A New Sufficient Condition for Polynomial Solvability of Cost-Based Abduction

Abstract

Cost-based abduction is a well established formalization of abduction for obtaining the most desirable hypotheses-set. However, slow inference-speed is its crucial problem-it is NP-complete. In order to overcome this problem, mathematical programming based methods have been shown to be effective. However, their performances were mainly evaluated empirically, not theoretically supported. Recently, a new condition was presented under which polynomial time cost-based abduction can be achieved by solving the relaxed linear programming problem, though inconsistencies among hypotheses were not considered. This paper presents a new sufficient condition for the polynomial solvability of cost-based abduction by linear programming relaxation, considering inconsistencies among hypotheses which heavily influence the time complexity of abduction. Testing the new condition is possible within polynomial time. Our theory is based on the constraint network of a previously presented Networked Bubble Propagation (NBP) method, a high-speed approximate cost-based abduction method.