\"]":1},{"[\"(2,0)\"]":1},{"[\"(0,2)\"]":1},{"[\"(3,1)\"]":2},{"[\"(1,1)\"]":1},{"[\"(3,2)\"]":2},{"[\"(3,3)\"]":2},{"[\"(0,3)\"]":1},{"[\"(0,0)\"]":1},{"[\"(1,0)\"]":1},{"[\"(2,1)\"]":2},{"[\"(1,2)\"]":1},{"[\"(2,2)\"]":2},{"[\"(2,3)\"]":2},{"[\"(1,3)\"]":2}]}
{"name":"step380","weight":1,"data":{"get_log_spanning_forests":5.41610040220442,"get_log_spanning_trees":[2.7080502011022105,2.7080502011022096],"get_isoperimetric_scores":[24.5,24.5]},"districting":[{"[\"(3,0)\"]":2},{"[\"(0,1)\"]":1},{"[\"(2,0)\"]":1},{"[\"(0,2)\"]":1},{"[\"(3,1)\"]":2},{"[\"(1,1)\"]":1},{"[\"(3,2)\"]":2},{"[\"(3,3)\"]":2},{"[\"(0,3)\"]":1},{"[\"(0,0)\"]":1},{"[\"(1,0)\"]":1},{"[\"(2,1)\"]":2},{"[\"(1,2)\"]":1},{"[\"(2,2)\"]":2},{"[\"(2,3)\"]":2},{"[\"(1,3)\"]":2}]}
{"name":"step390","weight":1,"data":{"get_log_spanning_forests":8.0507033814703,"get_log_spanning_trees":[4.02535169073515,4.02535169073515],"get_isoperimetric_scores":[18.0,18.0]},"districting":[{"[\"(3,0)\"]":1},{"[\"(0,1)\"]":1},{"[\"(2,0)\"]":1},{"[\"(0,2)\"]":2},{"[\"(3,1)\"]":1},{"[\"(1,1)\"]":1},{"[\"(3,2)\"]":2},{"[\"(3,3)\"]":2},{"[\"(0,3)\"]":2},{"[\"(0,0)\"]":1},{"[\"(1,0)\"]":1},{"[\"(2,1)\"]":1},{"[\"(1,2)\"]":2},{"[\"(2,2)\"]":2},{"[\"(2,3)\"]":2},{"[\"(1,3)\"]":2}]}
{"name":"step400","weight":1,"data":{"get_log_spanning_forests":8.0507033814703,"get_log_spanning_trees":[4.02535169073515,4.02535169073515],"get_isoperimetric_scores":[18.0,18.0]},"districting":[{"[\"(3,0)\"]":1},{"[\"(0,1)\"]":1},{"[\"(2,0)\"]":1},{"[\"(0,2)\"]":2},{"[\"(3,1)\"]":1},{"[\"(1,1)\"]":1},{"[\"(3,2)\"]":2},{"[\"(3,3)\"]":2},{"[\"(0,3)\"]":2},{"[\"(0,0)\"]":1},{"[\"(1,0)\"]":1},{"[\"(2,1)\"]":1},{"[\"(1,2)\"]":2},{"[\"(2,2)\"]":2},{"[\"(2,3)\"]":2},{"[\"(1,3)\"]":2}]}
{"name":"step410","weight":1,"data":{"get_log_spanning_forests":8.0507033814703,"get_log_spanning_trees":[4.02535169073515,4.02535169073515],"get_isoperimetric_scores":[18.0,18.0]},"districting":[{"[\"(3,0)\"]":1},{"[\"(0,1)\"]":1},{"[\"(2,0)\"]":1},{"[\"(0,2)\"]":2},{"[\"(3,1)\"]":1},{"[\"(1,1)\"]":1},{"[\"(3,2)\"]":2},{"[\"(3,3)\"]":2},{"[\"(0,3)\"]":2},{"[\"(0,0)\"]":1},{"[\"(1,0)\"]":1},{"[\"(2,1)\"]":1},{"[\"(1,2)\"]":2},{"[\"(2,2)\"]":2},{"[\"(2,3)\"]":2},{"[\"(1,3)\"]":2}]}
{"name":"step420","weight":1,"data":{"get_log_spanning_forests":5.416100402204419,"get_log_spanning_trees":[2.7080502011022096,2.7080502011022096],"get_isoperimetric_scores":[24.5,24.5]},"districting":[{"[\"(3,0)\"]":1},{"[\"(0,1)\"]":2},{"[\"(2,0)\"]":1},{"[\"(0,2)\"]":2},{"[\"(3,1)\"]":1},{"[\"(1,1)\"]":1},{"[\"(3,2)\"]":1},{"[\"(3,3)\"]":2},{"[\"(0,3)\"]":2},{"[\"(0,0)\"]":1},{"[\"(1,0)\"]":1},{"[\"(2,1)\"]":1},{"[\"(1,2)\"]":2},{"[\"(2,2)\"]":2},{"[\"(2,3)\"]":2},{"[\"(1,3)\"]":2}]}
{"name":"step430","weight":1,"data":{"get_log_spanning_forests":4.094344562222103,"get_log_spanning_trees":[2.7080502011022105,1.3862943611198921],"get_isoperimetric_scores":[24.5,32.0]},"districting":[{"[\"(3,0)\"]":1},{"[\"(0,1)\"]":2},{"[\"(2,0)\"]":1},{"[\"(0,2)\"]":2},{"[\"(3,1)\"]":1},{"[\"(1,1)\"]":1},{"[\"(3,2)\"]":2},{"[\"(3,3)\"]":2},{"[\"(0,3)\"]":2},{"[\"(0,0)\"]":1},{"[\"(1,0)\"]":1},{"[\"(2,1)\"]":1},{"[\"(1,2)\"]":1},{"[\"(2,2)\"]":2},{"[\"(2,3)\"]":2},{"[\"(1,3)\"]":2}]}
{"name":"step440","weight":1,"data":{"get_log_spanning_forests":8.0507033814703,"get_log_spanning_trees":[4.02535169073515,4.02535169073515],"get_isoperimetric_scores":[18.0,18.0]},"districting":[{"[\"(3,0)\"]":1},{"[\"(0,1)\"]":1},{"[\"(2,0)\"]":1},{"[\"(0,2)\"]":2},{"[\"(3,1)\"]":1},{"[\"(1,1)\"]":1},{"[\"(3,2)\"]":2},{"[\"(3,3)\"]":2},{"[\"(0,3)\"]":2},{"[\"(0,0)\"]":1},{"[\"(1,0)\"]":1},{"[\"(2,1)\"]":1},{"[\"(1,2)\"]":2},{"[\"(2,2)\"]":2},{"[\"(2,3)\"]":2},{"[\"(1,3)\"]":2}]}
{"name":"step450","weight":1,"data":{"get_log_spanning_forests":8.0507033814703,"get_log_spanning_trees":[4.02535169073515,4.02535169073515],"get_isoperimetric_scores":[18.0,18.0]},"districting":[{"[\"(3,0)\"]":1},{"[\"(0,1)\"]":1},{"[\"(2,0)\"]":1},{"[\"(0,2)\"]":2},{"[\"(3,1)\"]":1},{"[\"(1,1)\"]":1},{"[\"(3,2)\"]":2},{"[\"(3,3)\"]":2},{"[\"(0,3)\"]":2},{"[\"(0,0)\"]":1},{"[\"(1,0)\"]":1},{"[\"(2,1)\"]":1},{"[\"(1,2)\"]":2},{"[\"(2,2)\"]":2},{"[\"(2,3)\"]":2},{"[\"(1,3)\"]":2}]}
