TY - GEN

T1 - Distributed algorithms for low stretch spanning trees

AU - Becker, Ruben

AU - Emek, Yuval

AU - Ghaffari, Mohsen

AU - Lenzen, Christoph

N1 - Publisher Copyright:
© Ruben Becker, Yuval Emek, Mohsen Ghaffari, and Christoph Lenzen.

PY - 2019/10

Y1 - 2019/10

N2 - Given an undirected graph with integer edge lengths, we study the problem of approximating the distances in the graph by a spanning tree based on the notion of stretch. Our main contribution is a distributed algorithm in the CONGEST model of computation that constructs a random spanning tree with the guarantee that the expected stretch of every edge is O(log3 n), where n is the number of nodes in the graph. If the graph is unweighted, then this algorithm can be implemented to run in O(D) rounds, where D is the hop-diameter of the graph, thus being asymptotically optimal. In the weighted case, the run-time of our algorithm matches the currently best known bound for exact distance computations, i.e., Õ(min{√nD, √nD1/4 + n3/5 + D}). We stress that this is the first distributed construction of spanning trees leading to poly-logarithmic expected stretch with non-trivial running time.

AB - Given an undirected graph with integer edge lengths, we study the problem of approximating the distances in the graph by a spanning tree based on the notion of stretch. Our main contribution is a distributed algorithm in the CONGEST model of computation that constructs a random spanning tree with the guarantee that the expected stretch of every edge is O(log3 n), where n is the number of nodes in the graph. If the graph is unweighted, then this algorithm can be implemented to run in O(D) rounds, where D is the hop-diameter of the graph, thus being asymptotically optimal. In the weighted case, the run-time of our algorithm matches the currently best known bound for exact distance computations, i.e., Õ(min{√nD, √nD1/4 + n3/5 + D}). We stress that this is the first distributed construction of spanning trees leading to poly-logarithmic expected stretch with non-trivial running time.

KW - Ball decomposition

KW - CONGEST model

KW - Distributed graph algorithms

KW - Low-stretch spanning trees

KW - Star decomposition

UR - http://www.scopus.com/inward/record.url?scp=85074558237&partnerID=8YFLogxK

U2 - 10.4230/LIPIcs.DISC.2019.4

DO - 10.4230/LIPIcs.DISC.2019.4

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AN - SCOPUS:85074558237

T3 - Leibniz International Proceedings in Informatics, LIPIcs

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

A2 - Suomela, Jukka

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

Y2 - 14 October 2019 through 18 October 2019

ER -