Encoding multiple inheritance hierarchies for lattice operations

Abstract

Incremental updates to multiple inheritance hierarchies are becoming more prevalent with the increasing number of persistent applications supporting complex objects. Efficient computation of the lattice operations greatest lower bound (GLB), least upper bound (LUB), and subsumption is critical. Techniques for the compact encoding of a hierarchy are required that support the operations. One method is to plunge the given ordering into a Boolean lattice of binary words, and perform lattice operations via Boolean operators. An overview of the approach is given and several methods are examined and compared. A new method is proposed, based on the top–down encoding of Caseau but without the lattice completion requirement, which permits incremental updates to the hierarchy to add nodes at the leaves. The algorithm requires polynomial time and space for encoding, and supports efficient lattice computations in applications where the classes of objects are stored as codes. Experimental results illustrate its effectiveness, and an analysis is provided on the effect of the order of insertion on the encoding.