A Lower Bound for the On-Line Preemptive Machine Scheduling with lpNorm

Authors:
Tianping Shuai;Donglei Du
Affiliations:
School of Science, Beijing University of Posts and Telecommunications, China;Faculty of Business Administration, University of New Brunswick, Canada
Venue:
COCOON '08 Proceedings of the 14th annual international conference on Computing and Combinatorics
Year:
2008

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Abstract

We consider the on-line version of the preemptive schedulingproblem that minimizes the machine completion time vector in thelpnorm (a direct extension ofthe l∞norm: the makespan) on mparallel identical machines. We present a lower bound on thecompetitive ratio of any randomized on-line algorithm with respectto the general lpnorm. Thislower bound amounts to calculating a (non-convex) mathematicalprogram and generalizes the existing result on makespan. Whilesimilar technique has been utilized to provide the best possiblelower bound for makespan, the proposed lower bound failed toachieve the best possible lower bound for general lpnorm (though very close), and hence revealingintricate and essential difference between the generallpnorm and the makespan.