This paper introduces six ways for handling a chain of lexicographic ordering constraint between the origins of identical orthotopes (e.g., rectangles, boxes, hyper-rectangles) subject to the fact that they should not pairwise overlap. While the first two ways deal with the integration of a chain of lexicographic ordering constraint within a generic geometric constraint kernel, the four latter ...

Geometric lattices are characterized as those finite, atomic lattices such that every atom ordering induces a lexicographic shelling given by an edge labeling known as a minimal labeling. Equivalently, geometric lattices are shown to be exactly those finite lattices such that every ordering on the join-irreducibles induces a lexicographic shelling. This new characterization fits into a similar ...

We introduce a technique called lexicographic parsimony pressure, for controlling the significant growth of genetic programming trees during the course of an evolutionary computation run. Lexicographic parsimony pressure modifies selection to prefer smaller trees only when fitnesses are equal (or equal in rank). This technique is simple to implement and is not affected by specific differences i...

Let F be a field, V a finite subset of F. We introduce the lex game, which yields a combinatorial description of the lexicographic standard monomials of the ideal I(V ) of polynomials vanishing on V . As a consequence, we obtain a fast algorithm which computes the lexicographic standard monomials of I(V ). We apply the lex game to calculate explicitly the standard monomials for special types of...

Fast and frugal heuristics are well studied models of bounded rationality. Psychological research has proposed the take-the-best heuristic as a successful strategy in decision making with limited resources. Take-the-best searches for a sufficiently good ordering of cues (or features) in a task where objects are to be compared lexicographically. We investigate the computational complexity of fin...

The natural lexicographic semigroupoids associated with Cantor product spaces indexed by countable linear orders are classified. Applications are given to the classification of triangular operator algebras which are direct limits of upper-triangular matrix algebras. 0. Introduction Consider a Cantor space which is presented explicitly as an infinite product of finite topological spaces. The pro...

This paper introduces a propositional encoding for lexicographic path orders in connection with dependency pairs. This facilitates the application of SAT solvers for termination analysis of term rewrite systems based on the dependency pair method. We address two main inter-related issues and encode them as satisfiability problems of propositional formulas that can be efficiently handled by SAT ...

We consider a general multiobjective optimization problem with five basic optimality principles: efficiency, weak and proper Pareto optimality, strong efficiency and lexicographic optimality. We generalize the concept of tradeoff directions defining them as some optimal surface of appropriate cones. In convex optimization, the contingent cone can be used for all optimality principles except lex...

In this paper we present a novel termination order the predicative lexicographic path order (PLPO for short), a syntactic restriction of the lexicographic path order. As well as lexicographic path orders, several non-trivial primitive recursive equations, e.g., primitive recursion with parameter substitution, unnested multiple recursion, or simple nested recursion, can be oriented with PLPOs. I...

A short new proof of the fact that all shifted complexes are fixed by reverse lexicographic shifting is given. A notion of lexicographic shifting, ∆ lex — an operation that transforms a monomial ideal of S = k[x i : i ∈ N] that is finitely generated in each degree into a squarefree strongly stable ideal — is defined and studied. It is proved that (in contrast to the reverse lexicographic case) ...