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 ⫅ ℝd for any constant d. It can be used to upper bound the number of interfering edges. For real-world applications it can be regarded as Θ(log n). A main result is that a c-spanner construction as a communication network allows one 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 × dilation and dilation × 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.
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auf der Heide, F., Schindelhauer, C., Volbert, K. et al. Congestion, Dilation, and Energy in Radio Networks. Theory Comput Syst 37, 343–370 (2004). https://doi.org/10.1007/s00224-004-1124-z
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DOI: https://doi.org/10.1007/s00224-004-1124-z