{"name":"step460","weight":1,"data":{"get_log_spanning_forests":4.0943445622221,"get_log_spanning_trees":[1.3862943611198908,2.7080502011022096],"get_isoperimetric_scores":[32.0,24.5]},"districting":[{"[\"(3,0)\"]":1},{"[\"(0,1)\"]":1},{"[\"(2,0)\"]":1},{"[\"(0,2)\"]":2},{"[\"(3,1)\"]":1},{"[\"(1,1)\"]":1},{"[\"(3,2)\"]":1},{"[\"(3,3)\"]":2},{"[\"(0,3)\"]":2},{"[\"(0,0)\"]":1},{"[\"(1,0)\"]":1},{"[\"(2,1)\"]":2},{"[\"(1,2)\"]":2},{"[\"(2,2)\"]":2},{"[\"(2,3)\"]":2},{"[\"(1,3)\"]":2}]}
{"name":"step470","weight":1,"data":{"get_log_spanning_forests":4.0943445622221,"get_log_spanning_trees":[1.3862943611198908,2.7080502011022096],"get_isoperimetric_scores":[32.0,24.5]},"districting":[{"[\"(3,0)\"]":1},{"[\"(0,1)\"]":1},{"[\"(2,0)\"]":1},{"[\"(0,2)\"]":2},{"[\"(3,1)\"]":1},{"[\"(1,1)\"]":1},{"[\"(3,2)\"]":1},{"[\"(3,3)\"]":2},{"[\"(0,3)\"]":2},{"[\"(0,0)\"]":1},{"[\"(1,0)\"]":1},{"[\"(2,1)\"]":2},{"[\"(1,2)\"]":2},{"[\"(2,2)\"]":2},{"[\"(2,3)\"]":2},{"[\"(1,3)\"]":2}]}
{"name":"step480","weight":1,"data":{"get_log_spanning_forests":8.0507033814703,"get_log_spanning_trees":[4.02535169073515,4.02535169073515],"get_isoperimetric_scores":[18.0,18.0]},"districting":[{"[\"(3,0)\"]":1},{"[\"(0,1)\"]":1},{"[\"(2,0)\"]":1},{"[\"(0,2)\"]":2},{"[\"(3,1)\"]":1},{"[\"(1,1)\"]":1},{"[\"(3,2)\"]":2},{"[\"(3,3)\"]":2},{"[\"(0,3)\"]":2},{"[\"(0,0)\"]":1},{"[\"(1,0)\"]":1},{"[\"(2,1)\"]":1},{"[\"(1,2)\"]":2},{"[\"(2,2)\"]":2},{"[\"(2,3)\"]":2},{"[\"(1,3)\"]":2}]}
{"name":"step490","weight":1,"data":{"get_log_spanning_forests":8.0507033814703,"get_log_spanning_trees":[4.02535169073515,4.02535169073515],"get_isoperimetric_scores":[18.0,18.0]},"districting":[{"[\"(3,0)\"]":1},{"[\"(0,1)\"]":1},{"[\"(2,0)\"]":1},{"[\"(0,2)\"]":2},{"[\"(3,1)\"]":1},{"[\"(1,1)\"]":1},{"[\"(3,2)\"]":2},{"[\"(3,3)\"]":2},{"[\"(0,3)\"]":2},{"[\"(0,0)\"]":1},{"[\"(1,0)\"]":1},{"[\"(2,1)\"]":1},{"[\"(1,2)\"]":2},{"[\"(2,2)\"]":2},{"[\"(2,3)\"]":2},{"[\"(1,3)\"]":2}]}
{"name":"step500","weight":1,"data":{"get_log_spanning_forests":8.0507033814703,"get_log_spanning_trees":[4.02535169073515,4.02535169073515],"get_isoperimetric_scores":[18.0,18.0]},"districting":[{"[\"(3,0)\"]":1},{"[\"(0,1)\"]":1},{"[\"(2,0)\"]":1},{"[\"(0,2)\"]":2},{"[\"(3,1)\"]":1},{"[\"(1,1)\"]":1},{"[\"(3,2)\"]":2},{"[\"(3,3)\"]":2},{"[\"(0,3)\"]":2},{"[\"(0,0)\"]":1},{"[\"(1,0)\"]":1},{"[\"(2,1)\"]":1},{"[\"(1,2)\"]":2},{"[\"(2,2)\"]":2},{"[\"(2,3)\"]":2},{"[\"(1,3)\"]":2}]}
{"name":"step510","weight":1,"data":{"get_log_spanning_forests":8.0507033814703,"get_log_spanning_trees":[4.02535169073515,4.02535169073515],"get_isoperimetric_scores":[18.0,18.0]},"districting":[{"[\"(3,0)\"]":1},{"[\"(0,1)\"]":1},{"[\"(2,0)\"]":1},{"[\"(0,2)\"]":2},{"[\"(3,1)\"]":1},{"[\"(1,1)\"]":1},{"[\"(3,2)\"]":2},{"[\"(3,3)\"]":2},{"[\"(0,3)\"]":2},{"[\"(0,0)\"]":1},{"[\"(1,0)\"]":1},{"[\"(2,1)\"]":1},{"[\"(1,2)\"]":2},{"[\"(2,2)\"]":2},{"[\"(2,3)\"]":2},{"[\"(1,3)\"]":2}]}
{"name":"step520","weight":1,"data":{"get_log_spanning_forests":8.0507033814703,"get_log_spanning_trees":[4.02535169073515,4.02535169073515],"get_isoperimetric_scores":[18.0,18.0]},"districting":[{"[\"(3,0)\"]":1},{"[\"(0,1)\"]":1},{"[\"(2,0)\"]":1},{"[\"(0,2)\"]":2},{"[\"(3,1)\"]":1},{"[\"(1,1)\"]":1},{"[\"(3,2)\"]":2},{"[\"(3,3)\"]":2},{"[\"(0,3)\"]":2},{"[\"(0,0)\"]":1},{"[\"(1,0)\"]":1},{"[\"(2,1)\"]":1},{"[\"(1,2)\"]":2},{"[\"(2,2)\"]":2},{"[\"(2,3)\"]":2},{"[\"(1,3)\"]":2}]}
{"name":"step530","weight":1,"data":{"get_log_spanning_forests":8.0507033814703,"get_log_spanning_trees":[4.02535169073515,4.02535169073515],"get_isoperimetric_scores":[18.0,18.0]},"districting":[{"[\"(3,0)\"]":1},{"[\"(0,1)\"]":1},{"[\"(2,0)\"]":1},{"[\"(0,2)\"]":2},{"[\"(3,1)\"]":1},{"[\"(1,1)\"]":1},{"[\"(3,2)\"]":2},{"[\"(3,3)\"]":2},{"[\"(0,3)\"]":2},{"[\"(0,0)\"]":1},{"[\"(1,0)\"]":1},{"[\"(2,1)\"]":1},{"[\"(1,2)\"]":2},{"[\"(2,2)\"]":2},{"[\"(2,3)\"]":2},{"[\"(1,3)\"]":2}]}
