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Efficient implementation of lattice operations

Editor: Susan L. Graham Authors:

Hassan Aït-Kaci,

Patrick Lincoln,

Roger NasrAuthors Info & Claims

ACM Transactions on Programming Languages and Systems (TOPLAS), Volume 11, Issue 1

Pages 115 - 146

https://doi.org/10.1145/59287.59293

Published: 01 January 1989 Publication History

Abstract

Lattice operations such as greatest lower bound (GLB), least upper bound (LUB), and relative complementation (BUTNOT) are becoming more and more important in programming languages supporting object inheritance. We present a general technique for the efficient implementation of such operations based on an encoding method. The effect of the encoding is to plunge the given ordering into a boolean lattice of binary words, leading to an almost constant time complexity of the lattice operations. A first method is described based on a transitive closure approach. Then a more space-efficient method minimizing code-word length is described. Finally a powerful grouping technique called modulation is presented, which drastically reduces code space while keeping all three lattice operations highly efficient. This technique takes into account idiosyncrasies of the topology of the poset being encoded that are quite likely to occur in practice. All methods are formally justified. We see this work as an original contribution towards using semantic (vz., in this case, taxonomic) information in the engineering pragmatics of storage and retrieval of (vz., partially or quasi-ordered) information.

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Efficient implementation of lattice operations

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Reviews

Reviewer: David B. Benson

This paper is about the efficient implementation of multiple object inheritance. When the objects are permanent or nearly so, a program may use considerable computational effort to determine an encoding of the object inheritance data, which it uses at run-time to inexpensively compute lattice operators on the inheritance lattice. The paper describes, with exceptional clarity, a modulation method that provides for both time and space efficiency. This modulation technique is tuned to the object inheritance lattices likely to be met in practice. As the authors say in the abstract, “We see this work as an original contribution towards using semantic . . . information in the engineering pragmatics of storage and retrieval of . . . information.”

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Copyright © 1989 ACM.

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Published: 01 January 1989

Published in TOPLAS Volume 11, Issue 1

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