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A Fast Distributed Shortest Path Algorithm for a Class of Hierarchically Clustered Data Networks
IEEE Transactions on Computers
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)
An “all pairs shortest paths” distributed algorithm using 2n2 messages
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Fast Estimation of Diameter and Shortest Paths (Without Matrix Multiplication)
SIAM Journal on Computing
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Distributed computing: a locality-sensitive approach
Distributed computing: a locality-sensitive approach
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All pairs shortest paths using bridging sets and rectangular matrix multiplication
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Approximation algorithms for cycle packing problems
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
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ACM Transactions on Algorithms (TALG)
Faster Algorithms for Approximate Distance Oracles and All-Pairs Small Stretch Paths
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Efficient approximation algorithms for shortest cycles in undirected graphs
Information Processing Letters
Minimum Weight Cycles and Triangles: Equivalences and Algorithms
FOCS '11 Proceedings of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
Subquadratic time approximation algorithms for the girth
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Networks cannot compute their diameter in sublinear time
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
IEEE Transactions on Information Theory
Survey: Cycle bases in graphs characterization, algorithms, complexity, and applications
Computer Science Review
Optimal distributed all pairs shortest paths and applications
PODC '12 Proceedings of the 2012 ACM symposium on Principles of distributed computing
Optimal distributed all pairs shortest paths and applications
PODC '12 Proceedings of the 2012 ACM symposium on Principles of distributed computing
Efficient distributed source detection with limited bandwidth
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Fast routing table construction using small messages: extended abstract
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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This paper considers the problem of computing the diameter D and the girth g of an n-node network in the CONGEST distributed model. In this model, in each synchronous round, each vertex can transmit a different short (say, O(logn) bits) message to each of its neighbors. We present a distributed algorithm that computes the diameter of the network in O(n) rounds. We also present two distributed approximation algorithms. The first computes a 2/3 multiplicative approximation of the diameter in $O(D\sqrt n \log n)$ rounds. The second computes a 2−1/g multiplicative approximation of the girth in $O(D+\sqrt{gn}\log n)$ rounds. Recently, Frischknecht, Holzer and Wattenhofer [11] considered these problems in the CONGEST model but from the perspective of lower bounds. They showed an $\tilde{\Omega}(n)$ rounds lower bound for exact diameter computation. For diameter approximation, they showed a lower bound of $\tilde{\Omega}(\sqrt n)$ rounds for getting a multiplicative approximation of. Both lower bounds hold for networks with constant diameter. For girth approximation, they showed a lower bound of $\tilde{\Omega}(\sqrt n)$ rounds for getting a multiplicative approximation of on a network with constant girth. Our exact algorithm for computing the diameter matches their lower bound. Our diameter and girth approximation algorithms almost match their lower bounds for constant diameter and for constant girth.