{"name":"step540","weight":1,"data":{"get_log_spanning_forests":8.0507033814703,"get_log_spanning_trees":[4.02535169073515,4.02535169073515],"get_isoperimetric_scores":[18.0,18.0]},"districting":[{"[\"(3,0)\"]":1},{"[\"(0,1)\"]":1},{"[\"(2,0)\"]":1},{"[\"(0,2)\"]":2},{"[\"(3,1)\"]":1},{"[\"(1,1)\"]":1},{"[\"(3,2)\"]":2},{"[\"(3,3)\"]":2},{"[\"(0,3)\"]":2},{"[\"(0,0)\"]":1},{"[\"(1,0)\"]":1},{"[\"(2,1)\"]":1},{"[\"(1,2)\"]":2},{"[\"(2,2)\"]":2},{"[\"(2,3)\"]":2},{"[\"(1,3)\"]":2}]}
{"name":"step550","weight":1,"data":{"get_log_spanning_forests":8.0507033814703,"get_log_spanning_trees":[4.02535169073515,4.02535169073515],"get_isoperimetric_scores":[18.0,18.0]},"districting":[{"[\"(3,0)\"]":1},{"[\"(0,1)\"]":1},{"[\"(2,0)\"]":1},{"[\"(0,2)\"]":2},{"[\"(3,1)\"]":1},{"[\"(1,1)\"]":1},{"[\"(3,2)\"]":2},{"[\"(3,3)\"]":2},{"[\"(0,3)\"]":2},{"[\"(0,0)\"]":1},{"[\"(1,0)\"]":1},{"[\"(2,1)\"]":1},{"[\"(1,2)\"]":2},{"[\"(2,2)\"]":2},{"[\"(2,3)\"]":2},{"[\"(1,3)\"]":2}]}
{"name":"step560","weight":1,"data":{"get_log_spanning_forests":4.094344562222101,"get_log_spanning_trees":[2.7080502011022105,1.3862943611198906],"get_isoperimetric_scores":[24.5,32.0]},"districting":[{"[\"(3,0)\"]":1},{"[\"(0,1)\"]":1},{"[\"(2,0)\"]":1},{"[\"(0,2)\"]":2},{"[\"(3,1)\"]":2},{"[\"(1,1)\"]":1},{"[\"(3,2)\"]":2},{"[\"(3,3)\"]":2},{"[\"(0,3)\"]":2},{"[\"(0,0)\"]":1},{"[\"(1,0)\"]":1},{"[\"(2,1)\"]":1},{"[\"(1,2)\"]":2},{"[\"(2,2)\"]":1},{"[\"(2,3)\"]":2},{"[\"(1,3)\"]":2}]}
{"name":"step570","weight":1,"data":{"get_log_spanning_forests":4.094344562222101,"get_log_spanning_trees":[2.7080502011022105,1.3862943611198906],"get_isoperimetric_scores":[24.5,32.0]},"districting":[{"[\"(3,0)\"]":1},{"[\"(0,1)\"]":1},{"[\"(2,0)\"]":1},{"[\"(0,2)\"]":2},{"[\"(3,1)\"]":2},{"[\"(1,1)\"]":1},{"[\"(3,2)\"]":2},{"[\"(3,3)\"]":2},{"[\"(0,3)\"]":2},{"[\"(0,0)\"]":1},{"[\"(1,0)\"]":1},{"[\"(2,1)\"]":1},{"[\"(1,2)\"]":2},{"[\"(2,2)\"]":1},{"[\"(2,3)\"]":2},{"[\"(1,3)\"]":2}]}
{"name":"step580","weight":1,"data":{"get_log_spanning_forests":4.094344562222101,"get_log_spanning_trees":[2.7080502011022105,1.3862943611198906],"get_isoperimetric_scores":[24.5,32.0]},"districting":[{"[\"(3,0)\"]":1},{"[\"(0,1)\"]":1},{"[\"(2,0)\"]":1},{"[\"(0,2)\"]":2},{"[\"(3,1)\"]":2},{"[\"(1,1)\"]":1},{"[\"(3,2)\"]":2},{"[\"(3,3)\"]":2},{"[\"(0,3)\"]":2},{"[\"(0,0)\"]":1},{"[\"(1,0)\"]":1},{"[\"(2,1)\"]":1},{"[\"(1,2)\"]":2},{"[\"(2,2)\"]":1},{"[\"(2,3)\"]":2},{"[\"(1,3)\"]":2}]}
{"name":"step590","weight":1,"data":{"get_log_spanning_forests":4.094344562222101,"get_log_spanning_trees":[2.7080502011022105,1.3862943611198906],"get_isoperimetric_scores":[24.5,32.0]},"districting":[{"[\"(3,0)\"]":1},{"[\"(0,1)\"]":1},{"[\"(2,0)\"]":1},{"[\"(0,2)\"]":2},{"[\"(3,1)\"]":2},{"[\"(1,1)\"]":1},{"[\"(3,2)\"]":2},{"[\"(3,3)\"]":2},{"[\"(0,3)\"]":2},{"[\"(0,0)\"]":1},{"[\"(1,0)\"]":1},{"[\"(2,1)\"]":1},{"[\"(1,2)\"]":2},{"[\"(2,2)\"]":1},{"[\"(2,3)\"]":2},{"[\"(1,3)\"]":2}]}
{"name":"step600","weight":1,"data":{"get_log_spanning_forests":4.094344562222101,"get_log_spanning_trees":[2.7080502011022105,1.3862943611198906],"get_isoperimetric_scores":[24.5,32.0]},"districting":[{"[\"(3,0)\"]":1},{"[\"(0,1)\"]":1},{"[\"(2,0)\"]":1},{"[\"(0,2)\"]":2},{"[\"(3,1)\"]":2},{"[\"(1,1)\"]":1},{"[\"(3,2)\"]":2},{"[\"(3,3)\"]":2},{"[\"(0,3)\"]":2},{"[\"(0,0)\"]":1},{"[\"(1,0)\"]":1},{"[\"(2,1)\"]":1},{"[\"(1,2)\"]":2},{"[\"(2,2)\"]":1},{"[\"(2,3)\"]":2},{"[\"(1,3)\"]":2}]}
{"name":"step610","weight":1,"data":{"get_log_spanning_forests":4.094344562222101,"get_log_spanning_trees":[2.7080502011022105,1.3862943611198906],"get_isoperimetric_scores":[24.5,32.0]},"districting":[{"[\"(3,0)\"]":1},{"[\"(0,1)\"]":1},{"[\"(2,0)\"]":1},{"[\"(0,2)\"]":2},{"[\"(3,1)\"]":2},{"[\"(1,1)\"]":1},{"[\"(3,2)\"]":2},{"[\"(3,3)\"]":2},{"[\"(0,3)\"]":2},{"[\"(0,0)\"]":1},{"[\"(1,0)\"]":1},{"[\"(2,1)\"]":1},{"[\"(1,2)\"]":2},{"[\"(2,2)\"]":1},{"[\"(2,3)\"]":2},{"[\"(1,3)\"]":2}]}
{"name":"step620","weight":1,"data":{"get_log_spanning_forests":8.0507033814703,"get_log_spanning_trees":[4.02535169073515,4.02535169073515],"get_isoperimetric_scores":[18.0,18.0]},"districting":[{"[\"(3,0)\"]":1},{"[\"(0,1)\"]":1},{"[\"(2,0)\"]":1},{"[\"(0,2)\"]":2},{"[\"(3,1)\"]":1},{"[\"(1,1)\"]":1},{"[\"(3,2)\"]":2},{"[\"(3,3)\"]":2},{"[\"(0,3)\"]":2},{"[\"(0,0)\"]":1},{"[\"(1,0)\"]":1},{"[\"(2,1)\"]":1},{"[\"(1,2)\"]":2},{"[\"(2,2)\"]":2},{"[\"(2,3)\"]":2},{"[\"(1,3)\"]":2}]}
