Wireless mesh networks appear as an appealing solution to reduce the digital divide between rural and urban regions. However the placement of router nodes is still a critical issue when planning this type of network, especially in rural regions where we usually observe low density and sparse population. In this paper, we firstly provide a network model tied to rural regions by considering the area to cover as decomposed into a set of elementary areas which can be required or optional in terms of coverage and where a node can be placed or not. Afterwards, we try to determine an optimal number and positions of mesh router nodes while maximizing the coverage of areas of interest, minimizing the coverage of optional areas and ensuring connectivity of all mesh router nodes. For that we propose a particularized algorithm based on Metropolis approach to ensure an optimal coverage and connectivity with an optimal number of routers. The proposed algorithm is evaluated on different region instances. We obtained a required coverage between 94% and 97% and a coverage percentage of optional areas less than 16% with an optimal number of routers nr max-2 =1.3*nr min , (nr min being the minimum number of router which is the ratio between the total area requiring coverage and the area which can be covered by a router).professor and the chair of the Mathematics and Sciences Department, Texas A&M -Central Texas (Killeen,TX). His Current research interests include algorithm design and optimization with applications to communications systems and epidemiology.

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Wireless Mesh Network is presented as an appealing solution for bridging the digital divide between developed and under-developed regions. But the planning and deployment of these networks are not just a technical matter, since the success depends on many other factors tied to the related region. Although we observe some deployments, to ensure usefulness and sustainability, there is still a need of concrete design process model and proper network planning approach for rural regions, especially in Sub-Saharan Africa. This paper presents a design methodology to provide network connectivity from a landline node in a rural region at very low cost. We propose a methodology composed of ten steps, starting by a deep analysis of the region in order to identify relevant constraints and useful applications to sustain local activities and communication. Approach for planning the physical architecture of the network is based on an indoor-outdoor deployment for reducing the overall cost of the network.Comment: 9 pages, 2 figures, 3 table

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