The complexity of searching several classes of AND/OR graphs

Authors:
Howard E. Motteler;Laveen N. Kanal
Affiliations:
The Machine Intelligence and Pattern Analysis Laboratory, Department of Computer Science, University of Maryland, College Park, MD;The Machine Intelligence and Pattern Analysis Laboratory, Department of Computer Science, University of Maryland, College Park, MD
Venue:
IJCAI'85 Proceedings of the 9th international joint conference on Artificial intelligence - Volume 2
Year:
1985

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Abstract

The complexity of searching for a minimum cost solution graph of an AND/OR graph is analyzed for the class of AND/OR graphs representable by a context free grammar with coat functions; finding a minimum coat solution graph is then equivalent to finding a lowest coat derivation. Several classes of search problems are defined, based on properties of the cost functions and grammar. We show that certain of these classes have different, search complexities- specifically, we show that there are distinct classes for which the complexity of finding a minimum cost solution graph is non-recursive, exponential, NP- complete, and Q(n2), where is the size of the grammar representing the problem. The correspondence between problem structure and search complexity may serve as a guide for modeling real problems with AND/OR graphs.