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Effect of asynchronous execution and imperfect communication on max-sum belief propagation

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Abstract

Max-sum is a version of belief propagation that was adapted for solving distributed constraint optimization problems. It has been studied theoretically and empirically, extended to versions that improve solution quality and converge rapidly, and is applicable to multiple distributed applications. The algorithm was presented both as synchronous and asynchronous algorithms. However, neither the differences in the performance of the two execution versions nor the implications of imperfect communication (i.e., massage delay and message loss) on the two versions have been investigated to the best of our knowledge. We contribute to the body of knowledge on Max-sum by: (1) Establishing the theoretical differences between the two execution versions of the algorithm, focusing on the construction of beliefs; (2) Empirically evaluating the differences between the solutions generated by the two versions of the algorithm, with and without message delay or loss; and (3) Establishing both theoretically and empirically the positive effect of damping on reducing the differences between the two versions. Our results indicate that, in contrast to recent published results indicating that message latency has a drastic (positive) effect on the performance of distributed local search algorithms, the effect of imperfect communication on Damped Max-sum (DMS) is minor. The version of Max-sum that includes both damping and splitting of function nodes converges to high quality solutions very fast, even when a large percentage of the messages sent by agents do not arrive at their destinations. Moreover, the quality of solutions in the different versions of DMS is dependent of the number of messages that were received by the agents, regardless of the amount of time they were delayed or if these messages are only a portion of the total number of messages that was sent by the agents.

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Availability of data and materials:

The simulation’s code is available at https://github.com/benrachmut/CADCOP_2022_new.

Notes

  1. This work is an extension of our published paper in the International Conference on Principles and Practice of Constraint Programming (CP) 2021 [14].

  2. We say that a variable is involved in a constraint if it is one of the variables the constraint refers to.

  3. This is because this assignment results in a normalized cost that is lower than any alternative oscillating path. See [18, 35] for details.

  4. We consider a step to be an action that starts when a node in the graph received some messages (at least one), performed computation, and ends when it sent some messages (at least one).

  5. For an analysis on the size of the damping factor required, with respect to the largest number of neighbors (degree) that a node in the factor graph has, see the work by Zivan et al. [15].

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Funding

This research is partially supported by US-Israel Binational Science Foundation (BSF) grant #2018081 and US National Science Foundation (NSF) grant #1838364.

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Authors and Affiliations

  1. Industrial Engineering and Management, Ben-Gurion University of the Negev, David Ben Gurion Blvd, 8410501, Beer-Sheva, Israel

    Roie Zivan, Ben Rachmut & Omer Perry

  2. Computer Science and Engineering Department, Washington University in St. Louis, Brookings Drive, Saint Louis, MO, 63130, USA

    William Yeoh

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  1. Roie Zivan
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  2. Ben Rachmut
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  4. William Yeoh
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Contributions

This paper is a result of a number of years of investigation of both the Max-sum algorithm and the performance of distributed algorithms in scenarios with imperfect communication. The idea to investigate the performance of distributed algorithms in such environments was suggested by William Yeoh and Roie Zivan, and this research is part of a BSF granted project that they are the two PIs of. Most of the writing of the paper was done by Roie Zivan. The experimental work was done by Ben Rachmut and Omer Perri. Ben Rachmut wrote most of the experimental section. William Yeoh reviewed the results and the writing, and suggested improvements.

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Correspondence to Roie Zivan.

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Zivan, R., Rachmut, B., Perry, O. et al. Effect of asynchronous execution and imperfect communication on max-sum belief propagation. Auton Agent Multi-Agent Syst 37, 40 (2023). https://doi.org/10.1007/s10458-023-09621-w

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