A Total Unimodularity Based Branch-and-Bound Method for Integer Programming

We consider a novel solution method for integer programming problems with a 0-plusmn1 constraint matrix, which include set covering problem (SCP) and satisfiability problem (SAT) as special cases. Specifically, a branching rule is designed to actively make a satisfaction of total unimodularity (TU), thus speeding up the convergence of the search process in the branch-and-bound method. This TU-based branch-and-bound method is tested for a family of random 3-SAT problems and is compared with the IP solver of ILOG CPLEX. Computational experience shows that this new solution scheme is efficient