This paper addresses the spare capacity allocation (SCA) problem considering any single node failure in mesh networks. The SCA node failure problem aims at finding backup routes and providing sufficient spare capacity to protect traffic when any single node fails in communication network. Here, we introduce our novel matrix formulation of the arc-flow SCA node failure model. In this model, work...

Pipelines that operate on buffers often work well to mitigate the high latency inherent in interprocessor communication and in accessing data on disk. Running a single pipeline on each node works well when each pipeline stage consumes and produces data at the same rate. If a stage might consume data faster or slower than it produces data, a single pipeline becomes unwieldy. We describe how we h...

A graph G = (V,E) is called a hyper-ring with N nodes (N -HR for short) if V = {0, ..., N − 1} and E = {{u, v}|v − u modulo N is a power of 2}. The following results are shown. We prove that the node-connectivity κ of an N -HR is equal to its degree, say δ, by presenting an algorithm for the explicit construction of δ node-disjoint paths connecting nodes s and t. The length of these paths is bo...

The notation and terminology used in this paper are introduced in the following articles: [16], [13], [2], [3], [5], [1], [7], [9], [12], [10], [8], [18], [14], [11], [6], [15], and [17]. For simplicity, we use the following convention: x, r, a, x0, p are real numbers, n, i, m are elements of N, Z is an open subset of R, and f , f1, f2 are partial functions from R to R. Next we state a number o...

We solve a number of problems posed by Hedetniemi, Hedetniemi, Laskar, Markus, and Slater concerning pairs of disjoint sets in graphs which are dominating or independent and dominating.

The aim of this work is to provide a bridge between the theory of contextfree grammars developed in [10], [6] and universally free manysorted algebras([14]. The third scheme proved in the article allows to prove that two homomorphisms equal on the set of free generators are equal. The first scheme is a slight modification of the scheme in [6] and the second is rather technical, but since it was...

Network design problems traditionally are modelled by a graph where each edge (or node) has a fixed cost. We investigate optimization problems in a realistic model for wireless network design called activation network. The activation network setting can be defined as follows. We are given a directed or undirected graph G = (V,E) together with a family {fuv : (u, v) ∈ E} of monotone nondecreasin...

A network is a generalization of a phylogenetic tree, allowing properties that are not tree-like. With the growth of genomic data, much of which does not fit ideal tree models, there is greater need to understand the algorithmics and combinatorics of phylogenetic networks (Posada and Crandall 2001, Schierup and Hein 2000). Wang et al. (2001) studied the problem of constructing a phylogenetic ne...

Future mobile Ad hoc networks (MANETs) are expected to be based on all-IP architecture and be capable of carrying multitudinous real-time multimedia applications such as voice, video and data. It is very necessary for MANETs to have a reliable and efficient routing and quality of service (QoS) mechanism to support diverse applications which have variances and stringent requirements for delay, j...