Polynomial time approximation schemes for general multiprocessor job shop scheduling
Journal of Algorithms
On rectangle packing: maximizing benefits
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
A faster combinatorial approximation algorithm for scheduling unrelated parallel machines
Theoretical Computer Science
Santa Claus schedules jobs on unrelated machines
Proceedings of the forty-third annual ACM symposium on Theory of computing
Approximation Algorithms for Scheduling Parallel Jobs
SIAM Journal on Computing
A faster combinatorial approximation algorithm for scheduling unrelated parallel machines
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Approximation algorithms for min-max and max-min resource sharing problems, and applications
Efficient Approximation and Online Algorithms
Rectangle packing with one-dimensional resource augmentation
Discrete Optimization
Geometric quadrisection in linear time, with application to VLSI placement
Discrete Optimization
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We consider the problem of schedulingn independent jobs onm unrelated parallel machines where each job has to be processed by exactly one machine, processing jobj on machinei requiresp ijtime units, and the objective is to minimize the makespan, i.e., the maximum job completion time. Focusing on the case whenm is fixed, we present for both preemptive and nonpreemptive variants of the problem fully polynomial approximation schemes whose running times depend only linearly onn. We also study an extension of the problem where processing jobj on machinei incurs a cost ofc ij , and thus there are two optimization criteria: makespan and cost. We show that, for any fixedm, there is a fully polynomial approximation scheme that, given valuesT andC, computes for any fixed e > 0 a schedule in0( n) time with makespan at most (1 + e) T and cost at most (1 + e) C, if there exists a schedule of makespanT and costC.