TY - GEN

T1 - Reachability and shortest paths in the broadcast congest model

AU - Chechik, Shiri

AU - Mukhtar, Doron

N1 - Publisher Copyright:
© Shiri Chechik and Doron Mukhtar.

PY - 2019/10

Y1 - 2019/10

N2 - In this paper we study the time complexity of the single-source reachability problem and the single-source shortest path problem for directed unweighted graphs in the Broadcast CONGEST model. We focus on the case where the diameter D of the underlying network is constant. We show that for the case where D = 1 there is, quite surprisingly, a very simple algorithm that solves the reachability problem in 1(!) round. In contrast, for networks with D = 2, we show that any distributed algorithm (possibly randomized) for this problem requires Ω(pn/ log n ) rounds. Our results therefore completely resolve (up to a small polylog factor) the complexity of the single-source reachability problem for a wide range of diameters. Furthermore, we show that when D = 1, it is even possible to get an almost 3 – approximation for the all-pairs shortest path problem (for directed unweighted graphs) in just 2 rounds. We also prove a stronger lower bound of Ω(√n ) for the single-source shortest path problem for unweighted directed graphs that holds even when the diameter of the underlying network is 2. As far as we know this is the first lower bound that achieves Ω(√n ) for this problem.

AB - In this paper we study the time complexity of the single-source reachability problem and the single-source shortest path problem for directed unweighted graphs in the Broadcast CONGEST model. We focus on the case where the diameter D of the underlying network is constant. We show that for the case where D = 1 there is, quite surprisingly, a very simple algorithm that solves the reachability problem in 1(!) round. In contrast, for networks with D = 2, we show that any distributed algorithm (possibly randomized) for this problem requires Ω(pn/ log n ) rounds. Our results therefore completely resolve (up to a small polylog factor) the complexity of the single-source reachability problem for a wide range of diameters. Furthermore, we show that when D = 1, it is even possible to get an almost 3 – approximation for the all-pairs shortest path problem (for directed unweighted graphs) in just 2 rounds. We also prove a stronger lower bound of Ω(√n ) for the single-source shortest path problem for unweighted directed graphs that holds even when the diameter of the underlying network is 2. As far as we know this is the first lower bound that achieves Ω(√n ) for this problem.

KW - Broadcast CONGEST

KW - Distance estimation

KW - Distributed algorithms

KW - Small diameter

UR - http://www.scopus.com/inward/record.url?scp=85074554756&partnerID=8YFLogxK

U2 - 10.4230/LIPIcs.DISC.2019.11

DO - 10.4230/LIPIcs.DISC.2019.11

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AN - SCOPUS:85074554756

T3 - Leibniz International Proceedings in Informatics, LIPIcs

BT - 33rd International Symposium on Distributed Computing, DISC 2019

A2 - Suomela, Jukka

PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing

T2 - 33rd International Symposium on Distributed Computing, DISC 2019

Y2 - 14 October 2019 through 18 October 2019

ER -