{"name":"step630","weight":1,"data":{"get_log_spanning_forests":8.0507033814703,"get_log_spanning_trees":[4.02535169073515,4.02535169073515],"get_isoperimetric_scores":[18.0,18.0]},"districting":[{"[\"(3,0)\"]":1},{"[\"(0,1)\"]":1},{"[\"(2,0)\"]":1},{"[\"(0,2)\"]":2},{"[\"(3,1)\"]":1},{"[\"(1,1)\"]":1},{"[\"(3,2)\"]":2},{"[\"(3,3)\"]":2},{"[\"(0,3)\"]":2},{"[\"(0,0)\"]":1},{"[\"(1,0)\"]":1},{"[\"(2,1)\"]":1},{"[\"(1,2)\"]":2},{"[\"(2,2)\"]":2},{"[\"(2,3)\"]":2},{"[\"(1,3)\"]":2}]}
{"name":"step640","weight":1,"data":{"get_log_spanning_forests":8.0507033814703,"get_log_spanning_trees":[4.02535169073515,4.02535169073515],"get_isoperimetric_scores":[18.0,18.0]},"districting":[{"[\"(3,0)\"]":2},{"[\"(0,1)\"]":1},{"[\"(2,0)\"]":2},{"[\"(0,2)\"]":1},{"[\"(3,1)\"]":2},{"[\"(1,1)\"]":1},{"[\"(3,2)\"]":2},{"[\"(3,3)\"]":2},{"[\"(0,3)\"]":1},{"[\"(0,0)\"]":1},{"[\"(1,0)\"]":1},{"[\"(2,1)\"]":2},{"[\"(1,2)\"]":1},{"[\"(2,2)\"]":2},{"[\"(2,3)\"]":2},{"[\"(1,3)\"]":1}]}
{"name":"step650","weight":1,"data":{"get_log_spanning_forests":8.0507033814703,"get_log_spanning_trees":[4.02535169073515,4.02535169073515],"get_isoperimetric_scores":[18.0,18.0]},"districting":[{"[\"(3,0)\"]":2},{"[\"(0,1)\"]":1},{"[\"(2,0)\"]":2},{"[\"(0,2)\"]":1},{"[\"(3,1)\"]":2},{"[\"(1,1)\"]":1},{"[\"(3,2)\"]":2},{"[\"(3,3)\"]":2},{"[\"(0,3)\"]":1},{"[\"(0,0)\"]":1},{"[\"(1,0)\"]":1},{"[\"(2,1)\"]":2},{"[\"(1,2)\"]":1},{"[\"(2,2)\"]":2},{"[\"(2,3)\"]":2},{"[\"(1,3)\"]":1}]}
{"name":"step660","weight":1,"data":{"get_log_spanning_forests":8.0507033814703,"get_log_spanning_trees":[4.02535169073515,4.02535169073515],"get_isoperimetric_scores":[18.0,18.0]},"districting":[{"[\"(3,0)\"]":1},{"[\"(0,1)\"]":1},{"[\"(2,0)\"]":1},{"[\"(0,2)\"]":2},{"[\"(3,1)\"]":1},{"[\"(1,1)\"]":1},{"[\"(3,2)\"]":2},{"[\"(3,3)\"]":2},{"[\"(0,3)\"]":2},{"[\"(0,0)\"]":1},{"[\"(1,0)\"]":1},{"[\"(2,1)\"]":1},{"[\"(1,2)\"]":2},{"[\"(2,2)\"]":2},{"[\"(2,3)\"]":2},{"[\"(1,3)\"]":2}]}
{"name":"step670","weight":1,"data":{"get_log_spanning_forests":8.0507033814703,"get_log_spanning_trees":[4.02535169073515,4.02535169073515],"get_isoperimetric_scores":[18.0,18.0]},"districting":[{"[\"(3,0)\"]":2},{"[\"(0,1)\"]":1},{"[\"(2,0)\"]":2},{"[\"(0,2)\"]":1},{"[\"(3,1)\"]":2},{"[\"(1,1)\"]":1},{"[\"(3,2)\"]":2},{"[\"(3,3)\"]":2},{"[\"(0,3)\"]":1},{"[\"(0,0)\"]":1},{"[\"(1,0)\"]":1},{"[\"(2,1)\"]":2},{"[\"(1,2)\"]":1},{"[\"(2,2)\"]":2},{"[\"(2,3)\"]":2},{"[\"(1,3)\"]":1}]}
{"name":"step680","weight":1,"data":{"get_log_spanning_forests":8.0507033814703,"get_log_spanning_trees":[4.02535169073515,4.02535169073515],"get_isoperimetric_scores":[18.0,18.0]},"districting":[{"[\"(3,0)\"]":2},{"[\"(0,1)\"]":1},{"[\"(2,0)\"]":2},{"[\"(0,2)\"]":1},{"[\"(3,1)\"]":2},{"[\"(1,1)\"]":1},{"[\"(3,2)\"]":2},{"[\"(3,3)\"]":2},{"[\"(0,3)\"]":1},{"[\"(0,0)\"]":1},{"[\"(1,0)\"]":1},{"[\"(2,1)\"]":2},{"[\"(1,2)\"]":1},{"[\"(2,2)\"]":2},{"[\"(2,3)\"]":2},{"[\"(1,3)\"]":1}]}
{"name":"step690","weight":1,"data":{"get_log_spanning_forests":8.0507033814703,"get_log_spanning_trees":[4.02535169073515,4.02535169073515],"get_isoperimetric_scores":[18.0,18.0]},"districting":[{"[\"(3,0)\"]":2},{"[\"(0,1)\"]":1},{"[\"(2,0)\"]":2},{"[\"(0,2)\"]":1},{"[\"(3,1)\"]":2},{"[\"(1,1)\"]":1},{"[\"(3,2)\"]":2},{"[\"(3,3)\"]":2},{"[\"(0,3)\"]":1},{"[\"(0,0)\"]":1},{"[\"(1,0)\"]":1},{"[\"(2,1)\"]":2},{"[\"(1,2)\"]":1},{"[\"(2,2)\"]":2},{"[\"(2,3)\"]":2},{"[\"(1,3)\"]":1}]}
{"name":"step700","weight":1,"data":{"get_log_spanning_forests":8.0507033814703,"get_log_spanning_trees":[4.02535169073515,4.02535169073515],"get_isoperimetric_scores":[18.0,18.0]},"districting":[{"[\"(3,0)\"]":1},{"[\"(0,1)\"]":2},{"[\"(2,0)\"]":1},{"[\"(0,2)\"]":2},{"[\"(3,1)\"]":1},{"[\"(1,1)\"]":2},{"[\"(3,2)\"]":1},{"[\"(3,3)\"]":1},{"[\"(0,3)\"]":2},{"[\"(0,0)\"]":2},{"[\"(1,0)\"]":2},{"[\"(2,1)\"]":1},{"[\"(1,2)\"]":2},{"[\"(2,2)\"]":1},{"[\"(2,3)\"]":1},{"[\"(1,3)\"]":2}]}
