Efficient Distributed All-Pairs Algorithms: Management Using Optimal Cyclic Quorums

Scaling Distributed All-Pairs Algorithms: Manage Computation and Limit Data Replication with Quorums

In this paper we propose and prove that cyclic quorum sets can efficiently manage all-pairs computations and data replication. The quorums are O(N/√P) in size, up to 50% smaller than the dual N/√P array implementations, and significantly smaller than solutions requiring all data. Implementation evaluation demonstrated scalability on real datasets with a 7x speed up on 8 nodes with 1/3 the memor...

An Optimal Distributed Algorithm for All-pairs Shortest-path

In this paper the network problem of determining all-pairs shortest-path is examined. A distributed algorithm which runs in O(n) time on a network of n nodes is presented. The number of messages of the algorithm is O(e+n log n) where e is the number of communication links of the network. We prove that this algorithm is time optimal.

Efficient Edge Splitting-Off Algorithms Maintaining All-Pairs Edge-Connectivities

We present new edge splitting-off results maintaining all-pairs edge-connectivities of an undirected graph. We first give an alternate proof of Mader’s theorem, and use it to obtain a deterministic Õ(m + rmax · n2)-time complete edge splitting-off algorithm for unweighted graphs, where rmax denotes the maximum edge-connectivity requirement. This improves upon the best known algorithm by Gabow b...

All Pairs Shortest Paths Algorithms

Given a communication network or a road network one of the most natural algorithmic question is how to determine the shortest path from one point to another. In this paper we deal with one of the most fundamental problems of Graph Theory, the All Pairs Shortest Path (APSP) problem. We study three algorithms namely The FloydWarshall algorithm, APSP via Matrix Multiplication and the Johnson’s alg...

An 'All Pairs Shortest Path' Distributed Algorithm Using 2n² Messages