Wireless Mesh Networks (WMN s) have emerged as a key technology for next-generation wireless networking. By adding some Long-ranged Links, a wireless mesh network turns into a complex network with the characteristic of small worlds. As a communication backbone, the high fault tolerance is a significant property in communication of WMN s. In this paper, we design a novel malfunctioned router det...

The notion of resolving sets in a graph was introduced by Slater (1975) and Harary and Melter (1976) as a way of uniquely identifying every vertex in a graph. A set of vertices in a graph is a resolving set if for any pair of vertices x and y there is a vertex in the set which has distinct distances to x and y. A smallest resolving set in a graph is called a metric basis and its size, the metri...

We present a new style of metric generator in graphs. Specifically we introduce a metric generator based on a partition of the vertex set of a graph. The sets of the partition will work as the elements which will uniquely determine the position of each single vertex of the graph. A set W of vertices of a connected graph G strongly resolves two different vertices x, y / ∈ W if either dG(x,W ) = ...

Let G be a connected graph. A vertex w strongly resolves a pair u, v of vertices of G if there exists some shortest u − w path containing v or some shortest v − w path containing u. A set W of vertices is a strong resolving set for G if every pair of vertices of G is strongly resolved by some vertex of W . The smallest cardinality of a strong resolving set for G is called the strong metric dime...

Describing a procedure in which choice proceeds in a sequence, we propose two alternatives ways of resolving the decision problem whenever the outcome is sequence-sensitive. One way yields a rationalizable choice set, and the other way produces a weakly rationalizable choice set that is equivalent to von Neumann-Morgenstern's stable set. It is shown that for quasi-transitive rationalization, th...

Steepest edge criteria have often been shown to work well in Simplex or Active Set methods for Linear Programming (LP). It is therefore important that any technique for resolving degeneracy in LP should conveniently be able to use steepest edge criteria in the selection of the search direction. A recursive technique for resolving degeneracy 5] is of some interest in that it provides a guarantee...

Let G = (V, E) be a connected graph. The distance between two vertices u, v 2 V, denoted by d(u, v), is the length of a shortest u À v path in G. The distance between a vertex v 2 V and a pd(G), is the minimum number of sets in any resolving partition of G. In this article we study the partition dimension of Cartesian product graphs. More precisely, we show that for all pairs of connected graph...

In this paper, we investigate the concept of resolving dominating set in a graph. particular, characterize sets join, corona and lexicographic product two graphs determine domination number these graphs.

This paper describes a Chinese word segmentation system based on unigram language model for resolving segmentation ambiguities. The system is augmented with a set of pre-processors and post-processors to extract new words in