Graph algorithms are easy to visualize and indeed there already exists a variety of packages and programs to animate the dynamics when solving problems from graph theory. Still, and somewhat surprisingly, it can be difficult to understand the ideas behind the algorithm from the dynamic display alone.

CATBox consists of a software system for animating graph algorithms and a course book which we developed simultaneously. The software system presents both the algorithm and the graph and puts the user always in control of the actual code that is executed. He or she can set breakpoints, proceed in single steps and trace into subroutines. The graph, and additional auxiliary graphs like residual networks, are displayed and provide visual feedback. The course book, intended for readers at advanced undergraduate or graduate level, introduces the ideas and discusses the mathematical background necessary for understanding and verifying the correctness of the algorithms and their complexity. Computer exercises and examples replace the usual static pictures of algorithm dynamics.

For this volume we have chosen solely algorithms for classical problems from combinatorial optimization, such as minimum spanning trees, shortest paths, maximum flows, minimum cost flows, weighted and unweighted matchings both for bipartite and non-bipartite graphs.

We consider non-bipartite weighted matching, in particular in the geometrical case, a highlight of combinatorial optimization. In order to enable the reader to fully enjoy the beauty of the primal-dual solution algorithm for weighted matching, we present all mathematical material not only from the point of view of graph theory, but also with an emphasis on linear programming and its duality. This yields insightful and aesthetically pleasing pictures for matchings, but also for minimum spanning trees.

- You can look at a sample chapter covering computing maximal flows
in capacitated networks:
`CATBox-Sample-MaxFlows.pdf` - An animated GIF (remember those?) showing Dijkstra's algorithm for computing shortest paths.
- A short screencast demonstrating Dijkstra's algorithm for computing shortest paths.
- A short screencast demonstrating Kruskal's algorithm for computing minimal spanning trees.
- A teaser, showing off a future version of Gato in a Screencast explaining the preflow-push algorithm for computing maximal flows in capacitated networks in 3D.

There are two parts to the CATBox software: First, the open-source
animation software Gato © 1998-2010
Alexander Schliep,
and
Winfried Hochstättler and copyright © 1998-2001 ZAIK/ZPR, an institute at the Unversität zu Köln
licensed under the LGPL.

Second, there are algorithm implementations,
algorithm visualizations and problem instances which are © 1998-2010 Alexander Schliep,
Winfried Hochstättler, and © 2010 Springer Verlag Heidelberg.

OS |
Filename |
Description |

MacOS X | CATBox-1.1-MacOSX-10.5.dmg |
CATBox files including Gato binaries for MacOS X 10.5.x (Note: does not work with 10.6.x) . |

MacOS X | CATBox-1.1-MacOSX-10.6.dmg |
CATBox files including Gato binaries for MacOS X 10.6.x and later. |

Windows 7 | CATBox-1.1.exe |
CATBox files including Gato binaries for Windows 7 and Vista. |

Linux | CATBox files including Gato binaries for x86 32bit Linux. | |

All | CATBox-1.1-Src.tar.gz |
CATBox and Gato source files.(Note: does not work with MacOS 10.6.x; vendor Tk/Tkinter broken) |

- Python version 2.6.x. Gato will not run with Python 3.x.
- Tk version 8.4.7 or above.
- Tkinter module enabled in Python.

> python2.6 Python 2.6.2 (r262:71600, Aug 13 2009, 15:33:59) [GCC 4.0.1 (Apple Inc. build 5490)] on darwin Type "help", "copyright", "credits" or "license" for more information. >>> import Tkinter >>> t = Tkinter.Tk() >>>should produce a small window. From the command line you can then install Gato with the following commands.

> cd Gato > python2.6 setup.py installIf you prefer a different install location than your system-wide Python installation, you can specify a different one

> cd Gato > python2.6 setup.py install --prefix=/home/schliep/test/which will install Gato in

Hochstättler, Winfried and Schliep, Alexander. *CATBox – An Interactive Course in Combinatorial Optimization* (2010) [details]

Contact: Alexander Schliep (schliep@cs.rutgers.edu).