{"name":"step710","weight":1,"data":{"get_log_spanning_forests":8.0507033814703,"get_log_spanning_trees":[4.02535169073515,4.02535169073515],"get_isoperimetric_scores":[18.0,18.0]},"districting":[{"[\"(3,0)\"]":1},{"[\"(0,1)\"]":2},{"[\"(2,0)\"]":1},{"[\"(0,2)\"]":2},{"[\"(3,1)\"]":1},{"[\"(1,1)\"]":2},{"[\"(3,2)\"]":1},{"[\"(3,3)\"]":1},{"[\"(0,3)\"]":2},{"[\"(0,0)\"]":2},{"[\"(1,0)\"]":2},{"[\"(2,1)\"]":1},{"[\"(1,2)\"]":2},{"[\"(2,2)\"]":1},{"[\"(2,3)\"]":1},{"[\"(1,3)\"]":2}]}
{"name":"step720","weight":1,"data":{"get_log_spanning_forests":8.0507033814703,"get_log_spanning_trees":[4.02535169073515,4.02535169073515],"get_isoperimetric_scores":[18.0,18.0]},"districting":[{"[\"(3,0)\"]":2},{"[\"(0,1)\"]":2},{"[\"(2,0)\"]":2},{"[\"(0,2)\"]":1},{"[\"(3,1)\"]":2},{"[\"(1,1)\"]":2},{"[\"(3,2)\"]":1},{"[\"(3,3)\"]":1},{"[\"(0,3)\"]":1},{"[\"(0,0)\"]":2},{"[\"(1,0)\"]":2},{"[\"(2,1)\"]":2},{"[\"(1,2)\"]":1},{"[\"(2,2)\"]":1},{"[\"(2,3)\"]":1},{"[\"(1,3)\"]":1}]}
{"name":"step730","weight":1,"data":{"get_log_spanning_forests":4.094344562222103,"get_log_spanning_trees":[2.7080502011022114,1.3862943611198912],"get_isoperimetric_scores":[24.5,32.0]},"districting":[{"[\"(3,0)\"]":1},{"[\"(0,1)\"]":2},{"[\"(2,0)\"]":2},{"[\"(0,2)\"]":2},{"[\"(3,1)\"]":1},{"[\"(1,1)\"]":2},{"[\"(3,2)\"]":1},{"[\"(3,3)\"]":1},{"[\"(0,3)\"]":2},{"[\"(0,0)\"]":2},{"[\"(1,0)\"]":2},{"[\"(2,1)\"]":1},{"[\"(1,2)\"]":1},{"[\"(2,2)\"]":1},{"[\"(2,3)\"]":1},{"[\"(1,3)\"]":2}]}
{"name":"step740","weight":1,"data":{"get_log_spanning_forests":4.094344562222103,"get_log_spanning_trees":[2.7080502011022114,1.3862943611198912],"get_isoperimetric_scores":[24.5,32.0]},"districting":[{"[\"(3,0)\"]":1},{"[\"(0,1)\"]":2},{"[\"(2,0)\"]":2},{"[\"(0,2)\"]":2},{"[\"(3,1)\"]":1},{"[\"(1,1)\"]":2},{"[\"(3,2)\"]":1},{"[\"(3,3)\"]":1},{"[\"(0,3)\"]":2},{"[\"(0,0)\"]":2},{"[\"(1,0)\"]":2},{"[\"(2,1)\"]":1},{"[\"(1,2)\"]":1},{"[\"(2,2)\"]":1},{"[\"(2,3)\"]":1},{"[\"(1,3)\"]":2}]}
{"name":"step750","weight":1,"data":{"get_log_spanning_forests":5.41610040220442,"get_log_spanning_trees":[2.7080502011022096,2.7080502011022105],"get_isoperimetric_scores":[24.5,24.5]},"districting":[{"[\"(3,0)\"]":1},{"[\"(0,1)\"]":2},{"[\"(2,0)\"]":2},{"[\"(0,2)\"]":2},{"[\"(3,1)\"]":1},{"[\"(1,1)\"]":2},{"[\"(3,2)\"]":1},{"[\"(3,3)\"]":1},{"[\"(0,3)\"]":2},{"[\"(0,0)\"]":2},{"[\"(1,0)\"]":2},{"[\"(2,1)\"]":1},{"[\"(1,2)\"]":2},{"[\"(2,2)\"]":1},{"[\"(2,3)\"]":1},{"[\"(1,3)\"]":1}]}
{"name":"step760","weight":1,"data":{"get_log_spanning_forests":8.0507033814703,"get_log_spanning_trees":[4.02535169073515,4.02535169073515],"get_isoperimetric_scores":[18.0,18.0]},"districting":[{"[\"(3,0)\"]":2},{"[\"(0,1)\"]":2},{"[\"(2,0)\"]":2},{"[\"(0,2)\"]":1},{"[\"(3,1)\"]":2},{"[\"(1,1)\"]":2},{"[\"(3,2)\"]":1},{"[\"(3,3)\"]":1},{"[\"(0,3)\"]":1},{"[\"(0,0)\"]":2},{"[\"(1,0)\"]":2},{"[\"(2,1)\"]":2},{"[\"(1,2)\"]":1},{"[\"(2,2)\"]":1},{"[\"(2,3)\"]":1},{"[\"(1,3)\"]":1}]}
{"name":"step770","weight":1,"data":{"get_log_spanning_forests":8.0507033814703,"get_log_spanning_trees":[4.02535169073515,4.02535169073515],"get_isoperimetric_scores":[18.0,18.0]},"districting":[{"[\"(3,0)\"]":2},{"[\"(0,1)\"]":2},{"[\"(2,0)\"]":2},{"[\"(0,2)\"]":1},{"[\"(3,1)\"]":2},{"[\"(1,1)\"]":2},{"[\"(3,2)\"]":1},{"[\"(3,3)\"]":1},{"[\"(0,3)\"]":1},{"[\"(0,0)\"]":2},{"[\"(1,0)\"]":2},{"[\"(2,1)\"]":2},{"[\"(1,2)\"]":1},{"[\"(2,2)\"]":1},{"[\"(2,3)\"]":1},{"[\"(1,3)\"]":1}]}
{"name":"step780","weight":1,"data":{"get_log_spanning_forests":8.0507033814703,"get_log_spanning_trees":[4.02535169073515,4.02535169073515],"get_isoperimetric_scores":[18.0,18.0]},"districting":[{"[\"(3,0)\"]":2},{"[\"(0,1)\"]":2},{"[\"(2,0)\"]":2},{"[\"(0,2)\"]":1},{"[\"(3,1)\"]":2},{"[\"(1,1)\"]":2},{"[\"(3,2)\"]":1},{"[\"(3,3)\"]":1},{"[\"(0,3)\"]":1},{"[\"(0,0)\"]":2},{"[\"(1,0)\"]":2},{"[\"(2,1)\"]":2},{"[\"(1,2)\"]":1},{"[\"(2,2)\"]":1},{"[\"(2,3)\"]":1},{"[\"(1,3)\"]":1}]}
