**Post: #1**

RATE ALLOCATION & NETWORK LIFETIME PROBLEM FOR WIRELESS SENSOR NETWORKS

Abstract: In this paper, we consider an overarching problem that encompasses both performance metrics. In particular, we study the network capacity problem under a given network lifetime requirement. Specifically, for a wireless sensor network where each node is provisioned with an initial energy, if all nodes are required to live up to a certain lifetime criterion, Since the objective of maximizing the sum of rates of all the nodes in the network can lead to a severe bias in rate allocation among the nodes, we advocate the use of lexicographical max-min (LMM) rate allocation. To calculate the LMM rate allocation vector, we develop a polynomial-time algorithm by exploiting the parametric analysis (PA) technique from linear program (LP), which we call serial LP with Parametric Analysis (SLP-PA). We show that the SLP-PA can be also employed to address the LMM node lifetime problem much more efficiently than a state-of-the-art algorithm proposed in the literature. More important, we show that there exists an elegant duality relationship between the LMM rate allocation problem and the LMM node lifetime problem. Therefore, it is sufficient to solve only one of the two problems. Important insights can be obtained by inferring duality results for the other problem.