Multi-channel scheduling algorithms for fast aggregated convergecast in sensor networks

Fast and periodic collection of aggregated data is of considerable interest for mission-critical and continuous monitoring applications in sensor networks. In the many-to-one communication paradigm known as convergecast, we consider scenarios where data packets are aggregated at each hop en route to a sink node along a tree-based routing topology and focus on maximizing the data collection rate at the sink by employing TDMA scheduling and multiple frequency channels. Our key result in the paper lies in proving that minimizing the schedule length for an arbitrary network in the presence of multiple frequencies is NP-hard, and in designing approximation algorithms with worst-case provable performance guarantees for geometric networks. In particular, we design a constant factor approximation for networks modeled as unit disk graphs (UDG) where every node has a uniform transmission range, and a O(Delta(T)log n) approximation for general disk graphs where nodes have different transmission ranges; n is the number of nodes in the network and Delta(T) is the maximum node degree on a given routing tree T. We also prove that a constant factor approximation is achievable on UDG even for unknown routing topologies so long as the maximum node degree in the tree is bounded by a constant. We also show that finding the minimum number of frequencies required to remove all the interfering links in an arbitrary network in NP-hard. We give an upper bound on the maximum number of such frequencies required and propose a polynomial time algorithm that minimizes the schedule length under this scenario. Finally, we evaluate our algorithms through simulations and show various trends in performance for different network parameters.