{"name":"step790","weight":1,"data":{"get_log_spanning_forests":8.0507033814703,"get_log_spanning_trees":[4.02535169073515,4.02535169073515],"get_isoperimetric_scores":[18.0,18.0]},"districting":[{"[\"(3,0)\"]":2},{"[\"(0,1)\"]":2},{"[\"(2,0)\"]":2},{"[\"(0,2)\"]":1},{"[\"(3,1)\"]":2},{"[\"(1,1)\"]":2},{"[\"(3,2)\"]":1},{"[\"(3,3)\"]":1},{"[\"(0,3)\"]":1},{"[\"(0,0)\"]":2},{"[\"(1,0)\"]":2},{"[\"(2,1)\"]":2},{"[\"(1,2)\"]":1},{"[\"(2,2)\"]":1},{"[\"(2,3)\"]":1},{"[\"(1,3)\"]":1}]}
{"name":"step800","weight":1,"data":{"get_log_spanning_forests":8.0507033814703,"get_log_spanning_trees":[4.02535169073515,4.02535169073515],"get_isoperimetric_scores":[18.0,18.0]},"districting":[{"[\"(3,0)\"]":2},{"[\"(0,1)\"]":2},{"[\"(2,0)\"]":2},{"[\"(0,2)\"]":1},{"[\"(3,1)\"]":2},{"[\"(1,1)\"]":2},{"[\"(3,2)\"]":1},{"[\"(3,3)\"]":1},{"[\"(0,3)\"]":1},{"[\"(0,0)\"]":2},{"[\"(1,0)\"]":2},{"[\"(2,1)\"]":2},{"[\"(1,2)\"]":1},{"[\"(2,2)\"]":1},{"[\"(2,3)\"]":1},{"[\"(1,3)\"]":1}]}
{"name":"step810","weight":1,"data":{"get_log_spanning_forests":5.41610040220442,"get_log_spanning_trees":[2.7080502011022096,2.7080502011022105],"get_isoperimetric_scores":[24.5,24.5]},"districting":[{"[\"(3,0)\"]":1},{"[\"(0,1)\"]":2},{"[\"(2,0)\"]":2},{"[\"(0,2)\"]":2},{"[\"(3,1)\"]":1},{"[\"(1,1)\"]":2},{"[\"(3,2)\"]":1},{"[\"(3,3)\"]":1},{"[\"(0,3)\"]":2},{"[\"(0,0)\"]":2},{"[\"(1,0)\"]":2},{"[\"(2,1)\"]":1},{"[\"(1,2)\"]":2},{"[\"(2,2)\"]":1},{"[\"(2,3)\"]":1},{"[\"(1,3)\"]":1}]}
{"name":"step820","weight":1,"data":{"get_log_spanning_forests":5.41610040220442,"get_log_spanning_trees":[2.7080502011022096,2.7080502011022105],"get_isoperimetric_scores":[24.5,24.5]},"districting":[{"[\"(3,0)\"]":1},{"[\"(0,1)\"]":2},{"[\"(2,0)\"]":2},{"[\"(0,2)\"]":2},{"[\"(3,1)\"]":1},{"[\"(1,1)\"]":2},{"[\"(3,2)\"]":1},{"[\"(3,3)\"]":1},{"[\"(0,3)\"]":2},{"[\"(0,0)\"]":2},{"[\"(1,0)\"]":2},{"[\"(2,1)\"]":1},{"[\"(1,2)\"]":2},{"[\"(2,2)\"]":1},{"[\"(2,3)\"]":1},{"[\"(1,3)\"]":1}]}
{"name":"step830","weight":1,"data":{"get_log_spanning_forests":5.41610040220442,"get_log_spanning_trees":[2.7080502011022096,2.7080502011022105],"get_isoperimetric_scores":[24.5,24.5]},"districting":[{"[\"(3,0)\"]":1},{"[\"(0,1)\"]":2},{"[\"(2,0)\"]":2},{"[\"(0,2)\"]":2},{"[\"(3,1)\"]":1},{"[\"(1,1)\"]":2},{"[\"(3,2)\"]":1},{"[\"(3,3)\"]":1},{"[\"(0,3)\"]":2},{"[\"(0,0)\"]":2},{"[\"(1,0)\"]":2},{"[\"(2,1)\"]":1},{"[\"(1,2)\"]":2},{"[\"(2,2)\"]":1},{"[\"(2,3)\"]":1},{"[\"(1,3)\"]":1}]}
{"name":"step840","weight":1,"data":{"get_log_spanning_forests":4.094344562222101,"get_log_spanning_trees":[2.7080502011022096,1.3862943611198917],"get_isoperimetric_scores":[24.5,32.0]},"districting":[{"[\"(3,0)\"]":1},{"[\"(0,1)\"]":2},{"[\"(2,0)\"]":2},{"[\"(0,2)\"]":2},{"[\"(3,1)\"]":1},{"[\"(1,1)\"]":1},{"[\"(3,2)\"]":1},{"[\"(3,3)\"]":1},{"[\"(0,3)\"]":2},{"[\"(0,0)\"]":2},{"[\"(1,0)\"]":2},{"[\"(2,1)\"]":1},{"[\"(1,2)\"]":2},{"[\"(2,2)\"]":1},{"[\"(2,3)\"]":1},{"[\"(1,3)\"]":2}]}
{"name":"step850","weight":1,"data":{"get_log_spanning_forests":4.094344562222101,"get_log_spanning_trees":[2.7080502011022096,1.3862943611198917],"get_isoperimetric_scores":[24.5,32.0]},"districting":[{"[\"(3,0)\"]":1},{"[\"(0,1)\"]":2},{"[\"(2,0)\"]":2},{"[\"(0,2)\"]":2},{"[\"(3,1)\"]":1},{"[\"(1,1)\"]":1},{"[\"(3,2)\"]":1},{"[\"(3,3)\"]":1},{"[\"(0,3)\"]":2},{"[\"(0,0)\"]":2},{"[\"(1,0)\"]":2},{"[\"(2,1)\"]":1},{"[\"(1,2)\"]":2},{"[\"(2,2)\"]":1},{"[\"(2,3)\"]":1},{"[\"(1,3)\"]":2}]}
{"name":"step860","weight":1,"data":{"get_log_spanning_forests":4.094344562222101,"get_log_spanning_trees":[2.7080502011022096,1.3862943611198917],"get_isoperimetric_scores":[24.5,32.0]},"districting":[{"[\"(3,0)\"]":1},{"[\"(0,1)\"]":2},{"[\"(2,0)\"]":2},{"[\"(0,2)\"]":2},{"[\"(3,1)\"]":1},{"[\"(1,1)\"]":1},{"[\"(3,2)\"]":1},{"[\"(3,3)\"]":1},{"[\"(0,3)\"]":2},{"[\"(0,0)\"]":2},{"[\"(1,0)\"]":2},{"[\"(2,1)\"]":1},{"[\"(1,2)\"]":2},{"[\"(2,2)\"]":1},{"[\"(2,3)\"]":1},{"[\"(1,3)\"]":2}]}
{"name":"step870","weight":1,"data":{"get_log_spanning_forests":4.094344562222101,"get_log_spanning_trees":[2.7080502011022096,1.3862943611198917],"get_isoperimetric_scores":[24.5,32.0]},"districting":[{"[\"(3,0)\"]":1},{"[\"(0,1)\"]":2},{"[\"(2,0)\"]":2},{"[\"(0,2)\"]":2},{"[\"(3,1)\"]":1},{"[\"(1,1)\"]":1},{"[\"(3,2)\"]":1},{"[\"(3,3)\"]":1},{"[\"(0,3)\"]":2},{"[\"(0,0)\"]":2},{"[\"(1,0)\"]":2},{"[\"(2,1)\"]":1},{"[\"(1,2)\"]":2},{"[\"(2,2)\"]":1},{"[\"(2,3)\"]":1},{"[\"(1,3)\"]":2}]}
