Domination analysis for minimum multiprocessor scheduling

Authors:
Gregory Gutin;Tommy Jensen;Anders Yeo
Affiliations:
Department of Computer Science, Royal Holloway, University of London, Egham, Surrey, UK and Department of Computer Science, University of Haifa, Israel;Institut für Mathematik, Alpen-Adria-Universität Klagenfurt, Klagenfurt, Austria;Department of Computer Science, Royal Holloway, University of London, Egham, Surrey, UK
Venue:
Discrete Applied Mathematics
Year:
2006

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Abstract

Let P be a combinatorial optimization problem, and let A be an approximation algorithm for P. The domination ratio domr(A, s) is the maximal real q such that the solution x(I) obtained by A for any instance I of P of size s is not worse than at least the fraction q of the feasible solutions of I. We say that P admits an asymptotic domination ratio one (ADRO) algorithm if there is a polynomial time approximation algorithm A for P such that lims → ∞ domr(A, s) = 1. Alon, Gutin and Krivelevich [Algorithms with large domination ratio, J. Algorithms 50 (2004) 118-131] proved that the partition problem admits an ADRO algorithm. We extend their result to the minimum multiprocessor scheduling problem.