in recent years, routing has been the most focused area in ad hoc networks research. on-demand routing in particular, is widely developed in bandwidth constrained mobile wireless ad hoc networks because of its effectiveness and efficiency. most proposed on-demand routing protocols are built and relied on single route for each data session. whenever there is a link disconnection on the active ro...

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...

This papers presents a comprehensive and general form of the Tarjan’s unionfind algorithm dedicated to connected operators. An interesting feature of this form is to introduce the notion of separated domains. The properties of this form and its flexibility are discussed and highlighted with examples. In particular, we give clues to handle correctly the constraint of domain-disjointness preserva...