Heuristics: intelligent search strategies for computer problem solving
Heuristics: intelligent search strategies for computer problem solving
Generalized best-first search strategies and the optimality of A*
Journal of the ACM (JACM)
The multiple sequence alignment problem in biology
SIAM Journal on Applied Mathematics
Average-case analysis of heuristic search in tree-like networks
Search in Artificial Intelligence
Cost-error relationships in A* tree-searching
Journal of the ACM (JACM)
Performance of linear-space search algorithms
Artificial Intelligence
Theoretical Computer Science - Special issue: Genome informatics
Time complexity of iterative-deepening-A
Artificial Intelligence - Special issue on heuristic search in artificial intelligence
Algorithm for optimal winner determination in combinatorial auctions
Artificial Intelligence
Enhanced Iterative-Deepening Search
IEEE Transactions on Pattern Analysis and Machine Intelligence
Divide-and-Conquer Frontier Search Applied to Optimal Sequence Alignment
Proceedings of the Seventeenth National Conference on Artificial Intelligence and Twelfth Conference on Innovative Applications of Artificial Intelligence
Depth-First Branch-and-Bound versus Local Search: A Case Study
Proceedings of the Seventeenth National Conference on Artificial Intelligence and Twelfth Conference on Innovative Applications of Artificial Intelligence
An average-case analysis of graph search
Eighteenth national conference on Artificial intelligence
How to use limited memory in heuristic search
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 1
Searching graphs with A*: applications to job sequencing
IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans
Predicting the performance of IDA* using conditional distributions
Journal of Artificial Intelligence Research
The time complexity of A* with approximate heuristics on multiple-solution search spaces
Journal of Artificial Intelligence Research
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Many problems that arise in the real world have search spaces that are graphs rather than trees. Understanding the properties of search algorithms and analyzing their performance have been major objectives of research in AI. But most published work on the analysis of search algorithms has been focused on tree search, and comparatively little has been reported on graph search. One of the major obstacles in analyzing average-case complexity of graph search is that no single graph can serve as a suitable representative of graph search problems. In this paper we propose one possible approach to analyzing graph search. We take two problem domains for which the search graphs are directed acyclic graphs of similar structure, and determine the average case performance of the best-first search algorithm A* on these graphs. The first domain relates to one-machine job sequencing problems in which a set of jobs must be sequenced on a machine in such a way that a penalty function is minimized. The second domain concerns the Traveling Salesman Problem. Our mathematical formulation extends a technique that has been used previously for analyzing tree search. We demonstrate the existence of a gap in computational cost between two classes of problem instances. One class has exponential complexity and the other has polynomial complexity. For the job sequencing domain we provide supporting experimental evidence showing that problems exhibit a huge difference in computational cost under different conditions. For the Traveling Salesman Problem, our theoretical results reflect on the long-standing debate on the expected complexity of branch-and-bound algorithms for solving the problem, indicating that the complexity can be polynomial or exponential, depending on the accuracy of the heuristic function used.