The range assignment problem in non-homogeneous static ad-hoc networks

Abstract

Range assignment problems in Ad-Hoc wireless networks have been the subject of several recent studies. All these studies deal with the homogeneous case, i.e., all stations share the same energy cost function. However, this assumption does not well model realistic scenarios in which the energy cost of a station varies dramatically depending on the particular enviroment conditions of its location. We introduce the weighted version of the range assignment problem in which the cost a station × pays to transmit to another station depends on the distance between the stations and on the energy cost of station ×. Most of the algorithm results for the unweighted range assignment problem can not be applied to the weighted version. We thus provide a set of algorithmic results for this version and discuss some interesting related open questions.

On minimizing the total power of k-strongly connected wireless networks

“…In [1], a weighted version of the model is considered. To each transceiver t we associate an energy unit cost parameter c t , which measures the cost associated with assigning one unit of power to t. Note that different transceivers may have distinct energy unit costs due to differences between them, their environments and other factors.…”

“…Some researchers add an additional constraint parameter to the problem, the bounded diameter h of the induced communication graph, see results in [11][12][13]. Ambuhl et al [1] presented some algorithms for the weighted power assignment, solving it optimally for the broadcast, multi-source broadcast and strong connectivity problems for the linear case (they achieved the same running time for the connectivity problem as in [8]). They also presented some approximation algorithms for the multi-dimensional case.…”

“…Each transceiver t has a transmission range denoted by r t . This is customary to assume that the transmission power p(t) required to transmit to distance r t is proportional to r t a , where the distance-power gradient a is usually taken to be in the interval [1,2] (see [3]). Even though there is no direct equivalence between p(t) and r t a , in order to make the notation easier throughout the paper we use the equality p(t) = r t a .…”

“…Algorithm (PLANE-K-STRONG-CONNECT) 1. Find a Hamiltonian cycle h 0 as described in Lemma 3.1, where A 2 is the assignment given in [18] for asymmetric biconnectivity.…”

Weighted broadcast in linear radio networks

“…The first work on this problem appeared in [3]. For the unbounded case, the proposed algorithm runs in O(n 3 ) time and O(n 2 ) space.…”