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Fast Computation of Subsumption and Disjointness for Efficient Inferencing

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Accelerate inferencing using taxonomies by efficiently computing subsumption, disjointness, and other properties. Learn about methods like compressed transitive closure for quick processing. Generalize to directed acyclic graphs with constant-time is-a queries.

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Fast Computation of Subsumption and Disjointness for Efficient Inferencing

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  1. Accelerating Inferencing

  2. Assertion • Efficient inferencing using taxonomies require fast computation of subsumption, disjointness, least common ancestors, and other properties • The basic primitive required is the fast computation (preferably in constant time) of is-a queries • R. Agrawal, A. Borgida, H.V. Jagadish: Efficient Management of Transitive Relationship in Large Data Bases. Sigmod 89.

  3. Compressed Transitive Closure of Tree Graphs • Number each node to reflect its postorder traversal position • Assign to each node an index consisting of the lowest postorder number amongst its descendents • A node with postorder number k is-a node with postorder number j and index i iff i <= k < j. 1 12 1 7 11 6 1 2 5 7 10 1 4 5 9 10 8 2 3 7 7 8 2 3 2 is-a 6 but not 11

  4. Observations • We require O(n) storage and can determine is-a with only one range comparison. • Compressed closure is incrementally maintainable. • Generalizes to directed acyclic graphs • See the Sigmod paper for details

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