Solving Hard Combinatorial Problems with GSAT - A Case Study

In this paper, we investigate whether hard combinatorial problems such as the Hamiltonian circuit problem HCP (an NP-complete problem from graph theory) can be practically solved by transformation to the propositional satissability problem (SAT) and application of fast universal SAT-algorithms like GSAT to the transformed problem instances. By using the eecient transformation method proposed by Iwama and Miyazaki in 1994, one obtains a class of SAT-problems which are especially hard for SAT-algorithms based on local search such as GSAT. We identify structural properties of these problems which are responsible for GSAT's poor performance on this problem class. An empirical analysis indicates that several methods which have been designed to improve GSAT on structured problems are not eeective for SAT-transformed HCP-instances.