Finite Covering Problems
In this chapter we conduct a survey of the occurrence of finite covering problems in graph theory, operations research, and miscellaneous fields, seeking to unite such instances within a common framework. We then offer a unified approach to the solution of such problems. Elements of a general theory are presented, and two exhaustive solution methodologies are given, those we call the branching method and the algebraic method. The latter leads rather naturally to an introduction to distributive lattices and their application to discrete decision problems. This report should serve equally well as an introductory survey for readers wishing to become acquainted with the origins and the mathematical treatment of covering problems and as a classroom module for supplementing courses in mathematical modeling, applications of graph theory, discrete mathematical structures, and the like.
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