A trade-off between space and efficiency for routing tables
Journal of the ACM (JACM)
An optimal synchronizer for the hypercube
SIAM Journal on Computing
On sparse spanners of weighted graphs
Discrete & Computational Geometry
Proceedings of the thirteenth annual ACM symposium on Parallel algorithms and architectures
Spanners and message distribution in networks
Discrete Applied Mathematics - Special issue on international workshop on algorithms, combinatorics, and optimization in interconnection networks (IWACOIN '99)
Journal of the ACM (JACM)
Faster Algorithms for Approximate Distance Oracles and All-Pairs Small Stretch Paths
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Approximate distance oracles for unweighted graphs in expected O(n2) time
ACM Transactions on Algorithms (TALG)
Distance Oracles for Unweighted Graphs: Breaking the Quadratic Barrier with Constant Additive Error
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
Distance Oracles for Sparse Graphs
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Distance Oracles beyond the Thorup-Zwick Bound
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
Distance oracles for vertex-labeled graphs
ICALP'11 Proceedings of the 38th international conference on Automata, languages and programming - Volume Part II
On approximate distance labels and routing schemes with affine stretch
DISC'11 Proceedings of the 25th international conference on Distributed computing
Deterministic constructions of approximate distance oracles and spanners
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
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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={λ1,...,λℓ}. 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(kn1+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(kn ℓ1/k) at the expense of a huge stretch, the stretch of this construction grows exponentially in k, (2k−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, (2·3k−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.