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

Both 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 power assignment 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(Γ∆ logn) time slots if the maximal degree ∆ is known and O((∆ + logn)Γ logn) otherwise, where Γ is the ratio between the maximal and the minimal transmission range. We introduce a new network parameter ` that measures the length of the longest unidirectional path in the network. After showing that a dependence on ` is inevitable for distributed node coloring, we present an algorithm that O(Γ∆)-colors the network and runs in O((∆+`)Γ∆ logn) time slots. Simplifying this algorithm results in an MIS algorithm that runs in O((∆ + `)Γ logn) time slots. 1 ar X iv :1 40 2. 49 94 v1 [ cs .D S] 2 0 Fe b 20 14