Power Assignment Problems in Wireless Communication

TL;DR

This paper advances algorithms for power assignment in wireless networks, improving efficiency and providing new approximation methods for related problems like TSP and multicasting.

Contribution

It introduces faster algorithms for power assignment problems, including a linear-time approximation and novel solutions for TSP and multicasting in wireless communication.

Findings

Improved running time for $(1+ta)$-approximate solutions to power assignment.

Constant approximation algorithm for TSP with squared edge costs.

Efficient schemes for $k$-hop multicasts.

Abstract

A fundamental class of problems in wireless communication is concerned with the assignment of suitable transmission powers to wireless devices/stations such that the resulting communication graph satisfies certain desired properties and the overall energy consumed is minimized. Many concrete communication tasks in a wireless network like broadcast, multicast, point-to-point routing, creation of a communication backbone, etc. can be regarded as such a power assignment problem. This paper considers several problems of that kind; for example one problem studied before in \cite{Carrots, Bilo} aims to select and assign powers to $k$ of the stations such that all other stations are within reach of at least one of the selected stations. We improve the running time for obtaining a $(1+\epsilon)$-approximate solution for this problem from $n^{((\alpha/\epsilon)^{O(d)})}$ as reported by Bilo et al. (\cite{Bilo}) to $O(n+ {(\frac{k^{2d+1}}{\epsilon^d})}^{\min{\{2k, (\alpha/\epsilon)^{O(d)} \}}})$ that is, we obtain a running time that is \emph{linear} in the network size. Further results include a constant approximation algorithm for the TSP problem under squared (non-metric!) edge costs, which can be employed to implement a novel data aggregation protocol, as well as efficient schemes to perform $k$-hop multicasts.