Ptolemaic graphs are graphs that satisfy ptolemaic inequality for any four vertices. The graph class coincides with the intersection of chordal graphs and distance hereditary graphs. The graph class can also be seen as a natural generalization of block graphs (and hence trees). In this paper, a new characterization of ptolemaic graphs is presented. It is a canonical tree representation based on...

The Hierarchical Chinese Postman Problem (HCPP) is a Chinese Postman Problem with the arcs partitioned into priority classes ordered by a precedence relation. The problem under the sum criterion is polynomially solvable if the ordering is linear and each class is connected. For a known HCPP algorithm we give an O(n) improvement (n the number of nodes) leading to O(kn) with k the number of class...

Our work becomes integrated into the general problem of the stability of the network ad hoc. Some, works attacked(affected) this problem. Among these works, we find the modelling of the network ad hoc in the form of a graph. Thus the problem of stability of the network ad hoc which corresponds to a problem of allocation of frequency amounts to a problem of allocation of colors in the vertex of ...

At the previous FOGA workshop, we presented some initial results on using Markov models to analyze the transient behavior of genetic algorithms (GAs) being used as function optimizers (GAFOs). In that paper, the states of the Markov model were ordered via a simple and mathematically convenient lexicographic ordering used initially by Nix and Vose. In this paper, we explore alternative orderings...

This paper regards the application of interpolation tools offered by mathematical morphology to color images. The approach presented here uses the lexicographic ordering to compare values of the pixels. These comparisons are performed in a new, transformed color space the comparative color space, which is essential with respect to the visual importance of color channels for the human perception...

In default reasoning, usually not all possible ways of resolving conflicts between default rules are acceptable. Criteria expressing acceptable ways of resolving the conflicts may be hardwired in the inference mechanism, for example specificity in inheritance reasoning can be handled this way, or they may be given abstractly as an ordering on the default rules. In this article we investigate fo...

In this note I examine conditions under which a probability relation on a set of events is lexicographic. Chipman (1971) discussed the question of the minimal ordinal CT such that there exists an order-preserving function from an ordered set A (in his; paper A is fR with any order on it) to lRa with the lexicographic order on it. Since there always exists an ordinal /? such that there is an ord...

This paper presents a two-level optimization model for the optimal scheduling of an active distribution system in day-ahead and real-time market horizons. The operator transacts energy ancillary services with electricity market, plug-in hybrid electric vehicle parking lot aggregators, demand response aggregators. Further, can utilize switching procedure its zonal tie-line switches to mitigate e...

We consider the lexicographic max-min fair rate control problem at the link layer in a random access wireless network. In lexicographic max-min fair rate allocation, the minimum link rates are maximized in a lexicographic order. For the Aloha multiple access model, we propose iterative approaches that attain the optimal rates under very general assumptions on the network topology and communicat...

In this article an account is given of the experience in fieldwork by the Dictionary of the Flemish Dialects (Woordenboek van de Vlaamse Dialecten, WVD), Ghent University, Belgium. The focus is on the practical aspects with regard to methods of lexicographic fieldwork. It is maintained that the analysis of 'metalinguistical conversations' with groups of respondents in which their lexicographic ...