Local Deal-Agreement Algorithms for Load Balancing in Dynamic General Graphs

We study the classic load balancing problem on dynamic general graphs, where the graph changes arbitrarily between the computational rounds, remaining connected with no permanent cut. A lower bound of Ω( n 2 ) for the running time bound in the dynamic setting, where n is the number of nodes in the g...

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Published in:	Theory of computing systems Vol. 67; no. 2; pp. 348 - 382
Main Authors:	Dinitz, Yefim, Dolev, Shlomi, Kumar, Manish
Format:	Journal Article
Language:	English
Published:	New York Springer US 01.04.2023
Subjects:	Computer Science Theory of Computation Self-stabilization Asynchronous system General graph Distributed algorithm Deterministic algorithm Load balancing Dynamic graph
ISSN:	1432-4350, 1433-0490
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Abstract	We study the classic load balancing problem on dynamic general graphs, where the graph changes arbitrarily between the computational rounds, remaining connected with no permanent cut. A lower bound of Ω( n 2 ) for the running time bound in the dynamic setting, where n is the number of nodes in the graph, is known even for randomized algorithms. We solve the problem by deterministic distributed algorithms, based on a short local deal-agreement communication of proposal/deal in the neighborhood of each node. Our synchronous load balancing algorithms achieve a discrepancy of 𝜖 within the time of O ( n D log ( n K / 𝜖 ) ) for the continuous setting and the discrepancy of at most 2 D within the time of O ( n D log ( n K / D ) ) and a 1-balanced state within the additional time of O ( n D 2 ) for the discrete setting, where K is the initial discrepancy, and D is a bound for the graph diameter. Also, the stability of the achieved 1-balanced state is studied. The above results are extended to the case of unbounded diameter , essentially keeping the time bounds, via special averaging of the graph diameter over time. Our algorithms can be considered anytime ones, in the sense that they can be stopped at any time during the execution, since they never make loads negative and never worsen the state as the execution progresses. In addition, we describe a version of our algorithms, where each node may transfer load to and from several neighbors at each round, as a heuristic for better performance. The algorithms are generalized to the asynchronous distributed model. We also introduce a self-stabilizing version of our asynchronous algorithms.
AbstractList	We study the classic load balancing problem on dynamic general graphs, where the graph changes arbitrarily between the computational rounds, remaining connected with no permanent cut. A lower bound of Ω( n 2 ) for the running time bound in the dynamic setting, where n is the number of nodes in the graph, is known even for randomized algorithms. We solve the problem by deterministic distributed algorithms, based on a short local deal-agreement communication of proposal/deal in the neighborhood of each node. Our synchronous load balancing algorithms achieve a discrepancy of 𝜖 within the time of O ( n D log ( n K / 𝜖 ) ) for the continuous setting and the discrepancy of at most 2 D within the time of O ( n D log ( n K / D ) ) and a 1-balanced state within the additional time of O ( n D 2 ) for the discrete setting, where K is the initial discrepancy, and D is a bound for the graph diameter. Also, the stability of the achieved 1-balanced state is studied. The above results are extended to the case of unbounded diameter , essentially keeping the time bounds, via special averaging of the graph diameter over time. Our algorithms can be considered anytime ones, in the sense that they can be stopped at any time during the execution, since they never make loads negative and never worsen the state as the execution progresses. In addition, we describe a version of our algorithms, where each node may transfer load to and from several neighbors at each round, as a heuristic for better performance. The algorithms are generalized to the asynchronous distributed model. We also introduce a self-stabilizing version of our asynchronous algorithms.
Author	Dolev, Shlomi Dinitz, Yefim Kumar, Manish
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Cites_doi	10.1016/0888-613X(88)90148-X 10.1016/j.jnca.2017.02.013 10.7155/jgaa.00118 10.1002/cpe.4330020403 10.1007/s11227-021-04024-8 10.1016/j.tcs.2006.09.020 10.1016/j.jksuci.2018.01.003 10.1137/1.9780898719772 10.1016/j.asoc.2018.10.002 10.1145/3282435 10.1137/0221015 10.1007/s002240000092 10.1016/0743-7315(89)90021-X 10.7551/mitpress/6156.001.0001 10.1007/s00446-017-0300-8 10.1145/1959045.1959064 10.1109/SFCS.1998.743520 10.1137/1.9781611973082.34 10.1007/978-3-662-48653-5_36 10.1145/103418.103421 10.1145/167088.167250 10.1007/978-3-642-33536-5_14 10.1145/3409964.3461808 10.1109/FOCS.2012.86 10.1145/2332432.2332486 10.1145/2332432.2332486 10.4230/LIPIcs.OPODIS.2018.31 10.1145/1536414.1536433 10.1007/978-3-030-64348-5_9 10.1109/PCCC.1994.504130 10.1109/INFOCOM.2017.8057000 10.1145/1835698.1835780 10.1137/1.9781611973075.132 10.1145/225058.225272 10.1109/IPPS.1993.262906
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Title	Local Deal-Agreement Algorithms for Load Balancing in Dynamic General Graphs
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