A Constant-Factor Approximation for Wireless Capacity Maximization with Power Control in the SINR Model

Abstract

In modern wireless networks, devices are able to set the power for each transmission carried out. Experimental but also theoretical results indicate that such power control can improve the network capacity significantly. We study this problem in the physical interference model using SINR constraints.In the SINR capacity maximization problem, we are given n pairs of senders and receivers, located in a metric space (usually a so-called fading metric). The algorithm shall select a subset of these pairs and choose a power level for each of them with the objective of maximizing the number of simultaneous communications. This is, the selected pairs have to satisfy the SINR constraints with respect to the chosen powers.We present the first algorithm achieving a constant-factor approximation in fading metrics. The best previous results depend on further network parameters such as the ratio of the maximum and the minimum distance between a sender and its receiver. Expressed only in terms of n, they are (trivial) Ω(n) approximations.Our algorithm still achieves an O(log n) approximation if we only assume to have a general metric space rather than a fading metric. Furthermore, by using standard techniques the algorithm can also be used in single-hop and multi-hop scheduling scenarios. Here, we also get polylog n approximations.

Maximizing Capacity with Power Control under Physical Interference Model in Simplex Mode

“…Our algorithm can be generalized to an arbitrary metric. It still achieves a constant approximation bound in the fading metric and a logarithmic approximation bound in the general metric by using the bound on γ derived in [8].…”

“…MISL with power control is also NP-hard [1]. Approximation algorithms for MISL with power control has been studied in [11] and [8]. In [11], Wan et al assumed that a bounded set S of possible values of transmission power of all nodes and obtained an O (β)-approximation algorithm, where β is the power diversity of S, defined to be smallest integer k such that there exists a partition of S into k subsets in each of which any two elements differ by a factor of at most two.…”

“…In [11], Wan et al assumed that a bounded set S of possible values of transmission power of all nodes and obtained an O (β)-approximation algorithm, where β is the power diversity of S, defined to be smallest integer k such that there exists a partition of S into k subsets in each of which any two elements differ by a factor of at most two. In [8], Kesselheim assumed unlimited maximum transmission power and developed a constant-approximation algorithm in the fading metric and a logarithmic approximation algorithm in the general metric. The assumption on unlimited maximum transmission power is essential in their algorithm as it would technically avoid the major technical obstacle due to the ambient noise.…”

Extending wireless algorithm design to arbitrary environments via metricity

“…Taking the LINK CAPACITY problem as an example, approximation results carry over for numerous cases: fixed power [16]; arbitrary power control [20,21]; distributed setting based on regret minimization [2] and under jamming [7]; and the weighted version with linear power [17].…”

Optimizing compatible sets in wireless networks through integer programming

“…For example, the papers (Goussevskaia et al 2007(Goussevskaia et al , 2009) study the complexity of the problem and point out that it is N P-hard, also when the background noise is ignored. The paper (Brar et al 2006) investigates MWCSP in wireless mesh networks, proposing heuristic and approximate algorithms; other approximate algorithms for MWCSP can be found in Xu and Tang (2009) and Kesselheim (2011). The paper (Andrews and Dinitz 2009) presents a distributed algorithm for MWCSP based on game theory.…”