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Hierarchical arc consistency: exploiting structured domains in constraint satisfaction problems

Computational Intelligence 1985年第1期1卷 118-126页

作者： Mackworth, Alan K. Mulder, Jan A. Havens, William S. Laboratory for Computational Vision Department of Computer Science University of British Columbia Vancouver British Columbia V6T 1W5 Canada

Constraint satisfaction problems can be solved by network consistency algorithms that eliminate local inconsistencies before constructing global solutions. We describe a new algorithm that is useful when the variable domains can be structured hierarchically into recursive subsets with common properties and common relationships to subsets of the domain values for related variables. The algorithm, HAC, uses a technique known as hierarchical arc consistency. Its performance is analyzed theoretically and the conditions under which it is an improvement are outlined. The use of HAC in a program for understanding sketch maps, Mapsee3, is briefly discussed and experimental results consistent with the theory are reported. Copyright © 1985, Wiley Blackwell. All rights reserved

关键词： arc consistency computational vision constraint satisfaction problems map understanding network consistency algorithms

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Constraint satisfaction algorithms

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Computational Intelligence 1989年第3期5卷 188-224页

作者： Nadel, Bernard A. Computer Science Department Wayne State University Detroit Michigan 48202 United States

Constraint satisfaction problems are ubiquitous in artificial intelligence and many algorithms have been developed for their solution. This paper provides a unified survey of some of these, in terms of three classes: (i) tree search, (ii) arc consistency (AC), and (iii) hybrid tree search/arc consistency algorithms. It is shown that several important algorithms, when slightly rearranged, are of the latter hybrid form, but with arc consistency components that do not necessarily achieve full arc consistency at the tree nodes. Accordingly, we define several new partial AC procedures, AC1/5, AC1/4, AC1/3, and AC½, analogous to the well‐known full AC algorithms which Mackworth has called AC1, AC2, and AC3. The fractional suffixes on our AC algorithms are roughly proportional to the degree of partial arc consistency they achieve. Unlike traditional versions, our AC algorithms (full and partial) are presented in a parameterized form to allow them to be embedded efficiently at the nodes of a tree search process. Algorithm complexities are compared empirically, using the n‐queens problem and a new version called confused n‐queens. Gaschnig's Backmarking (a tree search algorithm) and Haralick's Forward Checking (a hybrid algorithm) are found to be the most efficient. For the hybrid algorithms, we find that it pays to do little arc consistency processing at the nodes, incurring more nodes, but sufficiently reducing the work per node so as to obtain less work over the whole tree. The unified view taken here suggests several new algorithms. Preliminary results show one of these to be the best algorithm so far. Copyright © 1989, Wiley Blackwell. All rights reserved

关键词： arc consistency algorithms Backjumping Backmarking Backtracking constraint satisfaction problem Forward Checking. network consistency algorithms tree search algorithms

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