Computing invariants in graphs of small bandwidth

Abstract

Many graph invariants (chromatic number, rook polynomial, Tutte polynomial, etc.) are known to be computable for general graphs in exponential time only. Algorithms for their computation usually depend on special properties of the invariants and are not extendable to slightly different problems. Some general framework (called composition method) for the construction of algorithms for the solution graph of related problems has been developed during the last two years. In this paper we will demonstrate the power of this method by automating and applying it to a class of well-known problems covering e.g. the chromatic and the Tutte polynomial. The obtained algorithms are comparable to existing hand optimized ones in running time and memory usage.