Minimizing Average Flow Time on Unrelated Machines
Approximation and Online Algorithms
Proceedings of the forty-first annual ACM symposium on Theory of computing
On scheduling in map-reduce and flow-shops
Proceedings of the twenty-third annual ACM symposium on Parallelism in algorithms and architectures
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We consider the problem of minimizing flow-time in the unrelatedmachines setting. We introduce a notion of(α,β) variability to capture settingswhere processing times of jobs on machines are not completelyarbitrary and give anO(βlogα) approximation forthis setting. As special cases, we get (1) anO(k) approximation when there are only kdifferent processing times (2) anO(logP)-approximation if each job can only go ona specified subset of machines, but has the same processingrequirement on each such machine. Further, the machines can havedifferent speeds. Here P is the ratio of the largest tothe smallest processing requirement, (3) an O(1/εlog 1/ε)- approximation algorithm for unrelated machines ifwe assume that our algorithm has machines which are anε-factor faster than the optimum algorithm'smachines. We also improve the lower bound on the approximabilityfor the problem of minimizing flow time on parallel machines from$\Omega(\sqrt{\log P/ \log\log P})$ toΩ(log1-ε P) forany ε 0.