@MISC{Krčál07aspecial, author = {Marek Krčál and et al.}, title = {A Special Case of Scheduling Unrelated Parallel Machines}, year = {2007} }

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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-hard 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 lower bound which works for restricted assignment, and which is still the state-of-the-art lower bound even for the most general case.