Energy, congestion and dilation in radio networks

Abstract

We investigate the problem of path selection in radio networks for a given set of sites in two-dimensional space. For some given static point-to-point communication demand we define measures for congestion, energy consumption and dilation that take interferences between communication links into account.We show that energy optimal path selection for radio networks can be computed in polynomial time. Then, we introduce the diversity g(V ) of a set V ⊆ Ê 2 . It can be used to upperbound the number of interfering edges. For real-world applications it can be regarded as Θ(log n). A main result of the paper is that a weak c-spanner construction as a communication network allows to approximate the congestionoptimal communication network by a factor of O(g(V ) 2 ).Furthermore, we show that there are vertex sets where only one of the performance parameters congestion, energy, and dilation can be optimized at a time. We show trade-offs lower bounding congestion × dilation and dilation × energy. For congestion and energy the situation is even worse. It is only possible to find a reasonable approximation for either congestion or energy minimization, while the other parameter is at least a polynomial factor worse than in the optimal network.

A Robust Interference Model for Wireless Ad-Hoc Networks

“…An exception in this respect is formed by [11], introducing an explicit definition of interference and establishing trade-offs between the concepts of congestion, power consumption, and dilation. With [11] more attention is also being paid to the fact that-if nodes are capable of adapting their transmission power, an assumption already made in early work that can be considered originators of topology control considerations [5,16]-interference ranges corre-late with the length of communication links.…”

“…With [11] more attention is also being paid to the fact that-if nodes are capable of adapting their transmission power, an assumption already made in early work that can be considered originators of topology control considerations [5,16]-interference ranges corre-late with the length of communication links. More precisely the interference range of a link depends on the transmission power levels chosen by the two nodes communicating over the respective link.…”

“…Where [11] defines interference based on current network traffic, [2] introduces a traffic-independent notion of interference. Moreover, the latter work shows that the above statement that graph sparseness or small degree implies low interference is misleading.…”

“…[11] introduces an instance which seems to yield inherently high interference: the so called exponential node chain is a one-dimensional graph G = (V, E) where the distance between two consecutive nodes grows exponentially from left to right as depicted in Figure 6. The distance between two nodes v i and v i+1 in V is thus 2 i .…”

“…We first look at a particular network where distances between nodes increase exponentially from left to right. [11] introduces this network as a high interference example yielding interference O(∆), where ∆ is the maximum node degree. We show that it is intriguingly possible to achieve interference O √ ∆ in our model for this network, which matches a lower bound also presented in this paper.…”