Practically handling some configuration isomorphisms

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 poly time algorithm is known for the general graph isomorphism problem, it is interesting to explore subproblems 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 nonweakly 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 are 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.