TY - GEN

T1 - Improved distance oracles and spanners for vertex-labeled graphs

AU - Chechik, Shiri

PY - 2012

Y1 - 2012

N2 - Consider an undirected weighted graph G = (V,E) with |V| = n and |E| = m, where each vertex v ∈ V is assigned a label from a set of labels L = {λ 1,...,λ ℓ}. We show how to construct a compact distance oracle that can answer queries of the form: "what is the distance from v to the closest λ-labeled vertex" for a given vertex v ∈ V and label λ ∈ L. This problem was introduced by Hermelin, Levy, Weimann and Yuster [ICALP 2011] where they present several results for this problem. In the first result, they show how to construct a vertex-label distance oracle of expected size O(kn 1+1/k ) with stretch (4k-5) and query time O(k). In a second result, they show how to reduce the size of the data structure to O(knℓ 1/k ) at the expense of a huge stretch, the stretch of this construction grows exponentially in k, (2 k -1). In the third result they present a dynamic vertex-label distance oracle that is capable of handling label changes in a sub-linear time. The stretch of this construction is also exponential in k, (2.3 k-1+1). We manage to significantly improve the stretch of their constructions, reducing the dependence on k from exponential to polynomial (4k-5), without requiring any tradeoff regarding any of the other variables. In addition, we introduce the notion of vertex-label spanners: subgraphs that preserve distances between every vertex v ∈ V and label λ ∈ L. We present an efficient construction for vertex-label spanners with stretch-size tradeoff close to optimal.

AB - Consider an undirected weighted graph G = (V,E) with |V| = n and |E| = m, where each vertex v ∈ V is assigned a label from a set of labels L = {λ 1,...,λ ℓ}. We show how to construct a compact distance oracle that can answer queries of the form: "what is the distance from v to the closest λ-labeled vertex" for a given vertex v ∈ V and label λ ∈ L. This problem was introduced by Hermelin, Levy, Weimann and Yuster [ICALP 2011] where they present several results for this problem. In the first result, they show how to construct a vertex-label distance oracle of expected size O(kn 1+1/k ) with stretch (4k-5) and query time O(k). In a second result, they show how to reduce the size of the data structure to O(knℓ 1/k ) at the expense of a huge stretch, the stretch of this construction grows exponentially in k, (2 k -1). In the third result they present a dynamic vertex-label distance oracle that is capable of handling label changes in a sub-linear time. The stretch of this construction is also exponential in k, (2.3 k-1+1). We manage to significantly improve the stretch of their constructions, reducing the dependence on k from exponential to polynomial (4k-5), without requiring any tradeoff regarding any of the other variables. In addition, we introduce the notion of vertex-label spanners: subgraphs that preserve distances between every vertex v ∈ V and label λ ∈ L. We present an efficient construction for vertex-label spanners with stretch-size tradeoff close to optimal.

UR - http://www.scopus.com/inward/record.url?scp=84866720195&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-33090-2_29

DO - 10.1007/978-3-642-33090-2_29

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AN - SCOPUS:84866720195

SN - 9783642330896

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

SP - 325

EP - 336

BT - Algorithms, ESA 2012 - 20th Annual European Symposium, Proceedings

T2 - 20th Annual European Symposium on Algorithms, ESA 2012

Y2 - 10 September 2012 through 12 September 2012

ER -