Computational geometry: an introduction
Computational geometry: an introduction
An algorithm for covering polygons with rectangles
Information and Control
Enumerative combinatorics
Dynamic subgraph connectivity with geometric applications
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Introduction to VLSI Systems
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
IEEE Design & Test
Journal of Intelligent Information Systems
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A set cover for a set S is a collection C of special subsets whose union is S. Given covers A and B for two sets, the set-cover difference problem is to construct a new cover for the elements covered by A but not B. Applications include testing equivalence of set covers and maintaining a set cover dynamically. In this paper, we solve the set-cover difference problem by defining a difference operation A-B, which turns out to be a pseudocomplement on a distributive lattice. We give an algorithm for constructing this difference, and show how to implement the algorithm for two examples with applications in computer science: face covers on a hypercube, and rectangle covers on a grid. We derive an upper bound on the time complexity of the algorithm, and give upper and lower bounds on complexity for face covers and rectangle covers.