Multi-Radio Wireless Sensor Networks: Energy Efficient Solutions for Radio Activation

Consider a wireless sensor network where each node has $K$ radios$r_1,r_2,\cdots,r_K$ such that the one hop reachability distance(resp. energy expended) of (resp. by) radio $r_i$ is greater than that of $r_j$, $1 \leq j < i \leq K$. Given such a network, the problem of energy efficient radio activation is to minimize the total energy spent by the active radios across all nodes in order to maintain a connected network. We show that this problem is NP-Hard. We initially pay attention to the case of $K=2$ and discuss a basic version of the radio activation problem in such networks. We propose approximation methodologies for solving this problem. Our analytical and experimental studies reveal that the greedy algorithm and the minimum spanning tree solution have the best {\em worst case} performance while the greedy algorithm has the best {\em average case} performance. To the best of our knowledge, this is one of the first few works to focus on %deterministic solutions for optimal radio activation in generic multi-radio wireless networks.