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

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Abstract

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.

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Data availability

The implementation of the compared baselines and our proposed algorithms are available and can be found in https://github.com/czy920/FDSP.

Notes

  1. Current work all finds the optimal assignments to guarantee the optimality when solving tree-structure problems with Max-sum.

  2. The main difference between Fast Max-Sum and Max-Sum is that the domain size of each variable in Fast Max-Sum is reduced to 2.

  3. One can easily prove that the pre-stored full assignments in bestEntryView are solutions to the corresponding problems according to the way we construct.

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Funding

The research leading to these results received funding from Fundamental Research Funds for the Central Universities (2018CDXYJSJ0026).

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Authors and Affiliations

  1. College of Computer Science, Chongqing University, Chongqing, 400044, China

    Junsong Gao, Ziyu Chen, Dingding Chen & Wenxin Zhang

  2. College of Electrical Engineering, Chongqing University, Chongqing, 400044, China

    Qiang Li

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  1. Junsong Gao
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Contributions

ZC and WZ contributed to the conception of the study; JG performed the experiment; JG, ZC and DC contributed significantly to analysis and manuscript preparation; JG performed the data analyses and wrote the manuscript; ZC, DC and QL helped perform the analysis with constructive discussions.

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Correspondence to Ziyu Chen.

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This paper is an extension to our AAAI paper [5]. Besides additional examples, experiments and proofs, we also present two heuristic variants including Concurrent-search based FDSP (CONC-FDSP) and Best-first search based FDSP (BFS-FDSP) which are not included in our AAAI paper.

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Gao, J., Chen, Z., Chen, D. et al. Toward fast belief propagation for distributed constraint optimization problems via heuristic search. Auton Agent Multi-Agent Syst 38, 15 (2024). https://doi.org/10.1007/s10458-024-09643-y

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