Additive AND/OR graphs

Authors:
A. Martelli;U. Montanari
Affiliations:
Consigllo Nazionale delle Ricerche, Istituto di Flaborazione dell 'Informazione, Pisa, Italy;Consigllo Nazionale delle Ricerche, Istituto di Flaborazione dell 'Informazione, Pisa, Italy
Venue:
IJCAI'73 Proceedings of the 3rd international joint conference on Artificial intelligence
Year:
1973

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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.