Bicriteria Parallel Task Scheduling. In proceedings of the 2nd Multidisciplinary International Conference on Scheduling : Theory and Applications (MISTA 2005), 18 -21 July 2005, New York, USA, pages 585-596, 2005.

Paper

In this paper, we study the problem of scheduling on k identical machines a set of parallel tasks with release dates and deadlines in order to optimize simultaneously two conflicting criteria, namely the Size (number of scheduled tasks) and the Weight (sum of the weight of scheduled tasks). We distinguish two variants of the problem: In the first one, tasks have to be scheduled in a contiguous subset of machines, whereas in the second one, they can be scheduled on any subset of machines. In both variants, we show that if the maximal number of required machines is greater than k/2 then there are no (alpha, beta)-approximate schedule for any two constants alpha and beta. Nevertheless, if the number of required machines is no more than k/2 then we propose a (3*alpha, 3*beta) -approximation algorithm for the contiguous case and a (6*alpha, 6*beta) -approximation for the non-contiguous case, where alpha (resp. beta) denotes the approximation ratio of a monocriterion algorithm maximizing the Size (resp. the Weight).

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@INPROCEEDINGS{2005-585-596-P, author = {F. Baille and E. Bampis and C. Laforest and C. Rapine},

title = {Bicriteria Parallel Task Scheduling},

booktitle = {In proceedings of the 2nd Multidisciplinary International Conference on Scheduling : Theory and Applications (MISTA 2005), 18 -21 July 2005, New York, USA},

year = {2005},

editor = {G. Kendall and L. Lei and M. Pinedo},

pages = {585--596},

note = {Paper},

abstract = {In this paper, we study the problem of scheduling on k identical machines a set of parallel tasks with release dates and deadlines in order to optimize simultaneously two conflicting criteria, namely the Size (number of scheduled tasks) and the Weight (sum of the weight of scheduled tasks). We distinguish two variants of the problem: In the first one, tasks have to be scheduled in a contiguous subset of machines, whereas in the second one, they can be scheduled on any subset of machines. In both variants, we show that if the maximal number of required machines is greater than k/2 then there are no (alpha, beta)-approximate schedule for any two constants alpha and beta. Nevertheless, if the number of required machines is no more than k/2 then we propose a (3*alpha, 3*beta) -approximation algorithm for the contiguous case and a (6*alpha, 6*beta) -approximation for the non-contiguous case, where alpha (resp. beta) denotes the approximation ratio of a monocriterion algorithm maximizing the Size (resp. the Weight).},

owner = {Faizah Hamdan},

timestamp = {2012.05.21},

webpdf = {2005-585-596-P.pdf} }