Exploiting the Induced Order on Type-Labeled Graphs for Fast Knowledge Retrieval

The graph structure of a conceptual graph can be used for efficient retrieval in complex (graphical) object databases. The aim is to replace most graph matching with efficient operations on precompiled codes for graphs. The unlabeled graph or “skeleton” of a type-labeled conceptual graph (without negated contexts) can be used as a filter for matching, subsumption testing, and unification. For two type-labeled graphs to match, their skeletons must first match. One type-labeled graph can subsume another only if its skeleton is included in that of the other. An skeleton-inclusion hierarchy can be constructed for a useful set of all possible skeletons up to a certain size. That hierarchy is then embedded in a Boolean lattice of bit-strings. Expensive graph comparison operations are traded for very fast bit-string logic operations on the codes. New graphs can be encoded at run time without recompiling the whole hierarchy: having found a graph's structural type, we then use it to hash to the code encoding the poset of all possible type-labeled graphs ordered by subsumption. Some of the order in that poset comes from the subgraph inclusion factor while other order comes from the “typelattice” (on concept-labels) factor. We show how they relate. We are investigating the bounds on code length and new methods of factorisation of conceptual graph databases.