{"name":"step880","weight":1,"data":{"get_log_spanning_forests":5.41610040220442,"get_log_spanning_trees":[2.7080502011022105,2.7080502011022096],"get_isoperimetric_scores":[24.5,24.5]},"districting":[{"[\"(3,0)\"]":1},{"[\"(0,1)\"]":2},{"[\"(2,0)\"]":1},{"[\"(0,2)\"]":2},{"[\"(3,1)\"]":1},{"[\"(1,1)\"]":2},{"[\"(3,2)\"]":1},{"[\"(3,3)\"]":2},{"[\"(0,3)\"]":2},{"[\"(0,0)\"]":1},{"[\"(1,0)\"]":1},{"[\"(2,1)\"]":1},{"[\"(1,2)\"]":2},{"[\"(2,2)\"]":1},{"[\"(2,3)\"]":2},{"[\"(1,3)\"]":2}]}
{"name":"step890","weight":1,"data":{"get_log_spanning_forests":5.41610040220442,"get_log_spanning_trees":[2.7080502011022105,2.7080502011022096],"get_isoperimetric_scores":[24.5,24.5]},"districting":[{"[\"(3,0)\"]":1},{"[\"(0,1)\"]":2},{"[\"(2,0)\"]":1},{"[\"(0,2)\"]":2},{"[\"(3,1)\"]":1},{"[\"(1,1)\"]":2},{"[\"(3,2)\"]":1},{"[\"(3,3)\"]":2},{"[\"(0,3)\"]":2},{"[\"(0,0)\"]":1},{"[\"(1,0)\"]":1},{"[\"(2,1)\"]":1},{"[\"(1,2)\"]":2},{"[\"(2,2)\"]":1},{"[\"(2,3)\"]":2},{"[\"(1,3)\"]":2}]}
{"name":"step900","weight":1,"data":{"get_log_spanning_forests":5.41610040220442,"get_log_spanning_trees":[2.7080502011022105,2.7080502011022096],"get_isoperimetric_scores":[24.5,24.5]},"districting":[{"[\"(3,0)\"]":1},{"[\"(0,1)\"]":2},{"[\"(2,0)\"]":1},{"[\"(0,2)\"]":2},{"[\"(3,1)\"]":1},{"[\"(1,1)\"]":2},{"[\"(3,2)\"]":1},{"[\"(3,3)\"]":2},{"[\"(0,3)\"]":2},{"[\"(0,0)\"]":1},{"[\"(1,0)\"]":1},{"[\"(2,1)\"]":1},{"[\"(1,2)\"]":2},{"[\"(2,2)\"]":1},{"[\"(2,3)\"]":2},{"[\"(1,3)\"]":2}]}
{"name":"step910","weight":1,"data":{"get_log_spanning_forests":5.416100402204419,"get_log_spanning_trees":[2.7080502011022096,2.7080502011022096],"get_isoperimetric_scores":[24.5,24.5]},"districting":[{"[\"(3,0)\"]":1},{"[\"(0,1)\"]":2},{"[\"(2,0)\"]":1},{"[\"(0,2)\"]":2},{"[\"(3,1)\"]":1},{"[\"(1,1)\"]":1},{"[\"(3,2)\"]":1},{"[\"(3,3)\"]":2},{"[\"(0,3)\"]":2},{"[\"(0,0)\"]":1},{"[\"(1,0)\"]":1},{"[\"(2,1)\"]":1},{"[\"(1,2)\"]":2},{"[\"(2,2)\"]":2},{"[\"(2,3)\"]":2},{"[\"(1,3)\"]":2}]}
{"name":"step920","weight":1,"data":{"get_log_spanning_forests":5.416100402204419,"get_log_spanning_trees":[2.7080502011022096,2.7080502011022096],"get_isoperimetric_scores":[24.5,24.5]},"districting":[{"[\"(3,0)\"]":1},{"[\"(0,1)\"]":2},{"[\"(2,0)\"]":1},{"[\"(0,2)\"]":2},{"[\"(3,1)\"]":1},{"[\"(1,1)\"]":1},{"[\"(3,2)\"]":1},{"[\"(3,3)\"]":2},{"[\"(0,3)\"]":2},{"[\"(0,0)\"]":1},{"[\"(1,0)\"]":1},{"[\"(2,1)\"]":1},{"[\"(1,2)\"]":2},{"[\"(2,2)\"]":2},{"[\"(2,3)\"]":2},{"[\"(1,3)\"]":2}]}
{"name":"step930","weight":1,"data":{"get_log_spanning_forests":5.416100402204419,"get_log_spanning_trees":[2.7080502011022096,2.7080502011022096],"get_isoperimetric_scores":[24.5,24.5]},"districting":[{"[\"(3,0)\"]":1},{"[\"(0,1)\"]":2},{"[\"(2,0)\"]":1},{"[\"(0,2)\"]":2},{"[\"(3,1)\"]":1},{"[\"(1,1)\"]":1},{"[\"(3,2)\"]":1},{"[\"(3,3)\"]":2},{"[\"(0,3)\"]":2},{"[\"(0,0)\"]":1},{"[\"(1,0)\"]":1},{"[\"(2,1)\"]":1},{"[\"(1,2)\"]":2},{"[\"(2,2)\"]":2},{"[\"(2,3)\"]":2},{"[\"(1,3)\"]":2}]}
{"name":"step940","weight":1,"data":{"get_log_spanning_forests":5.41610040220442,"get_log_spanning_trees":[2.7080502011022105,2.7080502011022096],"get_isoperimetric_scores":[24.5,24.5]},"districting":[{"[\"(3,0)\"]":1},{"[\"(0,1)\"]":2},{"[\"(2,0)\"]":1},{"[\"(0,2)\"]":2},{"[\"(3,1)\"]":1},{"[\"(1,1)\"]":2},{"[\"(3,2)\"]":1},{"[\"(3,3)\"]":2},{"[\"(0,3)\"]":2},{"[\"(0,0)\"]":1},{"[\"(1,0)\"]":1},{"[\"(2,1)\"]":1},{"[\"(1,2)\"]":2},{"[\"(2,2)\"]":1},{"[\"(2,3)\"]":2},{"[\"(1,3)\"]":2}]}
{"name":"step950","weight":1,"data":{"get_log_spanning_forests":5.41610040220442,"get_log_spanning_trees":[2.7080502011022105,2.7080502011022096],"get_isoperimetric_scores":[24.5,24.5]},"districting":[{"[\"(3,0)\"]":1},{"[\"(0,1)\"]":2},{"[\"(2,0)\"]":1},{"[\"(0,2)\"]":2},{"[\"(3,1)\"]":1},{"[\"(1,1)\"]":2},{"[\"(3,2)\"]":1},{"[\"(3,3)\"]":2},{"[\"(0,3)\"]":2},{"[\"(0,0)\"]":1},{"[\"(1,0)\"]":1},{"[\"(2,1)\"]":1},{"[\"(1,2)\"]":2},{"[\"(2,2)\"]":1},{"[\"(2,3)\"]":2},{"[\"(1,3)\"]":2}]}
