Polynomial solvability of cost-based abduction

In recent empirical studies we have shown that many interesting cost-based abduction problems can be solved efficiently by considering the linear program relaxation of their integer program formulation. We tie this to the concept of total unimodularity from network flow analysis, a fundamental result in polynomial solvability. From this, we can determine the polynomial solvability of abduction problems and, in addition, present a new heuristic for branch and bound in the non-polynomial cases.