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Graph balancing: a special case of scheduling unrelated parallel machines

Published:20 January 2008Publication History

ABSTRACT

We design a 1.75-approximation algorithm for a special case of scheduling parallel machines to minimize the makespan, namely the case where each job can be assigned to at most two machines with the same processing time on either machine. (This is a special case of so-called restricted assignment, where the set of eligible machines can be arbitrary for each job.) We also show that even for this special case it is NP-hart to compute better than 1.5 approximation.

This is the first improvement of the approximation ratio 2 of Lenstra, Shmoys, and Tardos [Approximation algorithms for scheduling unrelated parallel machines, Math. Program. 46:259--271, 1990], for any special case with unbounded number of machines. Our lower bound yields the same ratio as their bound which works for restricted assignment, and which is still the state-of-the-art lower bound even for the most general case.

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  1. Graph balancing: a special case of scheduling unrelated parallel machines

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              • Published in

                cover image ACM Conferences
                SODA '08: Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
                January 2008
                1289 pages
                • Program Chair:
                • Shang-Hua Teng

                Publisher

                Society for Industrial and Applied Mathematics

                United States

                Publication History

                • Published: 20 January 2008

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                • research-article

                Acceptance Rates

                Overall Acceptance Rate411of1,322submissions,31%

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