Cluster-Swap: A Distributed K-median Algorithm for Sensor Networks

In building practical sensor networks, it is often beneficial to use only a subset of sensors to take measurements because of computational, communication, and power limitations. Thus, selecting a subset of nodes to perform measurements whose results will closely mirror the results of having all the nodes perform measurements is an important problem. This node selection problem, depending on the character of the function that integrates measurements and the type of measurements, can be mapped into a more general problem called the k-median problem. In the k-median problem we select a centroid set - a subset of nodes - that minimizes the function, that is the sum of the minimal costs between each node and a node in the centroid set. The set of selected nodes is called ``centroids" or ``leader nodes", where the cluster of a leader node is defined by the set of nodes closest to the leader node. We develop an approximate k-median distributed algorithm called Cluster-Swap, which does not require significant computational power, and does not require every node to know its exact position in the n-dimensional space but only its relative location in relation to a subset of nodes. In addition, Cluster-Swap limits communication costs and is flexible to network changes. The locally optimal solution reached by our algorithm is an approximation whose error is bounded by the maximum cost and number of nodes in the cluster. The error bound gives a tighter bound than other similar algorithms, given that the random initial solution is within a described reasonable range. We empirically show that the solution given by our distributed algorithm is close to both the approximate solution generated by the cited Local search heuristics and also the globally optimal solution while using fewer resources.