Complexity of network synchronization
Journal of the ACM (JACM)
There is a planar graph almost as good as the complete graph
SCG '86 Proceedings of the second annual symposium on Computational geometry
A single source shortest path algorithm for a planar distributed network
Proceedings on STACS 85 2nd annual symposium on theoretical aspects of computer science
A new distributed algorithm to find breadth first search trees
IEEE Transactions on Information Theory
An optimal synchronizer for the hypercube
SIAM Journal on Computing
Randomized distributed shortest paths algorithms
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Generating sparse spanners for weighted graphs
SWAT '90 Proceedings of the second Scandinavian workshop on Algorithm theory
New sparseness results on graph spanners
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
Witnesses for Boolean matrix multiplication and for transitive closure
Journal of Complexity
Polylog-time and near-linear work approximation scheme for undirected shortest paths
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
On the all-pairs-shortest-path problem in unweighted undirected graphs
Journal of Computer and System Sciences - Special issue on selected papers presented at the 24th annual ACM symposium on the theory of computing (STOC '92)
All pairs shortest paths for graphs with small integer length edges
Journal of Computer and System Sciences - Special issue: papers from the 32nd and 34th annual symposia on foundations of computer science, Oct. 2–4, 1991 and Nov. 3–5, 1993
On the exponent of the all pairs shortest path problem
Journal of Computer and System Sciences - Special issue: papers from the 32nd and 34th annual symposia on foundations of computer science, Oct. 2–4, 1991 and Nov. 3–5, 1993
Near-Linear Time Construction of Sparse Neighborhood Covers
SIAM Journal on Computing
Fast estimation of diameter and shortest paths (without matrix multiplication)
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
All-Pairs Almost Shortest Paths
SIAM Journal on Computing
Distributed computing: a locality-sensitive approach
Distributed computing: a locality-sensitive approach
(1 + &egr;&Bgr;)-spanner constructions for general graphs
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Sparser: A Paradigm for Running Distributed Algorithms
WDAG '92 Proceedings of the 6th International Workshop on Distributed Algorithms
Computing Almost Shortest Paths,
Computing Almost Shortest Paths,
Sparse distance preservers and additive spanners
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Approximate distance oracles for unweighted graphs in Õ (n2) time
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
A faster distributed protocol for constructing a minimum spanning tree
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)
Distributed approximation: a survey
ACM SIGACT News
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
Graph distances in the streaming model: the value of space
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Computing almost shortest paths
ACM Transactions on Algorithms (TALG)
Spanners and emulators with sublinear distance errors
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
A faster distributed protocol for constructing a minimum spanning tree
Journal of Computer and System Sciences
A near-optimal distributed fully dynamic algorithm for maintaining sparse spanners
Proceedings of the twenty-sixth annual ACM symposium on Principles of distributed computing
On the K-simple shortest paths problem in weighted directed graphs
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Fast deterministic distributed algorithms for sparse spanners
Theoretical Computer Science
Efficient distributed approximation algorithms via probabilistic tree embeddings
Proceedings of the twenty-seventh ACM symposium on Principles of distributed computing
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Graph embedding through random walk for shortest paths problems
SAGA'09 Proceedings of the 5th international conference on Stochastic algorithms: foundations and applications
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
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
Transitive-closure spanners: a survey
Property testing
Transitive-closure spanners: a survey
Property testing
Improved approximation for the directed spanner problem
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
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
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
Optimal distributed all pairs shortest paths and applications
PODC '12 Proceedings of the 2012 ACM symposium on Principles of distributed computing
Deterministic distributed construction of linear stretch spanners in polylogarithmic time
DISC'07 Proceedings of the 21st international conference on Distributed Computing
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
Approximation algorithms for spanner problems and Directed Steiner Forest
Information and Computation
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We study the s-sources almost shortest paths (shortly, s-ASP) problem. Given an unweighted graph G = (V, E), and a subset S ⊈ V of s nodes, the goal is to compute almost shortest paths between all the pairs of nodes S x V. We devise an algorithm with running time O(¦E¦ n&rgr; + s · n1+&zgr;) for this problem that computes the paths Pu, w for all pairs (u, w) ∈ S x V such that the length of Pu, w is at most (1 + ∈) dG (u, w) + &bgr;(&zgr;, &rgr;, ∈), and &bgr;(&zgr;, &rgr;, ∈) is constant when &zgr;, &rgr; and ∈ are (one can choose arbitrarily small constants &zgr;, &rgr; and ∈).We also devise a distributed protocol for the s-ASP problem that computes the paths Pu, w as above, and has time and communication complexities of O(s · Diam(G) + n1+&zgr;/2) (resp., O(s · Diam(G) log3 n + n1+&zgr;/2 log n)) and O(¦E¦ n&rgr; + s · n1+&zgr; (resp., O(¦E¦nrgr; + s · n1+&zgr; + n1+&rgr;+&zgr;(&rgr;-&zgr;/2)/2)) in the synchronous (resp., asynchronous) setting.Our sequential algorithm, as well as the distributed protocol, is based on a novel algorithm for constructing (1 + ∈, &bgr;(&zgr;, &rgr;, ∈))-spanners of size O(n1+5), developed in this paper. This algorithm has running time of O(¦E¦ n&rgr;), which is significantly faster than the previously known algorithm of [20], whose running time is O(n2+&rgr;). We also develop the first distributed protocol for constructing (1 + ∈, &bgr;)-spanners. The time and communication complexities of this protocol are near-optimal.