Incremental SAT-Based Method with Native Boolean Cardinality Handling for the Hamiltonian Cycle Problem

Abstract

The Hamiltonian cycle problem (HCP) is the problem of finding a spanning cycle in a given graph. HCP is NP-complete and has been known as an important problem due to its close relationship to the travelling salesman problem (TSP), which can be seen as an optimization variant of finding a minimum cost cycle. In a different viewpoint, HCP is a special case of TSP. In this paper, we propose an incremental SAT-based method for solving HCP. The number of clauses needed for a CNF encoding of HCP often prevents SAT-based methods from being scalable. Our method reduces that number of clauses by relaxing some constraints and by handling specifically cardinality constraints. Our approach has been implemented on top of the SAT solver Sat4j using Scarab. An experimental evaluation is carried out on several benchmark sets and compares our incremental SAT-based method against an existing eager SAT-based method and specialized methods for HCP.