TY - GEN

T1 - Single-Source Shortest Paths in the CONGEST Model with Improved Bound

AU - Chechik, Shiri

AU - Mukhtar, Doron

N1 - Publisher Copyright:
© 2020 ACM.

PY - 2020/7/31

Y1 - 2020/7/31

N2 - We improve the time complexity of the single-source shortest path problem for weighted directed graphs (with non-negative integer weights) in the Broadcast CONGEST model of distributed computing. For polynomially bounded edge weights, the state-of-the-art algorithm for this problem requires [EQUATION] rounds [Forster and Nanongkai, FOCS 2018], which is quite far from the known lower bound of [EQUATION] rounds [Elkin, STOC 2014]; here D is the diameter of the underlying network and n is the number of vertices in it. For the approximate version of this problem, Forster and Nanongkai [FOCS 2018] obtained an upper bound of [EQUATION], and stated that achieving the same bound for the exact case remains a major open problem. In this paper we resolve the above mentioned problem by devising a new randomized algorithm for solving (the exact version of) this problem in [EQUATION] rounds. Our algorithm is based on a novel weight-modifying technique that allows us to compute bounded-hop distance approximation that preserves a certain form of the triangle inequality for the edges in the graph.

AB - We improve the time complexity of the single-source shortest path problem for weighted directed graphs (with non-negative integer weights) in the Broadcast CONGEST model of distributed computing. For polynomially bounded edge weights, the state-of-the-art algorithm for this problem requires [EQUATION] rounds [Forster and Nanongkai, FOCS 2018], which is quite far from the known lower bound of [EQUATION] rounds [Elkin, STOC 2014]; here D is the diameter of the underlying network and n is the number of vertices in it. For the approximate version of this problem, Forster and Nanongkai [FOCS 2018] obtained an upper bound of [EQUATION], and stated that achieving the same bound for the exact case remains a major open problem. In this paper we resolve the above mentioned problem by devising a new randomized algorithm for solving (the exact version of) this problem in [EQUATION] rounds. Our algorithm is based on a novel weight-modifying technique that allows us to compute bounded-hop distance approximation that preserves a certain form of the triangle inequality for the edges in the graph.

KW - broadcast CONGEST

KW - distributed algorithms

KW - overlay networks

KW - single-source shortest paths

UR - http://www.scopus.com/inward/record.url?scp=85090325409&partnerID=8YFLogxK

U2 - 10.1145/3382734.3405729

DO - 10.1145/3382734.3405729

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AN - SCOPUS:85090325409

T3 - Proceedings of the Annual ACM Symposium on Principles of Distributed Computing

SP - 464

EP - 473

BT - PODC 2020 - Proceedings of the 39th Symposium on Principles of Distributed Computing

PB - Association for Computing Machinery

T2 - 39th Symposium on Principles of Distributed Computing, PODC 2020

Y2 - 3 August 2020 through 7 August 2020

ER -