Betweenness centrality is a distance-based invariant of graphs. In this paper, we use lexicographic product to compute betweenness centrality of some important classes of graphs. Finally, we pose some open problems related to this topic.

Computers can help dialectologists to make full use of the information they have acquired: the basic dimensions of dialectal reaserch can be enlarged and its possible outcomes can become more sophisticated. In this paper, we show how a dialectal database, DBT-ALT, containing the data collected for the Atlante Lessicale Toscano ‘Lexical Atlas of Tuscany’ can be used as the starting point for the...

Given an ordered alphabet and a permutation, according to the lexicographic order, on the set of suffixes of a word w, we present in this article a linear time and space method to determine whether a word w′ has the same permutation on its suffixes. Using this method, we are then also able to build the class of all the words having the same permutation on their suffixes, first of all the smalle...

The purpose of this note is to compute the probability of logrolling for three different probabilistic cultures. The primary finding is that the restriction of preferences to be in accord with the condition of separable preferences creates enough additional structure among voters’ preference rankings to create an increase in the likelihood that a Condorcet winner will exist with both IC and IAC...

This paper describes a method for planning with rich qualitative, temporally extended preferences (QTEPs) using lookahead heuristics inspired by those employed in state-of-the-art classical planners. Key to our approach is a transformation of the planning domain into an equivalent but simplified planning domain. First, compound preference formulae are transformed into simpler, equivalent prefer...

according to the limit of resources in the subject of prioritization, one of the alternative methods is mcdm method. generally, mcdm models have been developed under certainty while we confront with under uncertainty in real world. in hierarchical mcdm methods, one of the main steps is to weigh criteria and computes each alternative weight using defined criteria in the next steps. one of the ea...

An identifying code in a graph is a set of vertices which intersects all the symmetric differences between pairs of neighbourhoods of vertices. Not all graphs have identifying codes; those that do are referred to as twin-free. In this paper, we design an algorithm that finds an identifying code in a twin-free graph on n vertices in O(n) binary operations, and returns a failure if the graph is n...

The purpose of this paper is to learn the order of criteria of lexicographic decision under various reasonable assumptions. We give a sample evaluation and an oracle based algorithm. In the worst case analysis we are dealing with the adversarial models. We show that if the distances of the samples are less than 4, then it is not learnable, but 4-distance samples are polynomial learnable.

A linear ordering (X,≺) is a Debreu chain (or has the Debreu property) if each subordering (Y,≺) of X can be embedded into X with an injective function that is both order-preserving and continuous with respect to the order topology on X and Y . The most typical example of a Debreu chain is the linearly ordered topological space (R, <, τ<) of real numbers endowed with its usual order < and the o...

In Tversky’s (1969) model of a lexicographic semiorder, a preference is generated via the sequential application of numerical criteria by declaring an alternative x better than an alternative y if the first criterion that distinguishes between x and y ranks x higher than y by an amount exceeding a fixed threshold. We generalize this idea to a fully fledged model of boundedly rational choice. We...