Storing a Sparse Table with 0(1) Worst Case Access Time
Journal of the ACM (JACM)
On sparse spanners of weighted graphs
Discrete & Computational Geometry
Fast Algorithms for Constructing t-Spanners and Paths with Stretch t
SIAM Journal on Computing
Near-Linear Time Construction of Sparse Neighborhood Covers
SIAM Journal on Computing
Compact roundtrip routing for digraphs
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Faster deterministic dictionaries
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Compact roundtrip routing in directed networks (extended abstract)
Proceedings of the nineteenth annual ACM symposium on Principles of distributed computing
Distributed computing: a locality-sensitive approach
Distributed computing: a locality-sensitive approach
Compact routing with minimum stretch
Journal of Algorithms
Journal of Algorithms
Proceedings of the thirteenth annual ACM symposium on Parallel algorithms and architectures
Journal of Algorithms
Journal of the ACM (JACM)
ACM Transactions on Algorithms (TALG)
Local computation of nearly additive spanners
DISC'09 Proceedings of the 23rd international conference on Distributed computing
f-sensitivity distance Oracles and routing schemes
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
Improved approximation for the directed spanner problem
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
SIROCCO'10 Proceedings of the 17th international conference on Structural Information and Communication Complexity
Node-Disjoint multipath spanners and their relationship with fault-tolerant spanners
OPODIS'11 Proceedings of the 15th international conference on Principles of Distributed Systems
Fully dynamic randomized algorithms for graph spanners
ACM Transactions on Algorithms (TALG)
Approximation algorithms for spanner problems and Directed Steiner Forest
Information and Computation
Multipath spanners via fault-tolerant spanners
MedAlg'12 Proceedings of the First Mediterranean conference on Design and Analysis of Algorithms
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We introduce the notion of roundtrip-spanners of weighted directed graphs and describe efficient algorithms for their construction. We show that for every integer k ≥ 1 and any ε 0, any directed graph on n vertices with edge weights in the range [1, W] has a (2k + ε)-roundtrip-spanner with O(min{(k2/ε) n1 + 1/k (log(nW), (k/ε)2 n1 + 1/k,(log n)2−1/k}) edges. We then extend these constructions and obtain compact roundtrip routing schemes. For every integer k ≥ 1 and every ε 0, we describe a roundtrip routing scheme that has stretch 4k + ε, and uses at each vertex a routing table of size Õ((k2/ε)n1/k log(nW)). We also show that any weighted directed graph with arbitrary/ positive edge weights has a 3-roundtrip-spanner with O(n3/2) edges. This result is optimal. Finally, we present a stretch 3 roundtrip routing scheme that uses local routing tables of size Õ(n1/2). This routing scheme is essentially optimal. The roundtrip-spanner constructions and the roundtrip routing schemes for directed graphs that we describe are only slightly worse than the best available spanners and routing schemes for undirected graphs. Our roundtrip routing schemes substantially improve previous results of Cowen and Wagner. Our results are obtained by combining ideas of Cohen, Cowen and Wagner, Thorup and Zwick, with some new ideas.