eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2019-10-08
4:1
4:14
10.4230/LIPIcs.DISC.2019.4
article
Distributed Algorithms for Low Stretch Spanning Trees
Becker, Ruben
1
Emek, Yuval
2
Ghaffari, Mohsen
3
Lenzen, Christoph
4
Gran Sasso Science Institute, L'Aquila, Italy
Technion - Israel Institute of Technology, Haifa, Israel
ETH Zurich, Switzerland
MPI for Informatics, Saarland Informatics Campus, Saarbrücken, Germany
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(log^{3} 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., O~ (min{sqrt{n D}, sqrt{n} D^{1 / 4} + n^{3 / 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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol146-disc2019/LIPIcs.DISC.2019.4/LIPIcs.DISC.2019.4.pdf
distributed graph algorithms
low-stretch spanning trees
CONGEST model
ball decomposition
star decomposition