Intrusion detection, area coverage and border surveillance are important applications of wireless sensor networks today. They can be (and are being) used to monitor large unprotected areas so as to detect intruders as they cross a border or as they penetrate a protected area. We consider the problem of how to optimally move mobile sensors to the fence (perimeter) of a region delimited by a simple polygon in order to detect intruders from either entering its interior or exiting from it. We discuss several related issues and problems, propose two models, provide algorithms and analyze their optimal mobility behavior.

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We investigate the problem of converting sets of sensors into strongly connected networks of sensors using multiple directional antennae. Consider a set S of n points in the plane modeling sensors of an ad hoc network. Each sensor uses a fixed number, say 1 ≤ k ≤ 5, of directional antennae modeled as a circular sector with a given spread (or angle) and range (or radius). We give algorithms for orienting the antennae at each sensor so that the resulting directed graph induced by the directed antennae on the nodes is strongly connected. We also study trade-offs between the total angle spread and range for maintaining connectivity.

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Extensive facility location models in networks deal with the location of special types of subgraphs such as paths or trees and can be considered as extensions of classical facility location models. In this paper we consider the problem of locating a path-shaped or tree-shaped (extensive) facility in trees, under the condition that existing facilities are already located. We introduce a parametric-pruning method to solve the conditional discrete/continuous extensive weighted 1-center location problems in trees in linear time. This improves the recent results of O(n log n) by Tamir et al. (J. Algebra 56:50-75, 2005).