The Promise of LP to Boost CSP Techniques for Combinatorial Problems

In recent years we have seen an increasing interest in combining CSP and LP based techniques for solving hard computational problems. While considerable progress has been made in the integration of these techniques for solving problems that exhibit a mixture of linear and combinatorial constraints, it has been surprisingly difficult to successfully integrate LP-based and CSP-based methods in a purely combinatorial setting. We propose a complete randomized backtrack search method for combinatorial problems that tightly couples CSP propagation techniques with randomized LP rounding. Our approach draws on recent results on approximation algorithms with theoretical guarantees, based on LP relaxations and randomized rounding techniques, as well on results that provide evidence that the run time distributions of combinatorial search methods are often heavy-tailed. We present experimental results that show that our hybrid CSP/LP backtrack search method outperforms the pure CSP and pure LP strategies on instances of a hard combinatorial problem.