postman_problems 0.1.1

2.1 Basic

Option 1. Install from PyPI: Stable release.

pip install postman_packages

Option 2. Install from GitHub: As this project develops, GitHub will have the most recent features, but no guarantees they’ll be stable.

1. Clone the repo.

   git clone https://github.com/brooksandrew/postman_problems.git
   cd postman_problems

2. Install with pip. Builds are tested on Python 2.7, 3.3, 3.4, 3.5, 3.6.

   pip install .

2.2 Viz

postman_problems leverages Graphviz for visualization which unlocks more robust visualizations than just NetworkX and matplotlib. However, this also comes with several dependencies. These are managed separately from the base package, so users can optimize graphs to their heart’s content unencumbered from the weight and hassle of installing viz dependencies, if they so choose.

1. Install optional Python visualization libraries.

   pip install postman_problems[viz]

2. Install Graphviz. You need this underlying software application in addition to the graphviz python package which wraps around it. Checkout the Graphviz Download page for the best way to install on your OS.

   For Mac, this should be as easy as:

   brew install graphviz

   For Linux,

   sudo apt-get install graphviz

   These are the installs I’m currently using on my builds for the tests on TravisCI. YMMV. For Windows users and for those where these methods fail, I defer to the Graphviz download docs.

3.1 CLI

The easiest way to start is with the command line installed with this package, chinese_postman.

There are several optional command line arguments, but the only one required is --edgelist. For the complete list of optional arguments run:

chinese_postman --help

The big ones are --viz_static and --viz_animation which when present will create the static (single) and animation of the CPP solution. Most of the other arguments control the visualizations with default values.

Below we solve the CPP on the Seven Bridges of Konigsberg network. The edgelist is provided in this repo, but you can swap this out for any comma delimited text file where the first two columns represent the node pairs in your network. The columns should have headers. Columns after the first two are treated as edge attributes.

chinese_postman --edgelist postman_problems/examples/seven_bridges/edgelist_seven_bridges.csv

If the chinese_postman entry point is not working for whatever reason, you can run the script directly with:

python postman_problems/chinese_postman.py --edgelist postman_problems/examples/seven_bridges/edgelist_seven_bridges.csv

You should see output that describes the CPP solution (Eulerian circuit) through each edge. Something like this:

('A', 'C', {'trail': 'c', 'distance': 2, 'id': 2})
('C', 'D', {'trail': 'g', 'distance': 3, 'id': 6})
('D', 'C', {'trail': 'g', 'distance': 3, 'id': 6, 'augmented': True})
('C', 'A', {'trail': 'd', 'distance': 10, 'id': 3})
('A', 'D', {'trail': 'e', 'distance': 1, 'id': 4})
('D', 'B', {'trail': 'f', 'distance': 9, 'id': 5})
('B', 'A', {'trail': 'a', 'distance': 3, 'id': 0})
('A', 'B', {'trail': 'b', 'distance': 5, 'id': 1})
('B', 'A', {'trail': 'a', 'distance': 3, 'id': 0, 'augmented': True})

The first two values of each tuple are the “from” and the “to” node respectively for each edge in the circuit.

The third value contains the edge attributes for each edge walked. These are mostly grabbed from the starting graph, with two exceptions:

• augmented is added to edges after their first walk (double backing… the thing we want to minimize)

• id is generated to aid computation in the case of parallel edges. This can generally be ignored.

3.2 Python

The postman solvers are modules that can also be imported and run within a Python environment. This might interest you if solving the CPP is just one step in your problem, you’d like to poke and prod at the output, or you’d like to tweak the visualization or optimization parameters beyond what’s provided from the CLI.

The snippet below should produce exactly the same output as printed above in CLI.

from postman_problems.graph import cpp

# find CPP solution
circuit, graph = cpp(edgelist_filename='postman_problems/examples/seven_bridges/edgelist_seven_bridges.csv',
                     start_node='D')

# print solution
for e in circuit:
    print(e)

4.1 Seven Bridges of Konigsberg

The Seven Bridges of Konigsberg is rather simple network with just 4 nodes and 7 edges. Although small, it does contain 2 parallel edges which introduce some complexity to the CPP computation.

This was the graph with which Leonhard Euler famously postulated in 1736 that there exists a path which visits each edge exactly once if all nodes have even degree. Although this wasn’t proven until the 1870s by Carl Hierholzer, Euler was right and this property is a key part of solving the Postman Problems.

This contrived example has been bundled and parameterized into a script that can be run with:

chinese_postman_seven_bridges

The example can also be run using the verbose method below which allows you to more easily parameterize more pieces. Many of the options provided below are defaults and can be excluded in practice. They are included here simply to convey what the possibilities are.

chinese_postman --edgelist postman_problems/examples/seven_bridges/edgelist_seven_bridges.csv \
--viz_static \
--viz_static_filename 'postman_problems/examples/seven_bridges/output/cpp_graph' \
--viz_static_engine 'dot' \
--viz_static_format 'svg' \
--viz_animation \
--viz_animation_filename 'postman_problems/examples/seven_bridges/output/cpp_graph.gif' \
--viz_images_dir 'postman_problems/examples/seven_bridges/output/img' \
--viz_animation_engine 'dot' \
--viz_animation_format 'png' \
--fps 2

base_cpp_graph.svg: This is the starting graph. Edges are annotated by distance.

cpp_graph.svg: Edges are annotated with the order in which they are walked, starting at 0. Edges walked more than once are annotated by a sequence of numbers (walk order) and bolded.

cpp_graph.gif: The nodes and edges in red indicate the current direction.

cpp_graph: dot representation of the graph is also provided. This is mostly for reference, but in rare cases you may want to tweak graphviz parameters directly here.

4.2 Sleeping Giant

This example is near and dear to my heart and the motivation for this project in the first place.

Sleeping Giant is a state park near my hometown in Hamden CT with a little challenge called the Giant Master Program. Those who hike every trail (see trail map) are awarded the honor of Giantmaster Marathoner and earn themselves a spot on the Giantmaster roster and the glory of a red highlight on their name.

That’s all I’ll say here. I wrote more about the personal motivation and Sleeping Giant specific data/problem in a DataCamp tutorial which also helped motivate this project.

chinese_postman_sleeping_giant

postman_problems/examples/sleeping_giant/cpp_graph.svg:

postman_problems/examples/sleeping_giant/cpp_graph.gif (omitted from package due to size): Can be viewed here