NDLI: Fault-tolerant spanners: better and simpler

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Fault-tolerant spanners: better and simpler

Content Provider	ACM Digital Library
Author	Krauthgamer, Robert Dinitz, Michael
Abstract	A natural requirement for many distributed structures is fault-tolerance: after some failures in the underlying network, whatever remains from the structure should still be effective for whatever remains from the network. In this paper we examine spanners of general graphs that are tolerant to vertex failures, and significantly improve their dependence on the number of faults r for all stretch bounds. For stretch k e 3 we design a simple transformation that converts every k-spanner construction with at most f(n) edges into an r-fault-tolerant k-spanner construction with at most $O(r^{3}$ log n) Å f(2n/r) edges. Applying this to standard greedy spanner constructions gives r-fault tolerant k-spanners with $Õ(r^{2}$ $n^{1+2/k+1})$ edges. The previous construction by Chechik, Langberg, Peleg, and Roddity [STOC 2009] depends similarly on n but exponentially on r (approximately like $k^{r}).$ For the case of k=2 and unit edge-lengths, an O(r log n)-approximation is known from recent work of Dinitz and Krauthgamer [STOC 2011], in which several spanner results are obtained using a common approach of rounding a natural flow-based linear programming relaxation. Here we use a different (stronger) LP relaxation and improve the approximation ratio to O(log n), which is, notably, independent of the number of faults r. We further strengthen this bound in terms of the maximum degree by using the Lovasz Local Lemma. Finally, we show that most of our constructions are inherently local by designing equivalent distributed algorithms in the LOCAL model of distributed computation.
Starting Page	169
Ending Page	178
Page Count	10
File Format	PDF
ISBN	9781450307192
DOI	10.1145/1993806.1993830
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2011-06-06
Publisher Place	New York
Access Restriction	Subscribed
Subject Keyword	Fault tolerance Spanners Approximation algorithms
Content Type	Text
Resource Type	Article

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