Exploiting Symmetries in Polyhedral Computations

TL;DR

This paper reviews techniques for exploiting symmetries in polyhedral computations across various areas, highlighting challenges and future directions for improving efficiency and applicability.

Contribution

It provides an overview of symmetry exploitation methods in polyhedral computations, identifying key challenges and potential future research directions.

Findings

Symmetry exploitation can significantly reduce computational complexity.

Current methods face challenges in scalability and generality.

Future research should focus on integrating symmetry techniques across different polyhedral problems.

Abstract

In this note we give a short overview on symmetry exploiting techniques in three different branches of polyhedral computations: The representation conversion problem, integer linear programming and lattice point counting. We describe some of the future challenges and sketch some directions of potential developments.