Wye-Delta-Wye Graph Reduction
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Wye-Delta-Wye Graph Reduction

This library provides experimental implementations of algorithms for reducing connected plane graphs to K1 (or 3-connected plane graphs to K4) using a sequence of series/parallel reductions and wye-delta-wye transformations. The six basic transformations are illustrated below.

Wye-Delta-Wye Transformations

For the reduction of 3-connected plane graphs to K4, the elementary transformations by Steinitz are used directly:

Elementary Transformations by Steinitz

The following algorithms are implemented:

Directory overview

  • bin: Java byte code (generated)
  • data: example plane graph data files (in adjacency list format)
  • doc: API documentation (generated)
  • scripts: Python and Sage scripts for generating plane graphs
  • src: Java source code
  • test: JUnit test cases

Usage instructions

Building the library and running the application requires Java SE 8.

The application provides a simple GUI for loading plane graphs from files and running algorithms on them. The GUI is launched if the program is run without any command-line arguments.

In addition, there is a more powerful command-line interface. Run the application with the argument help for CLI usage instructions.

$ java -jar bin/deltawye.jar help

  $ java -jar deltawye.jar <algorithm> <filename>
  $ java -jar deltawye.jar batch <count> <algorithm> <filename>


  <algorithm>   = steinitz <sg-strategy>
                | feoprovan <fp-start> <fp-strategy>
                | temperature <tr-strategy>
  <sg-strategy> = random | min | max | pole | nonpole
  <fp-start>    = random | min | max
  <fp-strategy> = random | minlabel | maxlabel | mindegree | maxdegree
  <tr-strategy> = random | short | long
  <count>       = <number of requested runs of the algorithm as integer>
  <filename>    = <path to graph data textfile in adjacency list format>


  $ java -jar deltawye.jar steinitz random data/icosahedron.txt

The command-line interface supports a batch mode that can be used to run a reduction algorithm a specified number of times on a given graph. A summary of the detected transformation sequences is written to standard output. For example:

$ java -jar bin/deltawye.jar batch 100 temperature random data/random/random-30.txt
Randomized Wye-Delta-Wye algorithm,
running on graph with 30 vertices and 77 edges.
Selection Strategy: RANDOM.
Batch run: 100 iterations.
Run 1 completed after 53 steps with 34 Delta-Wye and 19 Wye-Delta transformations.
Run 2 completed after 56 steps with 37 Delta-Wye and 19 Wye-Delta transformations.
Run 3 completed after 55 steps with 34 Delta-Wye and 21 Wye-Delta transformations.
Run 4 completed after 51 steps with 30 Delta-Wye and 21 Wye-Delta transformations.
Run 99 completed after 53 steps with 32 Delta-Wye and 21 Wye-Delta transformations.
Run 100 completed after 52 steps with 30 Delta-Wye and 22 Wye-Delta transformations.

  Shortest sequence: 41
  Longest sequence: 57
  Average length: 50.73

  Shortest sequence: 42
  Longest sequence: 58
  Average length: 51.73

Build option 1: Use Makefile

Show usage instructions:

$ make help

Build API documentation:

$ make doc

Generate executable JAR file:

$ make jar

Run the executable JAR file (GUI version):

$ make run

Build option 2: Run from JAR file

Step 1: Create an executable JAR file for the project

$ mkdir -p bin
$ javac -d bin -cp src src/deltawye/app/Main.java
$ jar cfe bin/deltawye.jar deltawye.app.Main -C bin deltawye

This should create the executable JAR file bin/deltawye.jar.

Step 2: Run the generated JAR file

$ java -jar bin/deltawye.jar

This should open the graphical interface of the application.

Build option 3: Run from bytecode

Step 1: Build Java bytecode from the project sources

$ mkdir -p bin
$ javac -d bin -cp src src/deltawye/app/Main.java

Step 2: Run the Java bytecode of the project (GUI version)

$ java -cp bin deltawye.app.Main


Copyright 2016 Mathias Schenner

This software is distributed under the MIT License.