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 -