An average-case analysis of graph search

Many problems in real-world applications require searching graphs. Understanding the performance of search algorithms has been one of the eminent tasks of heuristic search research. Despite the importance of graph search algorithms, the research of analyzing their performance is limited, and most work on search algorithm analysis has been focused on tree search algorithms. One of the major obstacles to analyzing graph search is that no single graph is an appropriate representative of graph search problems. In this paper, we propose one possible approach to analyzing graph search: Analyzing the performance of graph search algorithms on a representative graph of a cluster of problems. We specifically consider job-sequencing problems in which a set of jobs must be sequenced on a machine such that a penalty function is minimized. We analyze the performance of A* graph search algorithm on an abstract model that closely represents job sequencing problems. It is an extension to a model widely used previously for analyzing tree search. One of the main results of our analysis is the existence of a gap of computational cost between two classes of job sequencing problems, one with exponential and the other with polynomial complexity. We provide experimental results showing that real job sequencing problems indeed have a huge difference on computational costs under different conditions.