A new average case analysis for completion time scheduling

Authors:
Mark Scharbrodt;Thomas Schickinger;Angelika Steger
Affiliations:
Technische Universität München, München, Germany;Technische Universität München, München, Germany;Technische Universität München, München, Germany
Venue:
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Year:
2002

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Abstract

(MATH) We present a new average case analysis for the problem of scheduling n jobs on $m$ machines so that the sum of job completion times is minimized. Our analysis transfers the concept of competitive analysis --- which is a typical worst case notion --- to the average case. We show that the classic SEPT scheduling strategy with &OHgr;(n) worst case competitive ratio achieves ${\cal O}(1)$ on the average. Moreover, bounds on the probability distribution of the competitive ratio are derived which provide an in-depth understanding of the stochastic version of the min sum scheduling problem.