We consider the problem of maximizing the lifetime of a given multicast connection in a wireless network of energy-constrained (e.g. battery-operated) nodes, by choosing ideal transmission power levels for the nodes relaying the connection. We distinguish between two basic operating modes: In a static assignment, the power levels of the nodes are set at the beginning and remain unchanged until the nodes are depleted of energy. In a dynamic assignment, the powers can be adjusted during operation.We show that lifetime-maximizing static power assignments can be found in polynomial time, whereas for dynamic assignments, a quantized-time version of the problem is NP-hard. We then study the approximability of the quantized dynamic case and conclude that no polynomial time approximation scheme (PTAS) exists for the problem unless Ptime = NP. Finally, by considering two approximation heuristics for the dynamic case, we show experimentally that the lifetime of a dynamically maintained multicast connection can be made several times longer than what can be achieved by the best possible static assignment.
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