Speeding Up Problem Solving by Abstraction: A Graph Oriented Approach

This paper presents a new perspective on the traditional AI task of problem solving and the techniques of abstraction and refinement. The new perspective is based on the well known, but little exploited, relation between problem solving and the task of finding a path in a graph between two given nodes. The graph oriented view of abstraction suggests two new families of abstraction techniques, algebraic abstraction and STAR abstraction. The first is shown to be extremely sensitive to the exact manner in which problems are represented. STAR abstraction, by contrast, is very widely applicable and leads to significant speedup in all our experiments. The reformulation of traditional refinement techniques as graph algorithms suggests several enhancements, including an optimal refinement algorithm, and one radically new technique: alternating search direction. Experiments comparing these techniques on a variety of problems show that alternating opportunism (AltO) a variant of the new technique, is uniformly superior to all the others

Hierarchical A*: Searching Abstraction Hierarchies Efficiently

ion Hierarchies Efficiently R.C. Holte, M.B. Perez, R.M. Zimmer, A.J. MacDonald Abstract Abstraction, in search, problem solving, and planning, works by replacing one state space by another (the "abstract" space) that is easier to search. The results of the search in the abstract space are used to guide search in the original space. A natural application of this technique is to use the length of the abstract solution as a heuristic for A* in searching in the original space. However, there are two obstacles to making this work efficiently. The first is a theorem [Valtorta, 1984] stating that for a large class of abstractions, "embedding abstractions," every state expanded by blind search must also be expanded by A* when its heuristic is computed in this way. The second obstacle arises because in solving a problem A* needs repeatedly to do a full search of the abstract space while computing its heuristic. This paper introduces a new abstraction-induced search technique, "Hierarchical ..