Compact routing with minimum stretch
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Polylog-time and near-linear work approximation scheme for undirected shortest paths
Journal of the ACM (JACM)
Compact roundtrip routing in directed networks (extended abstract)
Proceedings of the nineteenth annual ACM symposium on Principles of distributed computing
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Approximate distance oracles for geometric graphs
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Roundtrip spanners and roundtrip routing in directed graphs
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Approximate Distance Oracles Revisited
ISAAC '02 Proceedings of the 13th International Symposium on Algorithms and Computation
t-Spanners as a Data Structure for Metric Space Searching
SPIRE 2002 Proceedings of the 9th International Symposium on String Processing and Information Retrieval
Exact and Approximate Distances in Graphs - A Survey
ESA '01 Proceedings of the 9th Annual European Symposium on Algorithms
Compact roundtrip routing in directed networks
Journal of Algorithms
Journal of the ACM (JACM)
New constructions of (α, β)-spanners and purely additive spanners
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Spanners and emulators with sublinear distance errors
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
On graph problems in a semi-streaming model
Theoretical Computer Science - Automata, languages and programming: Algorithms and complexity (ICALP-A 2004)
Approximate distance oracles for unweighted graphs in expected O(n2) time
ACM Transactions on Algorithms (TALG)
Approximate distance oracles for graphs with dense clusters
Computational Geometry: Theory and Applications
A simple and linear time randomized algorithm for computing sparse spanners in weighted graphs
Random Structures & Algorithms
Dynamic algorithms for graph spanners
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
A near-optimal distributed fully dynamic algorithm for maintaining sparse spanners
Proceedings of the twenty-sixth annual ACM symposium on Principles of distributed computing
t-Spanners for metric space searching
Data & Knowledge Engineering
Approximate distance oracles for geometric spanners
ACM Transactions on Algorithms (TALG)
Fully dynamic algorithm for graph spanners with poly-logarithmic update time
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Roundtrip spanners and roundtrip routing in directed graphs
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
All-pairs nearly 2-approximate shortest paths in O(n2polylogn) time
Theoretical Computer Science
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Approximating Shortest Paths in Graphs
WALCOM '09 Proceedings of the 3rd International Workshop on Algorithms and Computation
A simple linear time algorithm for computing a (2k - 1)-spanner of o(n1+1/k) size in weighted graphs
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Faster algorithms for all-pairs small stretch distances in weighted graphs
FSTTCS'07 Proceedings of the 27th international conference on Foundations of software technology and theoretical computer science
Local computation of nearly additive spanners
DISC'09 Proceedings of the 23rd international conference on Distributed computing
Additive spanners and (α, β)-spanners
ACM Transactions on Algorithms (TALG)
Additive spanners in nearly quadratic time
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
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
Computing graph spanners in small memory: fault-tolerance and streaming
COCOON'10 Proceedings of the 16th annual international conference on Computing and combinatorics
Fast distributed graph partition and application
IPDPS'06 Proceedings of the 20th international conference on Parallel and distributed processing
Transitive-closure spanners: a survey
Property testing
Transitive-closure spanners: a survey
Property testing
Sparse spanners vs. compact routing
Proceedings of the twenty-third annual ACM symposium on Parallelism in algorithms and architectures
Improved approximation for the directed spanner problem
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Multiplicative approximations of random walk transition probabilities
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Context-aware nearest neighbor query on social networks
SocInfo'11 Proceedings of the Third international conference on Social informatics
Fast deterministic distributed algorithms for sparse spanners
SIROCCO'06 Proceedings of the 13th international conference on Structural Information and Communication Complexity
Deterministic constructions of approximate distance oracles and spanners
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Improved dynamic algorithms for maintaining approximate shortest paths under deletions
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Approximate distance oracles for graphs with dense clusters
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
Fully dynamic randomized algorithms for graph spanners
ACM Transactions on Algorithms (TALG)
Deterministic distributed construction of linear stretch spanners in polylogarithmic time
DISC'07 Proceedings of the 21st international conference on Distributed Computing
Approximation algorithms for spanner problems and Directed Steiner Forest
Information and Computation
Parallel graph decompositions using random shifts
Proceedings of the twenty-fifth annual ACM symposium on Parallelism in algorithms and architectures
Improved multicriteria spanners for Ad-Hoc networks under energy and distance metrics
ACM Transactions on Sensor Networks (TOSN)
Shortest-path queries in static networks
ACM Computing Surveys (CSUR)
Hi-index | 0.00 |
The distance between two vertices in a weighted graph is the weight of a minimum-weight path between them (where the weight of a path is the sum of the weights of the edges in the path). A path has stretch t if its weight is at most t times the distance between its end points. We present algorithms that compute paths of stretch $2\leq t\leq\log n$ on undirected graphs G=(V,E) with nonnegative weights. The stretch t is of the form $t=\beta(2+\epsilon')$, where $\beta$ is integral and $\epsilon'0$ is at least as large as some fixed $\epsilon0$. We present an $\tilde{O}((m+k)n^{(2+\epsilon)/t})$ time randomized algorithm that finds paths between k specified pairs of vertices and an $\tilde{O}((m+ns)n^{2(1+\log_n m+\epsilon)/t})$ deterministic algorithm that finds paths from $s$ specified sources to all other vertices (for any fixed $\epsilon0$), where n=|V| and m=|E|. This improves significantly over the slower $\tilde{O}(\min\{k,n\}m)$ exact shortest paths algorithms and a previous $\tilde{O}(mn^{64/t}+kn^{32/t})$ time algorithm by Awerbuch {et al.}\ [Proc. 34th IEEE Annual Symposium on Foundations of Computer Science, IEEE, Piscataway, NJ, 1993, pp. 638--647]. A t-spanner of a graph G is a set of weighted edges on the vertices of G such that distances in the spanner are not smaller and within a factor of t from the corresponding distances in G. Previous work was concerned with bounding the size and efficiently constructing t-spanners. We construct t-spanners of size $\tilde{O}(n^{1+(2+\epsilon)/t})$ in $\tilde{O}(mn^{(2+\epsilon)/t})$ expected time (for any fixed $\epsilon0$), which constitutes a faster construction (by a factor of n3+2/t /m) of sparser spanners than was previously attainable. We also provide efficient parallel constructions. Our algorithms are based on pairwise covers and a novel approach to construct them efficiently.