TY - JOUR

T1 - Single-source shortest paths in the CONGEST model with improved bounds

AU - Chechik, Shiri

AU - Mukhtar, Doron

N1 - Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.

PY - 2022/8

Y1 - 2022/8

N2 - Computing shortest paths from a single source is one of the central problems studied in the CONGEST model of distributed computing. After many years in which no algorithmic progress was made, Elkin [STOC ‘17] provided the first improvement over the distributed Bellman-Ford algorithm. Since then, several improved algorithms have been published. The state-of-the-art algorithm for weighted directed graphs (with polynomially bounded non-negative integer weights) requires O~(min{nD1/2,nD1/4+n3/5+D}) rounds [Forster and Nanongkai, FOCS ‘18], which is still quite far from the known lower bound of Ω~(n+D) rounds [Elkin, STOC ‘04]; here D is the diameter of the underlying network and n is the number of vertices in it. For the (1 + o(1)) -approximate version of this problem and the same class of graphs, Forster and Nanongkai [FOCS ‘18] obtained a better upper bound of O~(nD1/4+D) rounds. In the same paper, they 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 computing shortest paths from a single source in O~(nD1/4+D) rounds. Our algorithm is based on a novel weight-modifying technique that allows us to compute approximate distances that preserve a certain form of the triangle inequality for the edges in the graph.

AB - Computing shortest paths from a single source is one of the central problems studied in the CONGEST model of distributed computing. After many years in which no algorithmic progress was made, Elkin [STOC ‘17] provided the first improvement over the distributed Bellman-Ford algorithm. Since then, several improved algorithms have been published. The state-of-the-art algorithm for weighted directed graphs (with polynomially bounded non-negative integer weights) requires O~(min{nD1/2,nD1/4+n3/5+D}) rounds [Forster and Nanongkai, FOCS ‘18], which is still quite far from the known lower bound of Ω~(n+D) rounds [Elkin, STOC ‘04]; here D is the diameter of the underlying network and n is the number of vertices in it. For the (1 + o(1)) -approximate version of this problem and the same class of graphs, Forster and Nanongkai [FOCS ‘18] obtained a better upper bound of O~(nD1/4+D) rounds. In the same paper, they 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 computing shortest paths from a single source in O~(nD1/4+D) rounds. Our algorithm is based on a novel weight-modifying technique that allows us to compute approximate distances that preserve a certain form of the triangle inequality for the edges in the graph.

KW - Distributed algorithms

KW - Overlay networks

KW - Single-source shortest paths

UR - http://www.scopus.com/inward/record.url?scp=85120091524&partnerID=8YFLogxK

U2 - 10.1007/s00446-021-00412-8

DO - 10.1007/s00446-021-00412-8

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AN - SCOPUS:85120091524

SN - 0178-2770

VL - 35

SP - 357

EP - 374

JO - Distributed Computing

JF - Distributed Computing

IS - 4

ER -