Classes of lexicographic equivalence in Euclidean combinatorial optimisation on arrangements
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We consider an application of regular partitions of a space to the solution of Euclidean combinatorial optimisation problems, in particular, conditional optimisation problems on arrangements. We introduce the notion of points of the space equivalent with respect to arrangements and show that the introduced relation between points is an equivalence relation. We give algorithms to search for an element of the set of arrangements which is a representative of the combinatorial class closest to a given class with respect to the lexicographic order (increasing or decreasing).
We consider also a new class of optimisation problems, namely, problems of linear conditional lexicographic maximisation on arrangements. We suggest and analyse algorithms for solving the problems of this class. The algorithms are based on the ordered checking of admissible points in the lexicographic (increasing or decreasing) order and use the algorithms to search for the closest element of the set of arrangements mentioned above.
Copyright 2007, Walter de Gruyter
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- A class of subcritical branching processes with immigration and infinite number of types of particles
- Bounds for extremal values of the mean number of cells containing a given number of particles
- Limit theorems for the number of solutions of a system of random linear equations belonging to a given set
- On the Stein–Tikhomirov method and its applications in nonclassical limit theorems
- Shifted products of independent random variables with values in finite groups
- Optimal management of two parallel stacks in two-level memory
- An upper bound for the number of product-free sets in a class of groups
- Mark sequences in multigraphs
- Classes of lexicographic equivalence in Euclidean combinatorial optimisation on arrangements
- Representations over Galois ring of a linear recurring sequence of maximal period over Galois field
Articles in the same Issue
- A class of subcritical branching processes with immigration and infinite number of types of particles
- Bounds for extremal values of the mean number of cells containing a given number of particles
- Limit theorems for the number of solutions of a system of random linear equations belonging to a given set
- On the Stein–Tikhomirov method and its applications in nonclassical limit theorems
- Shifted products of independent random variables with values in finite groups
- Optimal management of two parallel stacks in two-level memory
- An upper bound for the number of product-free sets in a class of groups
- Mark sequences in multigraphs
- Classes of lexicographic equivalence in Euclidean combinatorial optimisation on arrangements
- Representations over Galois ring of a linear recurring sequence of maximal period over Galois field
