Abstract
We give three results related to online nonclairvoyant speed scaling to minimize total flow time plus energy. We give a nonclairvoyant algorithm LAPS, and show that for every power function of the form P(s)=s α, LAPS is O(1)-competitive; more precisely, the competitive ratio is 8 for α=2, 13 for α=3, and \(\frac{2\alpha^{2}}{\ln\alpha}\) for α>3. We then show that there is no constant c, and no deterministic nonclairvoyant algorithm A, such that A is c-competitive for every power function of the form P(s)=s α. So necessarily the achievable competitive ratio increases as the steepness of the power function increases. Finally we show that there is a fixed, very steep, power function for which no nonclairvoyant algorithm can be O(1)-competitive.
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This work of H.L. Chan was done when he was a postdoc in University of Pittsburgh. T.W. Lam is partially supported by HKU Grant 7176104. J. Edmonds supported in part by NSERC Canada. A. Marchetti-Spaccamela supported in part by MIUR FIRB grant RBIN047MH9 and by EU ICT-FET grant 215270 FRONTS. K. Pruhs supported in part by an IBM faculty award, and by NSF grants CNS-0325353, CCF-0514058, IIS-0534531, and CCF-0830558.
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Chan, HL., Edmonds, J., Lam, TW. et al. Nonclairvoyant Speed Scaling for Flow and Energy. Algorithmica 61, 507–517 (2011). https://doi.org/10.1007/s00453-010-9420-2
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DOI: https://doi.org/10.1007/s00453-010-9420-2