Near-Optimal Deterministic Steiner Tree Maintenance in Sensor Networks

We consider the group communication maintenance problem between a set of k mobile agents that are tracked by a static sensor network. We develop a scalable deterministic distributed algorithm for maintaining a Steiner tree of the agents so that group communication between them can be provided in the minimum cost possible. The main idea is that our algorithm maintains a virtual tree of mobile agents which can be immediately converted to an actual Steiner tree at all times. Our algorithm achieves the Steiner tree with total length at most O (log k) times the length of the minimum Steiner tree in the constant-doubling graph model. The total communication cost (messages) to maintain the Steiner tree is only O (min {log n, log D}) times the optimal communication cost, where n and D, respectively, are the number of nodes and the diameter of the network. We also develop improved algorithms for the k-center, sparse aggregation, and distributed matching problems. Experimental evaluation results show the benefits of our algorithms compared to previous algorithms. These four problems are NP-hard and, to the best of our knowledge, our algorithms are the first near-optimal deterministic algorithms for maintaining approximate solutions to these problems with low maintenance costs in a distributed setting.