Optimizing Movement in Convex and Non-convex Path-Networks to Establish Connectivity

Abstract

We solve a min-max movement problem in which there are n sensors in path network in plane, where any sensor communicates only with its two immediate neighbors and only at a given maximum communication distance \(\lambda \). We need to move sensors so that each sensor is in the communication range of its two neighbors, keeping the path topology intact. We present an \(O(n^3)\) algorithm for min-max movement problem in a convex path-network which minimizes the maximum movement among the sensors. We also generalize our algorithm for ring, non-convex path, tethered and heterogeneous networks.