TY - GEN

T1 - Fault tolerant additive spanners

AU - Braunschvig, Gilad

AU - Chechik, Shiri

AU - Peleg, David

PY - 2012

Y1 - 2012

N2 - Graph spanners are sparse subgraphs that preserve the distances of the original graph, up to some small multiplicative factor or additive term (known as the stretch of the spanner). A number of algorithms are known for constructing sparse spanners with small multiplicative or additive stretch. Recently, the problem of constructing fault-tolerant multiplicative spanners for general graphs was given some algorithms. This paper addresses the analogous problem of constructing fault tolerant additive spanners for general graphs. We establish the following general result. Given an n-vertex graph G, if H 1 is an ordinary additive spanner for G with additive stretch α, and H 2 is a fault tolerant multiplicative spanner for G, resilient against up to f edge failures, with multiplicative stretch μ, then H∈=∈H 1∈∪∈H 2 is an additive fault tolerant spanner of G, resilient against up to f edge failures, with additive stretch where is the number of failures that have actually occurred. This allows us to derive a poly-time algorithm for constructing an additive fault tolerant spanner H of G, relying on the existence of algorithms for constructing fault tolerant multiplicative spanners and (ordinary) additive spanners. In particular, based on some known spanner construction algorithms, we show how to construct for any n-vertex graph G an additive fault tolerant spanner with additive stretch and size O(fn 4/3).

AB - Graph spanners are sparse subgraphs that preserve the distances of the original graph, up to some small multiplicative factor or additive term (known as the stretch of the spanner). A number of algorithms are known for constructing sparse spanners with small multiplicative or additive stretch. Recently, the problem of constructing fault-tolerant multiplicative spanners for general graphs was given some algorithms. This paper addresses the analogous problem of constructing fault tolerant additive spanners for general graphs. We establish the following general result. Given an n-vertex graph G, if H 1 is an ordinary additive spanner for G with additive stretch α, and H 2 is a fault tolerant multiplicative spanner for G, resilient against up to f edge failures, with multiplicative stretch μ, then H∈=∈H 1∈∪∈H 2 is an additive fault tolerant spanner of G, resilient against up to f edge failures, with additive stretch where is the number of failures that have actually occurred. This allows us to derive a poly-time algorithm for constructing an additive fault tolerant spanner H of G, relying on the existence of algorithms for constructing fault tolerant multiplicative spanners and (ordinary) additive spanners. In particular, based on some known spanner construction algorithms, we show how to construct for any n-vertex graph G an additive fault tolerant spanner with additive stretch and size O(fn 4/3).

UR - http://www.scopus.com/inward/record.url?scp=84868035971&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-34611-8_22

DO - 10.1007/978-3-642-34611-8_22

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AN - SCOPUS:84868035971

SN - 9783642346101

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 206

EP - 214

BT - Graph-Theoretic Concepts in Computer Science - 38th International Workshop, WG 2012, Revised Selcted Papers

T2 - 38th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2012

Y2 - 26 June 2012 through 28 June 2012

ER -