Isoperimetric Tools

This webpage offers a set of online tools for dealing with isoperimetric-type problems on graphs and posets.
In the future, I plan to implement more graph and poset algorithms related to my current interests.

To run these tools, you have to have Java version 1.5 or later installed on your computer. Your browser has to report a MIME type of application/x-java-jnlp-file for files with extension jnlp (JNLP is a short for Java Network Launch Protocol). Usually, the browser is automatically configured for JNLP in case the Sun JRE is installed. You can check/configure the browser by assigning the javaws application (a part of JRE) with the file type application/x-java-jnlp-file.

All your comments, suggestions, and reports on problems with these tools will be greatly appreciated.
You can email me them at sb@mcs.uwsuper.edu.

Poset Tools

• Gallery of posets
• Display the Hasse diagram
• The Maximum Weight/Rank Ideal Problem (MWI/MRI)
  • The MWI problem for the cartesian product of two posets
• Shadows in the n-cube
• Poset Test for Macaulayness ⁽¹⁾

Graph tools ⁽²⁾

• Display a graph defined by the ball sequence and its adjacency list
• Display the cartesian product of graphs defined by the ball sequences
• Generating symmetric ball-sequences
• Compute the ball size
• The Vertex Isoperimetric Problem (VIP)
  • The VIP problem for the cartesian product of two graphs
  • The VIP problem for oriented graphs
• The Edge Isoperimetric Problem (EIP)
  • The EIP problem for the cartesian product of two graphs

Links to other poset packages

• A Mathematica Package for Studying Posets (by Curtis Greene, Eugenie Hunsicker)
• The posets Package (by John Stembridge)
• Lattice Drawing (by Ralph Freese)
• Interactive Poset and Lattice Drawing Java Applet (by Peter Jipsen)
• Online Java Lattice Building Application for Concept Lattices (JaLaBA)
• Posets (by Kevin Gilbert)
• The wizard of COS (Combinatorial Object Server) (by Frank Ruskey)

Credits

⁽¹⁾ A part of a Student Project with Aqila Dissanayake, 2005.
⁽²⁾ Design of these graph tools was partially supported in 2003 by:
Spanish Ministry of Science and Technology under project BFM2002-00412
and the Catalan Research Council under project SGR00258.

Last modified: Mon, Jan 23, 2023.