{"name":"step960","weight":1,"data":{"get_log_spanning_forests":5.416100402204419,"get_log_spanning_trees":[2.7080502011022096,2.7080502011022096],"get_isoperimetric_scores":[24.5,24.5]},"districting":[{"[\"(3,0)\"]":1},{"[\"(0,1)\"]":2},{"[\"(2,0)\"]":1},{"[\"(0,2)\"]":2},{"[\"(3,1)\"]":1},{"[\"(1,1)\"]":1},{"[\"(3,2)\"]":1},{"[\"(3,3)\"]":2},{"[\"(0,3)\"]":2},{"[\"(0,0)\"]":1},{"[\"(1,0)\"]":1},{"[\"(2,1)\"]":1},{"[\"(1,2)\"]":2},{"[\"(2,2)\"]":2},{"[\"(2,3)\"]":2},{"[\"(1,3)\"]":2}]}
{"name":"step970","weight":1,"data":{"get_log_spanning_forests":8.0507033814703,"get_log_spanning_trees":[4.02535169073515,4.02535169073515],"get_isoperimetric_scores":[18.0,18.0]},"districting":[{"[\"(3,0)\"]":1},{"[\"(0,1)\"]":1},{"[\"(2,0)\"]":1},{"[\"(0,2)\"]":2},{"[\"(3,1)\"]":1},{"[\"(1,1)\"]":1},{"[\"(3,2)\"]":2},{"[\"(3,3)\"]":2},{"[\"(0,3)\"]":2},{"[\"(0,0)\"]":1},{"[\"(1,0)\"]":1},{"[\"(2,1)\"]":1},{"[\"(1,2)\"]":2},{"[\"(2,2)\"]":2},{"[\"(2,3)\"]":2},{"[\"(1,3)\"]":2}]}
{"name":"step980","weight":1,"data":{"get_log_spanning_forests":8.0507033814703,"get_log_spanning_trees":[4.02535169073515,4.02535169073515],"get_isoperimetric_scores":[18.0,18.0]},"districting":[{"[\"(3,0)\"]":1},{"[\"(0,1)\"]":1},{"[\"(2,0)\"]":1},{"[\"(0,2)\"]":2},{"[\"(3,1)\"]":1},{"[\"(1,1)\"]":1},{"[\"(3,2)\"]":2},{"[\"(3,3)\"]":2},{"[\"(0,3)\"]":2},{"[\"(0,0)\"]":1},{"[\"(1,0)\"]":1},{"[\"(2,1)\"]":1},{"[\"(1,2)\"]":2},{"[\"(2,2)\"]":2},{"[\"(2,3)\"]":2},{"[\"(1,3)\"]":2}]}
{"name":"step990","weight":1,"data":{"get_log_spanning_forests":8.0507033814703,"get_log_spanning_trees":[4.02535169073515,4.02535169073515],"get_isoperimetric_scores":[18.0,18.0]},"districting":[{"[\"(3,0)\"]":1},{"[\"(0,1)\"]":1},{"[\"(2,0)\"]":1},{"[\"(0,2)\"]":2},{"[\"(3,1)\"]":1},{"[\"(1,1)\"]":1},{"[\"(3,2)\"]":2},{"[\"(3,3)\"]":2},{"[\"(0,3)\"]":2},{"[\"(0,0)\"]":1},{"[\"(1,0)\"]":1},{"[\"(2,1)\"]":1},{"[\"(1,2)\"]":2},{"[\"(2,2)\"]":2},{"[\"(2,3)\"]":2},{"[\"(1,3)\"]":2}]}
{"name":"step1000","weight":1,"data":{"get_log_spanning_forests":8.0507033814703,"get_log_spanning_trees":[4.02535169073515,4.02535169073515],"get_isoperimetric_scores":[18.0,18.0]},"districting":[{"[\"(3,0)\"]":1},{"[\"(0,1)\"]":1},{"[\"(2,0)\"]":1},{"[\"(0,2)\"]":2},{"[\"(3,1)\"]":1},{"[\"(1,1)\"]":1},{"[\"(3,2)\"]":2},{"[\"(3,3)\"]":2},{"[\"(0,3)\"]":2},{"[\"(0,0)\"]":1},{"[\"(1,0)\"]":1},{"[\"(2,1)\"]":1},{"[\"(1,2)\"]":2},{"[\"(2,2)\"]":2},{"[\"(2,3)\"]":2},{"[\"(1,3)\"]":2}]}

File Extension and Compression

Atlas files use the file extension .jsonl if the file in Atlas is plain, uncompressed text. If the Atlas is compressed it will either use the file extension .jsonl.gz or .jsonl.bz2.

The .gz extension signifies the use of the standard Gnu Zip tools (gzip, gunzip, zcat) and can be read by a number of libraries and command line tools. These tools use the standard Deflate algorithm to compress data.

The .bz2 extension signifies the use of the standard BZip2 tools (bzip2, bzcat) and also can be read by a number of libraries and command line tools. These tools use the standard Burrows–Wheeler algorithm to compress data.

The Bzip2 compression format typically results in a smaller file than the Gzip compression format. However, the Bzip2 compression is slower to compress and uncompress. We also explored saving files by saving the incremental changes in the maps. However, it was decided that the advantage of using standard compression tools was significant in light of the very high compression ratios they delivered out of the box.

Work Directly with Compressed Files

One nice feature of the AtlasIO libraries, both in Julia and Python, is that they can read and write compressed files directly. This both increase the speed of writing and decreases the size of the Atlas files significantly.

Corrupted Compressed Files

One downside of directly writing compressed files is that the files can not be directly examined during the run and might be left in a corrupted state if the run is interrupted. A corrupted file can typically easily be largely recovered using

zcat atlas-corrupted.jsonl.gz > atlas-fixed.jsonl

You can also use the zcat command to examine a file during a run.