Arbitrary Transmission Power in the SINR Model: Local Broadcasting, Coloring and MIS

In the light of energy conservation and the expansion of existing networks, wireless networks face the challenge of nodes with heterogeneous transmission power. However, for more realistic models of wireless communication only few algorithmic results are known. In this paper we consider nodes with arbitrary, possibly variable, transmission power in the so-called physical or SINR model. Our first result is a bound on the probabilistic interference from all simultaneously transmitting nodes on receivers. This result implies that current local broadcasting algorithms can be generalized to the case of non-uniform transmission power with minor changes. The algorithms run in $\O(\Gamma^{2} \Delta \log n)$ time slots if the maximal degree $\Delta$ is known, and $\O((\Delta + \log n)\Gamma^{2} \log n)$ otherwise, where $\Gamma$ is the ratio between the maximal and the minimal transmission range. The broad applicability of our result on bounding the interference is further highlighted, by generalizing a distributed coloring algorithm to this setting.