A Framework for Searching AND/OR Graphs with Cycles

TL;DR

This paper introduces a comprehensive theoretical framework for searching cyclic AND/OR graphs, and presents two algorithms, S1 and S2, that effectively solve the problem with proven correctness and complexity analysis.

Contribution

It provides the first complete theoretical framework for cyclic AND/OR graph search and develops two new algorithms, S1 and S2, for uninformed and heuristically guided search.

Findings

Both S1 and S2 produce correct results in all tested cases.

S1 is a simple modification of the Bottom-up algorithm.

S2 extends Bottom-up with heuristics, replicating HS and AO* algorithms.

Abstract

Search in cyclic AND/OR graphs was traditionally known to be an unsolved problem. In the recent past several important studies have been reported in this domain. In this paper, we have taken a fresh look at the problem. First, a new and comprehensive theoretical framework for cyclic AND/OR graphs has been presented, which was found missing in the recent literature. Based on this framework, two best-first search algorithms, S1 and S2, have been developed. S1 does uninformed search and is a simple modification of the Bottom-up algorithm by Martelli and Montanari. S2 performs a heuristically guided search and replicates the modification in Bottom-up's successors, namely HS and AO*. Both S1 and S2 solve the problem of searching AND/OR graphs in presence of cycles. We then present a detailed analysis for the correctness and complexity results of S1 and S2, using the proposed framework. We have observed through experiments that S1 and S2 output correct results in all cases.