Pairs Shortest Paths Research Articles

On the parallel computation of the algebraic path problem

The algebraic path problem is a general description of a class of problems, including some important graph problems such as transitive closure, all pairs shortest paths, minimum spanning tree, etc. In this work, the algebraic path problem is solved on a processor array with a reconfigurable bus system. The proposed algorithms are based on repeated matrix multiplications. The multiplication of two n*n matrices takes O(log n) time in the worst case, but, for some special cases, O(1) time is possible. It is shown that three instances of the algebraic path problem, transitive closure, all pairs shortest paths, and minimum spanning tree, can be solved in O(log n) time, which is as fast as on the CRCW PRAM. >

Simulation and theoretical results on cluster management and directory management in dynamic hierarchical networks

A cluster management scheme for dynamic networks, the purpose of which is to maintain the cluster structure of the hierarchical network as a balanced-tree topology is presented. The theoretical time complexity bounds of the cluster management scheme for node birth and death are derived. The effects of the cluster management on gate-connected fixed-node networks under heavy intercluster traffic situations are discussed. In order to show that the scheme can handle realistic communication networks, routing tables and OD pair shortest path routing are used. The settle-down time, throughput, and end-to-end link delays of a network that uses cluster management and a network of the same topology that only uses flooding are compared. >