Matrix multiplication via arithmetic progressions
Journal of Symbolic Computation - Special issue on computational algebraic complexity
Clique partitions, graph compression and speeding-up algorithms
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
On the exponent of the all pairs shortest path problem
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
A new upper bound on the complexity of the all pairs shortest path problem
Information Processing Letters
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)
Finding Even Cycles Even Faster
SIAM Journal on Discrete Mathematics
Fast distributed construction of small k-dominating sets and applications
Journal of Algorithms
Fast Estimation of Diameter and Shortest Paths (Without Matrix Multiplication)
SIAM Journal on Computing
IP routing protocols: RIP, OSPF, BGP, PNNI and Cisco routing protocols
IP routing protocols: RIP, OSPF, BGP, PNNI and Cisco routing protocols
Efficient identification of Web communities
Proceedings of the sixth ACM SIGKDD international conference on Knowledge discovery and data mining
All-Pairs Almost Shortest Paths
SIAM Journal on Computing
Distributed computing: a locality-sensitive approach
Distributed computing: a locality-sensitive approach
Distributed computation on graphs: shortest path algorithms
Communications of the ACM
Communications of the ACM
Computing almost shortest paths
Proceedings of the twentieth annual ACM symposium on Principles of distributed computing
Distributed Algorithms
All Pairs Shortest Paths in Undirected Graphs with Integer Weights
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Improved algorithm for all pairs shortest paths
Information Processing Letters
Journal of the ACM (JACM)
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
More algorithms for all-pairs shortest paths in weighted graphs
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
A Distributed Algorithm for Shortest Paths
IEEE Transactions on Computers
Witnesses for Boolean matrix multiplication and for shortest paths
SFCS '92 Proceedings of the 33rd Annual Symposium on Foundations of Computer Science
Efficient distributed approximation algorithms via probabilistic tree embeddings
Proceedings of the twenty-seventh ACM symposium on Principles of distributed computing
A New Combinatorial Approach for Sparse Graph Problems
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
Distributed verification and hardness of distributed approximation
Proceedings of the forty-third annual ACM symposium on Theory of computing
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
Multiplying matrices faster than coppersmith-winograd
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Efficient computation of distance sketches in distributed networks
Proceedings of the twenty-fourth annual ACM symposium on Parallelism in algorithms and architectures
Distributed algorithms for network diameter and girth
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part II
Distributed algorithms for network diameter and girth
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part II
Efficient distributed source detection with limited bandwidth
Proceedings of the 2013 ACM symposium on Principles of distributed computing
Fast routing table construction using small messages: extended abstract
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
DACCER: Distributed Assessment of the Closeness CEntrality Ranking in complex networks
Computer Networks: The International Journal of Computer and Telecommunications Networking
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We present an algorithm to compute All Pairs Shortest Paths (APSP) of a network in a distributed way. The model of distributed computation we consider is the message passing model: in each synchronous round, every node can transmit a different (but short) message to each of its neighbors. We provide an algorithm that computes APSP in O(n) communication rounds, where n denotes the number of nodes in the network. This implies a linear time algorithm for computing the diameter of a network. Due to a lower bound these two algorithms are optimal up to a logarithmic factor. Furthermore, we present a new lower bound for approximating the diameter D of a graph: Being allowed to answer D+1 or D can speed up the computation by at most a factor D. On the positive side, we provide an algorithm that achieves such a speedup of D and computes an (1+εepsilon) multiplicative approximation of the diameter. We extend these algorithms to compute or approximate other problems, such as girth, radius, center and peripheral vertices. At the heart of these approximation algorithms is the S-Shortest Paths problem which we solve in O(|S|+D) time.