Showing papers on "Longest path problem published in 1973"

Additive AND/OR graphs

Abstract: Additive AND/OR graphs are defined as AND/ OR graphs without circuits, which can be considered as folded AND/OR trees; i. e. the cost of a common subproblem is added to the cost as many times as the subproblem occurs, but it is computed only once. Additive AND/OR graphs are naturally obtained by reinterpreting the dynamic programming method in the light of the problem-reduction approach. An example of this reduction is given. A top-down and a bottom-up method are proposed for searching additive AND/OR graphs. These methods are, respectively, extensions of the "arrow" method proposed by Nilsson for searching AND/OR trees and Dijkstra's algorithm for finding the shortest path. A proof is given that the two methods find an optimal solution whenever a solution exists.

On the determination of the shortes path in a network having gains

Abstract: The shortest path problem has been solved by FORD and FULKERSON [1] using a network method. COOK and HOLSEY [2] have given an algorithm for a generalization of te problem by applying dynamic programming to a network having time dependent edges. E. KLAFSZKY [3] has described a procedure using the flow method of FORD and FULKERSON which gives the shortest path in addition to the length of the path. CHARNES and RAIKE [4] applied linear programming to another generalization of te shortest path problem. This generalized problem is dealt with in this paper. The problem can be solved by the FORD and FULKERSON's procedure following the train of thought described by E. KLAFSZKY.