Given a simple graph G = (V,E), a subset S of the vertices is called a global defensive alliance if S is a dominating set and for every vertex v in S at least half of the vertices in the closed neighborhood of v are in S. Similarly, a subset S is called a global offensive alliance if S is a dominating set and for every vertex v not in S at least half of the vertices in the closed neighborhood o...

which reduce to (n + 1) for a = b = c = 1. We refine Cayley’s formula by showing that Pn(a, b, c) counts rooted forests by the number of trees and the number of proper vertices, which are vertices that are less than all of their proper descendants. Moreover, other evaluations of Pn(a, b, c) have similar interpretations for other types of trees and forests: k-ary trees, forests of ordered trees,...

Gossiping is the process of information diiusion in which each node of a network holds a packet that must be communicated to all other nodes in the network. We consider the problem of gossiping in communication networks under the restriction that communicating nodes can exchange up to a xed number p of packets at each round. In the rst part of the paper we study the extremal case p = 1 and we e...

This study considers the addition of relation to an organization structure such that the communication of information between every member in the organization becomes the most efficient. This paper proposes a model of adding relation to a linking pin organization structure where every pair of siblings in a complete K-ary tree of height H is adjacent. When a new edge between the root and a node ...

It is known that task scheduling problem of an intree with unit time tasks and unit time communication delays onto a limited number of processors is NP-hard. In this paper, we show that such a problem is approximable within a factor of 3 if we assume a complete k-ary intree with at most (k − 1) constant communication delay. Also we prove that the problem is approximable within a factor of 2 if ...

I-language over simple type structure is considered. Type Y== (0 --t (0 -+ 0)) + (0 -+ 0) is called a binary tree type because of the isomorphism between binary trees and closed terms of this type. Therefore any closed term of type Y+(Y-P ... -P (Y + Y) ) represents an n-ary tree function. The problem is to characterize tree operations represented by the closed terms of the examined type. It is...

Genetic algorithms (GAs) are probabilistic search algorithms that are loosely based on biological evolution. Analyzing genetic algorithms has proven di cult, for a variety of reasons, but a landscape paradigm that rigorously models the search of GAs has become increasingly popular in their analysis. So far much of this analysis concerns binary representations, where each member of the populatio...

In spread spectrum based watermarking schemes, it is a challenging task to embed multiple bits of information into the host signal. M -ary modulation has been proposed as an effective approach to multibit watermarking. It has been proved that an M -ary modulation based watermarking system outperforms significantly a binary modulation based watermarking system. However, in the existing M -ary mo...

We perform a comparison of the performance and efficiency of four different function evaluation methods: black-box functions, binary trees, n-ary trees and string parsing. The test consists in evaluating 8 different functions of two variables x, y over 5000 floating point values of the pair (x, y). The outcome of the test indicates that the n-ary tree representation of algebraic expressions is ...

A concept of systolic dissemination of information in interconnection networks is presented, and the complexity of systolic gossip and broadcast in one-way (telegraph) and two-way (telephone) communication mode is investigated. The following main results are established: (i) a general relation between systolic broadcast and systolic gossip, (ii) optimal systolic gossip algorithms on paths in bo...