Minimum Cost Topology Construction for Rural Wireless Mesh Networks

Abstract

Abstract-IEEE 802.11 WiFi equipment based wireless mesh networks have recently been proposed as an inexpensive approach to connect far-flung rural areas. Such networks are built using high-gain directional antennas that can establish long-distance wireless point-to-point links. Some nodes in the network (called gateway nodes) are directly connected to the wired internet, and the remaining nodes connect to the gateway(s) using one or more hops.The dominant cost of constructing such a mesh network is the cost of constructing antenna towers at nodes. The cost of a tower depends on its height, which in turn depends on the length of its links and the physical obstructions 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 required to establish the selected links is minimized. We show that this problem is NPhard and that a better than O(log n) approximation cannot be expected, where n is the number of vertices in the graph. We then present the first algorithm in the literature, for this problem, with provable performance bounds. More precisely, we present a greedy algorithm that is an O(log n) approximation algorithm for this problem. Finally, through simulations, we compare our approximation algorithm with both the optimal solution, and a naive heuristic.

Minimum shared‐power edge cut

“…He gave a pseudo-polynomial time algorithm for the minimum s-t path problem in this model; Cabello and Colin de Verdière [6] recently proved that this problem is weakly NP-hard. Panigrahi et al [29] gave an O(log n)-approximation algorithm for the minimum spanning tree problem in the installation cost model, and this was shown to be best possible assuming P ≠ NP [28,29].…”

Rural Wireless Mesh Network: A Design Methodology

“…Panigrahi et al [11] provide amelioration of both [9] [10]. For [11], they provide an algorithm with the worstcase logarithmic bound for prior heuristic. They provide an approach that can handle any number of obstructions between two nodes, while the prior heuristic considers only one obstruction.…”

Designing wireless metropolitan-area networks using mathematical optimization

“…Reference [21] focuses on providing only connectivity, rather than capacitated links, to route specific demands. Similarly, [10] and [11] focus only on minimizing mast heights, without accounting for capacitated links that must satisfy demand requirements. Other work has dealt with aspects of metropolitan area wireless networks orthogonal to ours, such as routing and scheduling [5] and providing delay guarantees [9], or problems of metropolitan-area network design and routing using wireline technologies such as fiber optics (see [8], [6], [18], and [13]).…”

“…• Constraint (11) ensures that at any given site i, the mast installed is of adequate height to support the most demanding of all the line-ofsight links that must be established at that site.…”