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We address the problem of efficient data gathering in a wireless networkthrough multi-hop communication. We focus on the objective of minimizing themaximum flow time of a data packet. We prove that no polynomial time algorithmfor this problem can have approximation ratio less than $\Omega(m^{1/3)$ when$m$ packets have to be transmitted, unless $P = NP$. We then use resourceaugmentation to assess the performance of a FIFO-like strategy. We prove thatthis strategy is 5-speed optimal, i.e., its cost remains within the optimalcost if we allow the algorithm to transmit data at a speed 5 times higher thanthat of the optimal solution we compare to.

Minimizing Flow Time in the Wireless Gathering Problem