Execution Ordering in AND/OR Graphs with Failure Probabilities

Abstract

In this paper we consider finding solutions for problems represented using AND/OR graphs, which contain tasks that can fail when executed. In our setting each node represent an atomic task which is associated with a failure probability and a rollback penalty. This paper reports the following contributions - (a) an algorithm for finding the optimal ordering of the atomic tasks in a given solution graph which minimizes the expected penalty, (b) an algorithm for finding the optimal ordering in the presence of user defined ordering constraints, and (c) a counter example showing the lack of optimal substructure property for the problem of finding the solution graph having minimum expected penalty, and a pseudo-polynomial algorithm for finding the solution graph with minimum expected penalty.