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16th IEEE International Conference on Tools with Artificial Intelligence (ICTAI'04)
Practically Handling Some Configuration Isomorphisms
Boca Raton, Florida
November 15-November 17
ISBN: 0-7695-2236-X
Laurent Henocque, Laboratoire des Sciences de l?Information et des Syst?mes
Nicolas Prcovic, Laboratoire des Sciences de l?Information et des Syst?mes
Configuring consists in simulating the realization of a complex product from a catalog of component parts, using known relations between types, and picking values for object attributes. A configuration can be viewed as a graph of interconnected components. An inherent difficulty in solving configuration problems is the existence of many structural isomorphisms. A practical way of dealing with isomorphisms is by isolating one configuration in each equivalence class called a canonical representative. Since no polytime algorithm is known for the general graph isomorphism problem, it is interesting to explore sub-problems that can efficiently be exploited by backtrack search procedures. We describe a formalism independent approach to detect a large number of structure related configuration isomorphisms. The algorithm has the essential property that isomorphism detection is both incremental and can be performed in pseudo linear time, two essential conditions for backtrack search. Backtrack occurs as soon as a non weakly canonical DAG structure is generated for a configuration, which allows to extend the range of practically tractable problems, as shown experimentally. Weakly canonical configurations explicitly expose their automorphism group, which is readily available thanks to the lexicographic ordering chosen. The efficiency of the approach is assessed both theoretically and by experimental results obtained for a range of realistic configuration problems.
Citation:
Laurent Henocque, Nicolas Prcovic, "Practically Handling Some Configuration Isomorphisms," ictai, pp.90-97, 16th IEEE International Conference on Tools with Artificial Intelligence (ICTAI'04), 2004
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