Continuous Representations and Functional Extensions in Combinatorial Optimization

Abstract

The concepts of functional representation of a set of points of the Euclidean arithmetic space and an extension of functions from the set onto its superset are introduced. Functional representations of sets are related to their extensions. Strict functional representations of the Boolean set, general permutation, and polypermutation sets are derived. The advantages of applying strict representations of Euclidean combinatorial sets to construct functional extensions from them and to solve combinatorial problems are presented.