Proceedings of the thirteenth annual ACM symposium on Parallel algorithms and architectures
(1 + &egr;&Bgr;)-spanner constructions for general graphs
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Computing almost shortest paths
Proceedings of the twentieth annual ACM symposium on Principles of distributed computing
Approximate distance oracles for geometric graphs
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
All pairs shortest paths using bridging sets and rectangular matrix multiplication
Journal of the ACM (JACM)
Maintaining all-pairs approximate shortest paths under deletion of edges
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Sparse distance preservers and additive spanners
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Approximate Distance Oracles Revisited
ISAAC '02 Proceedings of the 13th International Symposium on Algorithms and Computation
Exact and Approximate Distances in Graphs - A Survey
ESA '01 Proceedings of the 9th Annual European Symposium on Algorithms
Approximate distance oracles for unweighted graphs in Õ (n2) time
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete 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
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
External-memory exact and approximate all-pairs shortest-paths in undirected graphs
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Computing almost shortest paths
ACM Transactions on Algorithms (TALG)
All-pairs shortest paths for unweighted undirected graphs in o(mn) time
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Spanners and emulators with sublinear distance errors
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
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
On the K-simple shortest paths problem in weighted directed graphs
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Spanners for bounded tree-length graphs
Theoretical Computer Science
Efficient search ranking in social networks
Proceedings of the sixteenth ACM conference on Conference on information and knowledge management
Approximate distance oracles for geometric spanners
ACM Transactions on Algorithms (TALG)
Distributed algorithms for ultrasparse spanners and linear size skeletons
Proceedings of the twenty-seventh ACM symposium on Principles of distributed computing
All-pairs nearly 2-approximate shortest paths in O(n2polylogn) time
Theoretical Computer Science
Approximating Shortest Paths in Graphs
WALCOM '09 Proceedings of the 3rd International Workshop on Algorithms and Computation
Efficient approximation algorithms for shortest cycles in undirected graphs
Information Processing Letters
ACM Transactions on Algorithms (TALG)
As Good as It Gets: Competitive Fault Tolerance in Network Structures
SSS '09 Proceedings of the 11th International Symposium on Stabilization, Safety, and Security of Distributed Systems
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
Efficient approximation algorithms for shortest cycles in undirected graphs
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
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)
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Additive spanners in nearly quadratic time
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
f-sensitivity distance Oracles and routing schemes
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
Streaming and fully dynamic centralized algorithms for constructing and maintaining sparse spanners
ACM Transactions on Algorithms (TALG)
On the $k$ Shortest Simple Paths Problem in Weighted Directed Graphs
SIAM Journal on Computing
Faster Algorithms for All-pairs Approximate Shortest Paths in Undirected Graphs
SIAM Journal on Computing
All-pairs shortest paths with a sublinear additive error
ACM Transactions on Algorithms (TALG)
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
An experimental study on approximating K shortest simple paths
ESA'11 Proceedings of the 19th European conference on Algorithms
Determining the diameter of small world networks
Proceedings of the 20th ACM international conference on Information and knowledge management
Approximate distance oracles with improved preprocessing time
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Subquadratic time approximation algorithms for the girth
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Improved output-sensitive quantum algorithms for Boolean matrix multiplication
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Deterministic constructions of approximate distance oracles and spanners
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Approximate shortest paths in weighted graphs
Journal of Computer and System Sciences
Localized and compact data-structure for comparability graphs
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Improved dynamic algorithms for maintaining approximate shortest paths under deletions
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
All-pairs nearly 2-approximate shortest-paths in O(n2 polylog n) time
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
Approximate distance oracles for graphs with dense clusters
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
A symbolic approach to the all-pairs shortest-paths problem
WG'04 Proceedings of the 30th international conference on Graph-Theoretic Concepts in Computer Science
Constant-time all-pairs geodesic distance query on triangle meshes
I3D '12 Proceedings of the ACM SIGGRAPH Symposium on Interactive 3D Graphics and Games
Some results on approximate 1-median selection in metric spaces
Theoretical Computer Science
Approximating average parameters of graphs
APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation
Partitioned multi-indexing: bringing order to social search
Proceedings of the 21st international conference on World Wide Web
Optimal distributed all pairs shortest paths and applications
PODC '12 Proceedings of the 2012 ACM symposium on Principles of distributed computing
All-pairs shortest paths for unweighted undirected graphs in o(mn) time
ACM Transactions on Algorithms (TALG)
Distributed algorithms for network diameter and girth
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part II
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
Streaming and fully dynamic centralized algorithms for constructing and maintaining sparse spanners
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
Faster approximation of distances in graphs
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
Fault tolerant additive spanners
WG'12 Proceedings of the 38th international conference on Graph-Theoretic Concepts in Computer Science
ACM Transactions on Algorithms (TALG)
Deterministic sublinear-time approximations for metric 1-median selection
Information Processing Letters
Efficient distributed source detection with limited bandwidth
Proceedings of the 2013 ACM symposium on Principles of distributed computing
Fast approximation algorithms for the diameter and radius of sparse graphs
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Small stretch pairwise spanners
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
Shortest-path queries in static networks
ACM Computing Surveys (CSUR)
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Let G=(V,E) be an unweighted undirected graph on n vertices. A simple argument shows that computing all distances in G with an additive one-sided error of at most 1 is as hard as Boolean matrix multiplication. Building on recent work of Aingworth et al. [SIAM J. Comput., 28 (1999), pp. 1167--1181], we describe an $\Ot(\min\{n^{3/2}m^{1/2},n^{7/3}\})$-time algorithm APASP2 for computing all distances in G with an additive one-sided error of at most 2. Algorithm APASP2 is simple, easy to implement, and faster than the fastest known matrix-multiplication algorithm. Furthermore, for every even k2, we describe an ${\tilde{O}}(\min\{n^{2-{2}/{(k+2)}}m^{{2}/{(k+2)}}, n^{2+{2}/{(3k-2)}}\})$-time algorithm APASPk for computing all distances in G with an additive one-sided error of at most k. We also give an ${\tilde{O}}(n^2)$-time algorithm ${\bf APASP}_\infty$ for producing stretch 3 estimated distances in an unweighted and undirected graph on n vertices. No constant stretch factor was previously achieved in ${\tilde{O}}(n^2)$ time.We say that a weighted graph F=(V,E') k-emulates an unweighted graph G=(V,E) if for every $u,v\in V$ we have $\delta_G(u,v)\le \delta_F(u,v)\le \delta_G(u,v)+k$. We show that every unweighted graph on n vertices has a 2-emulator with ${\tilde{O}}(n^{3/2})$ edges and a 4-emulator with ${\tilde{O}}(n^{4/3})$ edges. These results are asymptotically tight.Finally, we show that any weighted undirected graph on n vertices has a 3-spanner with ${\tilde{O}}(n^{3/2})$ edges and that such a 3-spanner can be built in ${\tilde{O}}(mn^{1/2})$ time. We also describe an ${\tilde{O}}(n(m^{2/3}+n))$-time algorithm for estimating all distances in a weighted undirected graph on n vertices with a stretch factor of at most 3.