The edge tenacity Te(G) of a graph G is dened as:Te(G) = min {[|X|+τ(G-X)]/[ω(G-X)-1]|X ⊆ E(G) and ω(G-X) > 1} where the minimum is taken over every edge-cutset X that separates G into ω(G - X) components, and by τ(G - X) we denote the order of a largest component of G. The objective of this paper is to determine this quantity for split graphs. Let G = (Z; I; E) be a noncomplete connected split...

We are interested in the design of robust (or resilient) capacitated rooted Steiner networks case terminals with uniform demands. Formally, we given a graph, capacity, and cost functions on edges, root, subset vertices called terminals, bound k $$ number possible edge failures. first study problem where = 1 k=1 network that want to must be tree covering root terminals: give complexity results p...

the edge tenacity te(g) of a graph g is dened as:te(g) = min {[|x|+τ(g-x)]/[ω(g-x)-1]|x ⊆ e(g) and ω(g-x) > 1} where the minimum is taken over every edge-cutset x that separates g into ω(g - x) components, and by τ(g - x) we denote the order of a largest component of g. the objective of this paper is to determine this quantity for split graphs. let g = (z; i; e) be a noncomplete connected spli...

This paper presents a novel methodology for the calculation of angular indexes an electrical system from stationary analysis, using load flow and nose curves (P–V) in each buses to perform control actions preserve or improve voltage stability. The are proposed considering method based on concepts cutset angle (CA) center (COA). target is fast estimation voltage-stability margins through appropr...

The high repair cost of (n, k) Maximum Distance Separable (MDS) erasure codes has recently motivated a new class of codes, called Regenerating Codes, that optimally trade off storage cost for repair bandwidth. In this paper, we address bandwidth-optimal (n, k, d) Exact-Repair MDS codes, which allow for any failed node to be repaired exactly with access to arbitrary d survivor nodes, where k ≤ d...

The following equivalent results in the Boolean lattice 2 are proven. (a) Every fibre of 2 contains a maximal chain. (b) Every cutset of 2 contains a maximal antichain. (c) Every red-blue colouring of the vertices of 2 produces either a red maximal chain or a blue maximal antichain. (d) Given any n antichains in 2 there is a disjoint maximal antichain. Statement (a) is then improved to: (a') Ev...

A new coding scheme for general N -node relay networks is presented for unicast, multicast, and broadcast. The proposed distributed decode–forward scheme combines and generalizes Marton coding for single-hop broadcast channels and the Cover–El Gamal partial decode–forward coding scheme for 3-node relay channels. The key idea of the scheme is to precode all the codewords of the entire network at...

This paper introduces a direction-sensitive and locally reorientable compact binary tree, called the Z tree, for representing digital images. A rotation operation is de ned on a subset of its node, called square nodes, to spatially reorganize the four grand children of any given square-node. The goal is to adapt the Z tree in order to produce a minimal cutset representation of homogeneous regio...

We argue that parameterized complexity is a useful tool with which to study global constraints. In particular, we show that many global constraints which are intractable to propagate completely have natural parameters which make them fixedparameter tractable and which are easy to compute. This tractability tends either to be the result of a simple dynamic program or of a decomposition which has...