A Multi-Valued Decision Diagram-Based Approach to Constrained Optimal Path Problems over Directed Acyclic Graphs

Numerous combinatorial optimization problems can be reduced to the optimal path problem over directed acyclic graphs (DAGs). The constrained version of the optimal path problem requires the solution to satisfy a given logical constraint. BDD-constrained search (BCS) is an efficient algorithm for the constrained optimal path problem over DAGs. This algorithm considers edges as variables and constraints as Boolean functions and maintains constraints via binary decision diagrams (BDDs), a compact form of Boolean functions. However, BCS involves redundant operations during the search process. To reduce these redundant operations, we use vertices instead of edges as variables and hence represent constraints as multi-valued functions. Due to the multi-valued representation of constraints, we propose a novel algorithm, namely MDD-constrained search (MCS), by using multi-valued decision diagrams (MDDs) instead of BDDs, an efficient representation of multi-valued functions. In addition, we improve MCS via domain reduction in multi-valued functions. Experimental results prove that our proposed algorithm outperforms BCS.