ALCOMFT-TR-03-128

Friedhelm Meyer auf der Heide, Christian Schindelhauer, Klaus Volbert and Matthias Grünewald
Congestion, Dilation, and Energy in Radio Networks
Paderborn. Work package 2. December 2003.

Abstract: We investigate the problem of path selection in radio networks for a given static set of n sites in two- and three-dimensional space. For static point-to-point communication we define measures for congestion, dilation, and energy consumption that take interferences among 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\subseteq \REAL^\ddim for any constant \ddim. It can be used to upper bound the number of interfering edges. For real-world applications it can be regarded as Theta(log n). A main result is that a c-spanner construction as a communication network allows to approximate the congestion-optimal path system by a factor of O(g(V)²).

Furthermore, we show that there are vertex sets where only one of the performance parameters congestion, dilation, and energy can be optimized at a time. We show trade-offs lower bounding congestion x dilation and dilation x energy. The trade-off between congestion and dilation increases with switching from two-dimensional to three-dimensional space. 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.

Postscript file: ALCOMFT-TR-03-128.ps.gz (159 kb).