Toward fast belief propagation for distributed constraint optimization problems via heuristic search

Belief propagation (BP) approaches, such as Max-sum and its variants, are important methods to solve large-scale Distributed Constraint Optimization Problems. However, these algorithms face a huge challenge since their computational complexity scales exponentially with the arity of each constraint function. Current accelerating techniques for BP use sorting or branch-and-bound (BnB) strategy to reduce the search space. However, the existing BnB-based methods are mainly designed for specific problems, which limits their applicability. On the other hand, though several generic sorting-based methods have been proposed, they require significantly high preprocessing as well as memory overhead, which prohibits their adoption in some realistic scenarios. In this paper, we aim to propose a series of generic and memory-efficient heuristic search techniques to accelerate belief propagation. Specifically, by leveraging dynamic programming, we efficiently build function estimations for every partial assignment scoped in a constraint function in the preprocessing phase. Then, by using these estimations to build upper bounds and employing a branch-and-bound in a depth-first fashion to reduce the search space, we propose our first method called FDSP. Next, we enhance FDSP by adapting a concurrent-search strategy and leveraging the upper bounds as guiding information and propose its first heuristic variant framework called CONC-FDSP. Finally, by choosing to expand the partial assignment with the highest upper bound in each step of exploration, we propose the second heuristic variant of FDSP, called BFS-FDSP. We prove the correctness of our methods theoretically, and our empirical evaluations indicate their superiority for accelerating Max-sum in terms of both time and memory, compared with the state-of-the-art.