Given a wireless network G = (V , E), we consider a maximum critical energy problem [J. Park, S. Sahni, Maximum lifetime broadcasting in wireless networks, IEEE Transactions on Computers 54 (9) (2005) 1081-1090] that has an objective of increasing the chances of doing a sequence of broadcasts. We present an optimal generalized solution algorithm running in improved optimal O(|V | + |E|) time, where V stands for a set of nodes and E stands for a set of links in the network. Our approach is

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... able in an omnidirectional antenna model and can be used to solve the problem of multicasting traffic so as to maximize the lifetime of the network [A. Orda, B.-A. Yassour, Maximum-lifetime routing algorithms for networks with omnidirectional and directional antennas, in: Proc. ACM MOBIHOC, 2005] and a data gathering problem [K. Kalpakis, K. Dasgupta, P. Namjoshi, Maximum lifetime data gathering and aggregation in wireless sensor networks, Computer Networks 42 (2003) 697-716; Y. Xue, Y. Cui, K. Nahrstedt, Maximizing lifetime for data aggregation in wireless sensor networks, ACM Moble Networks and Applications 10 (6) (2005) 853-864] with an improved running time.