In this paper it is tried to estimate the reliability of a fully connected network of some unreliable nodes and unreliable connections (edges) between them. The proliferation of electronic messaging has been witnessed during the last few years. The acute problem of node failure and connection failure is frequently encountered in communication through various types of networks. We know that a ne...

Let G = (V,E) be a connected undirected graph, where V is the set of nodes and E denotes the set of edges. Given a non-negative weight function w : E → IR+ associated with its edges and a subset X ⊆ V of terminal nodes, the Steiner problem in graphs (SPG) consists in finding a minimum weighted connected subtree of G spanning all terminal nodes in X . The solution of SPG is a Steiner minimum tre...

Given a graph with n nodes and minimum degree , we give a polynomial time algorithm that constructs a partition of the nodes of the graph into two sets X and Y such that the sum of the minimum degrees in X and in Y is at least and the cardinalities of X and Y diier by at most (+ 1 if n 6 = (mod2)). The existence of such a partition was shown by 4].

Wireless Sensor networks (WSNs) are used to monitor and control the physical environment in different classes of applications. Due to the dense deployment of sensors and as the sensor observations are spatially correlated with respect to location of sensor nodes, it is not necessary for every sensor to transmit its data. Therefore, because the resource constraints of nodes, it is necessary to s...

Let G = (V, E) be a connected undirected graph, where V = {1, . . . , n} is the set of nodes and E the set of edges. Consider that there are associated positive costs, ce, to each edge e ∈ E. Given a positive integer valued function d : V → N on the nodes, the Min-Degree Constrained Minimum Spanning Tree (md-MST) problem consists in finding a spanning tree T of G with minimum total edge cost, g...

A precise positioning of transmitting nodes enhances the performance of Cognitive Radio (CR), by enabling more efficient dynamic allocation of channels and transmit powers for unlicensed users. Most localization techniques rely on random positioning of sensor nodes where, few sensor nodes may have a small separation between adjacent nodes. Closely spaced nodes introduces correlated observations...

Several different interpolation schemes have been proposed for improving the accuracy of lattice Boltzmann simulations in the vicinity of a solid boundary. However, these methods require at least two or three fluid nodes between nearby solid surfaces, a condition that may not be fulfilled in dense suspensions or porous media for example. Here we propose an interpolation of the equilibrium distr...

In this survey paper, we discuss the development of the Generalized Minimum Spanning Tree Problem, denoted by GMSTP, and we focus on the integer programming formulations of the problem. The GMSTP is a variant of the classical minimum spanning tree problem (MST), in which the nodes of an undirected graph are partitioned into node sets (clusters) and we are looking for a minimum cost tree spannin...

The Generalized Minimum Spanning Tree Problem, denoted GMST, is a variant of the classical Minimum Spanning Tree problem, and consists of finding a minimum-cost tree spanning a subset of nodes which includes exactly one node from every cluster in an undirected graph whose nodes are partitioned into clusters and whose edges are defined between nodes belonging to different clusters. The GMST prob...

Probing is a promising approach for network monitoring. An important problem that needs to be addressed while developing probing-based solutions is the selection of probe station nodes. Probe station nodes are the nodes that are instrumented with the functionality of sending probes and analyzing probe results. The placement of probe stations affects the diagnosis capability of the probes sent b...