A Network-flow based Integral Optimal Algorithm for Lexicographic Maximum Lifetime Routing in Wireless Sensor Networks

Longevity is one the key design goals in the wireless sensor networks. In many applications, longevity of all the sensor nodes in the network is equally important. Therefore, it is imperative to design network protocols that would keep the maximum number of nodes alive for longest possible duration. Towards this goal we study the lexicographic maximum lifetime (Lex-max-life) routing scheme. The objective of Lex-max-life routing is to maximize the time until the lirst set of sensor nodes deplete their battery energies (among all the nodes), then maximize the depletion time for the second set of sensor nodes if the depletion time for the first set of nodes is as long as possible, and then maximize the depletion time for the third set of nodes if the depletion times for the first and second set of nodes are as long as possible and so on. In our previous work by M. Patel et al. (2006), we have shown that if sensor nodes are equipped with non-adaptive transmitters then the Lex-max-life routing problem can be reduced to a min-cost flow or a convex-cost flow problem using a novel cost scaling technique. Hence, we obtain an integral optimal solution in polynomial time. However, the cost scaling technique is not suitable for large problem instances because the cost numbers grow very fast. In this paper, we propose a novel vectorial representation of link costs. The Lex-max-life routing problem is solved by a vectorial version of min-cost flow or convex-cost flow algorithm which (i) Improves running time complexity and (ii) Circumvents the number explosion phenomenon. Thus, developed algorithm is computationally very efficient, scalable and easy to implement.