# Topology Construction for Rural Wireless Mesh Networks - A Geometric Approach

## Abstract

Wireless mesh networks based on the IEEE 802.11 technology have recently been proposed and studied as an approach to bridge the digital divide. Point-to-point links are established in the nodes of such networks using high gain directional antennas. Some nodes are directly linked to the wired internet, and the others link to these using a small number of hops.

Minimization of system cost is an important objective in these networks, since generally the rural populations are low-paying. The dominant cost in this setting is that of constructing the antenna towers required to achieve Line-of-Sight connectivity. The cost of a tower depends upon its height, which in turn depends upon the length of its links and the physical obstacles along those links. We investigate the problem of selecting which links should be established such that all nodes are connected, while the cost of constructing the antenna towers is minimized. We formulate this as a geometric optimization problem, and develop an efficient approximation algorithm for the problem using techniques from facility location and geometric set cover. Our algorithm stands up well to experimental comparison with a computed lower bound and other approaches tried before. On the theoretical side, we are able to show that our algorithm guarantees a constant approximation factor...

## Keywords

Wireless networks Computational geometry## Preview

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