Distributed Algorithms for Low Stretch Spanning Trees
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.
distributed graph algorithms
low-stretch spanning trees
CONGEST model
ball decomposition
star decomposition
Mathematics of computing~Graph algorithms
Theory of computation~Distributed algorithms
4:1-4:14
Regular Paper
Ruben
Becker
Ruben Becker
Gran Sasso Science Institute, L'Aquila, Italy
This work has been partially supported by the Italian MIUR PRIN 2017 Project ALGADIMAR "Algorithms, Games, and Digital Markets".
Yuval
Emek
Yuval Emek
Technion - Israel Institute of Technology, Haifa, Israel
This work has been supported in part by an Israeli Science Foundation grant number 1016/17.
Mohsen
Ghaffari
Mohsen Ghaffari
ETH Zurich, Switzerland
Christoph
Lenzen
Christoph Lenzen
MPI for Informatics, Saarland Informatics Campus, Saarbrücken, Germany
10.4230/LIPIcs.DISC.2019.4
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Ruben Becker, Yuval Emek, Mohsen Ghaffari, and Christoph Lenzen
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