Showing papers on "Longest path problem published in 1968"

On an asymptotic optimization problem in finite, directed, weighted graphs

Abstract: This paper is concerned with finite, directed, branch-weighted graphs, where each weight is a real number bearing the connotation of “payoff.” The “average payoff” of a k-branch path is defined as the sum of the weights along this path divided by k. It is shown that, as k approaches infinity, the maximum average payoff obtainable with paths initiating at a particular vertex is exactly the maximum of the average payoffs of all proper cycles reachable from that vertex. This result leads to a simple algorithm for finding a path which exhibits this maximum.

Path Finding with Associative Memory

Abstract: —This note discusses possible advantages to be gained through use of associative memory in finding the shortest path through a large graph having edges of unequal lengths. An algorithm is described which exploits associative memory's highly parallel search and arithmetic capabilities and which is economical in storage requirements.