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
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Compact roundtrip routing with topology-independent node names
Proceedings of the twenty-second annual symposium on Principles of distributed computing
Compact roundtrip routing in directed networks
Journal of Algorithms
Efficient algorithms for constructing (1+,ε, β)-spanners in the distributed and streaming models
Proceedings of the twenty-third annual ACM symposium on Principles of distributed computing
Sparse source-wise and pair-wise distance preservers
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
New constructions of (α, β)-spanners and purely additive spanners
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Computing almost shortest paths
ACM Transactions on Algorithms (TALG)
Fast deterministic distributed algorithms for sparse spanners
Theoretical Computer Science
Compact roundtrip routing with topology-independent node names
Journal of Computer and System Sciences
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Additive spanners and (α, β)-spanners
ACM Transactions on Algorithms (TALG)
Lower bounds for local monotonicity reconstruction from transitive-closure spanners
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Near-optimal multicriteria spanner constructions in wireless ad hoc networks
IEEE/ACM Transactions on Networking (TON)
Transitive-closure spanners: a survey
Property testing
Transitive-closure spanners: a survey
Property testing
Fast deterministic distributed algorithms for sparse spanners
SIROCCO'06 Proceedings of the 13th international conference on Structural Information and Communication Complexity
Deterministic distributed construction of linear stretch spanners in polylogarithmic time
DISC'07 Proceedings of the 21st international conference on Distributed Computing
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
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We introduce the notion of roundtrip-spanners of weighted directed graphs and describe efficient algorithms for their construction. For every integer k ≥ 1 and any ε 0, we show that any directed graph on n vertices with edge weights in the range [1, W] has a (2k + ε)-roundtrip-spanner with O(k2/εn1+1/klog(nW)) 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/εn1/klog(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.