We address the problem of efficient data gathering in a wireless network through multi-hop communication. We focus on the objective of minimizing the maximum flow time of a data packet. We prove that no polynomial time algorithm for 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 resource augmentation to assess the performance of a FIFO-like strategy. We prove that this strategy is 5-speed optimal, i.e., its cost remains within the optimal cost if we allow the algorithm to transmit data at a speed 5 times higher than that of the optimal solution we compare to.
@InProceedings{bonifaci_et_al:LIPIcs.STACS.2008.1338, author = {Bonifaci, Vincenzo and Korteweg, Peter and Marchetti-Spaccamela, Alberto and Stougie, Leen}, title = {{Minimizing Flow Time in the Wireless Gathering Problem}}, booktitle = {25th International Symposium on Theoretical Aspects of Computer Science}, pages = {109--120}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-06-4}, ISSN = {1868-8969}, year = {2008}, volume = {1}, editor = {Albers, Susanne and Weil, Pascal}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2008.1338}, URN = {urn:nbn:de:0030-drops-13381}, doi = {10.4230/LIPIcs.STACS.2008.1338}, annote = {Keywords: Wireless networks, data gathering, approximation algorithms, distributed algorithms} }
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