Improving Backtrack Search for Solving the TCSP

Abstract

In this paper, we address the task of finding the minimal network of a Temporal Constraint Satisfaction Problem (TCSP). We report the integration of three approaches to improve the performance of the exponential-time backtrack search (BT-TCSP) proposed by Dechter et al. [6] for this purpose. The first approach consists of using a new efficient algorithm ($\triangle$STP) [21] for solving the Simple Temporal Problem (STP), an operation that must be executed at each node expansion during BT-TCSP. The second approach improves BT-TCSP itself by exploiting the topology of the temporal network. This is accomplished in three ways: finding and exploiting articulation points (AP), checking the graph for new cycles (NewCyc), and using a new heuristic for edge ordering (EdgeOrd). The third approach is a filtering algorithm, $\triangle$AC, which is used as a preprocessing step to BT-TCSP, and which significantly reduces the size of the TCSP [22]. In addition to introducing two new techniques, NewCyc and EdgeOrd, this paper discusses an extensive evaluation of the merits of the above three approaches. Our experiments on randomly generated problems demonstrate significant improvements in the number of nodes visited, constraint checks, and CPU time.