An incremental algorithm to construct a lattice of set intersections

Authors:
Derrick G. Kourie;Sergei Obiedkov;Bruce W. Watson;Dean van der Merwe
Affiliations:
Department of Computer Science, University of Pretoria, Pretoria 0002, South Africa;Department of Computer Science, University of Pretoria, Pretoria 0002, South Africa and Department of Applied Mathematics, Higher School of Economics, Moscow, Russia;Department of Computer Science, University of Pretoria, Pretoria 0002, South Africa;Department of Computer Science, University of Pretoria, Pretoria 0002, South Africa
Venue:
Science of Computer Programming
Year:
2009

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Abstract

An incremental algorithm to construct a lattice from a collection of sets is derived, refined, analyzed, and related to a similar previously published algorithm for constructing concept lattices. The lattice constructed by the algorithm is the one obtained by closing the collection of sets with respect to set intersection. The analysis explains the empirical efficiency of the related concept lattice construction algorithm that had been observed in previous studies. The derivation highlights the effectiveness of a correctness-by-construction approach to algorithm development.