Determinantal polynomial systems are those involving maximal minors of some given matrix. An important situation where these arise is the computation critical values a map restricted to an algebraic set. This leads directly strategy for, among other problems, optimisation. Computing Gröbner bases classical method for solving in general. For practical computations, this consists two main stages....

In this paper, we describe a general method for building coverings, that we call lexicographic covering. The name comes from the fact that the scheme although more general than that is particularly fitted to the case where the transitions of an automaton are given an ordering at each state and thus the computations in the automaton may be lexicographic ordered. The lexicographic covering allows...

The median of a set vertices P graph G is the all x minimizing sum distances from to P. In this paper, we present linear time algorithm compute medians in graphs. We also associated ?1-cube complexes. Our based on majority rule characterization graphs and fast computation parallelism classes edges (?-classes) via Lexicographic Breadth First Search (LexBFS). show that any LexBFS ordering satisfi...

We consider two models of computation for Tarski’s order preserving function f related to fixed points in a complete lattice: the oracle function model and the polynomial function model. We develop a complete understanding under the oracle function model for finding a Tarski’s fixed point as well as determining the uniqueness of Tarski’s fixed point in both the lexicographic ordering and the co...

Many theoretical constructs of interest to psychologists are multidimensional and derive from the integration of several input variables. We show that input variables that are measured on ordinal scales cannot be combined to produce a stable weakly ordered output variable that allows trading off the input variables. Instead a partial order is obtained in which the amount of ordering depends on ...

Lexicographic depth first search (LexDFS) is a graph search protocol which has already proved to be a powerful tool on cocomparability graphs, a subfamily of perfect graphs. Cocomparability graphs have been well studied through their complements (comparability graphs) and their corresponding posets. Recently however LexDFS has led to a number of elegant near linear time algorithms on cocomparab...

We correct errors in the proof of [7, Theorem 19] and in the description of [7, Table 1]. We also fix some typos and notational issues. We thank Thomas Kahle for pointing out the mistake in the table and Robert Krone for finding the gap in our original proof. We begin with a comment to avoid confusion in the proof of [7, Proposition 13]. Let dlex be the partial ordering of [P]k (as defined in [...

In random geometric graphs, vertices are randomly distributed on [0, 1] and pairs of vertices are connected by edges whenever they are sufficiently close together. Layout problems seek a linear ordering of the vertices of a graph such that a certain measure is minimized. In this paper, we study several layout problems on random geometric graphs: Bandwidth, Minimum Linear Arrangement, Minimum Cu...

This paper presents an argumentation-based framework for the modelling of, and automated reasoning about multi-attribute preferences of a qualitative nature. The framework presents preferences according to the lexicographic ordering that is well-understood by humans. Preferences are derived in part from knowledge. Knowledge, however, may be incomplete or uncertain. The main contribution of the ...

We consider the problem of learning a user’s ordinal preferences on multiattribute domains, assuming that the user’s preferences may be modelled as a kind of lexicographic ordering. We introduce a general graphical representation called LP-structures which captures various natural classes of such ordering in which both the order of importance between attributes and the local preferences over ea...