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Improved Bounds for Scheduling Conflicting Jobs with Minsum Criteria
"... We consider a general class of scheduling problems where a set of conflicting jobs needs to be scheduled (preemptively or nonpreemptively) on a set of machines so as to minimize the weighted sum of completion times. The conflicts among the jobs are formed as an arbitrary conflict graph. Building on ..."
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Cited by 5 (2 self)
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We consider a general class of scheduling problems where a set of conflicting jobs needs to be scheduled (preemptively or nonpreemptively) on a set of machines so as to minimize the weighted sum of completion times. The conflicts among the jobs are formed as an arbitrary conflict graph. Building on the framework of Queyranne and Sviridenko (J. of Scheduling, 5:287305, 2002), we present a general technique for reducing the weighted sum of completion times problem to the classical makespan minimization problem. Using this technique, we improve the best known results for scheduling conflicting jobs with minsum objective, on several fundamental classes of graphs, including line graphs, (k +1)claw free graphs and perfect graphs. In particular, we obtain the first constant factor approximation ratio for nonpreemptive scheduling on interval graphs. We also improve the results of Kim (SODA 2003, 97–98) for scheduling jobs on line graphs and for resourceconstrained scheduling.
Min sum edge coloring in multigraphs via configuration LP
 In Proc. of IPCO’08, LNCS
, 2008
"... We consider the scheduling of biprocessor jobs under sum objective (BPSMS). Given a collection of unitlength jobs where each job requires the use of two processors, find a schedule such that no two jobs involvingthe same processorrun concurrently. The objectiveis to minimize the sum of the completi ..."
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Cited by 2 (1 self)
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We consider the scheduling of biprocessor jobs under sum objective (BPSMS). Given a collection of unitlength jobs where each job requires the use of two processors, find a schedule such that no two jobs involvingthe same processorrun concurrently. The objectiveis to minimize the sum of the completion times of the jobs. Equivalently, we would like to find a sum edge coloring of a given multigraph, i.e. a partition of its edge set into matchings M1,...,Mt minimizing ∑ t i=1 iMi. This problem is APXhard, even in the case of bipartite graphs [M04]. This special case is closely related to the classic open shop scheduling problem. We give a 1.8298approximation algorithm for BPSMS improving the previously best ratio known of 2 [BBH + 98]. The algorithm combines a configuration LP with greedy methods, using nonstandard randomized rounding on the LP fractions. We also give an efficient combinatorial 1.8886approximation algorithm for the case of simple graphs. Keywords: Edge Scheduling, Configuration LP, Approximation Algorithms 1
Sum Edge Colorings of Multigraphs . . .
"... We consider the scheduling of biprocessor jobs under sum objective (BPSMS). Given a collection of unitlength jobs where each job requires the use of two processors, find a schedule such that no two jobs involving the same processor run concurrently. The objective is to minimize the sum of the compl ..."
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We consider the scheduling of biprocessor jobs under sum objective (BPSMS). Given a collection of unitlength jobs where each job requires the use of two processors, find a schedule such that no two jobs involving the same processor run concurrently. The objective is to minimize the sum of the completion times of the jobs. Equivalently, we would like to find a sum edge coloring of a given multigraph, i.e. a partition of its edge set into matchings M1,..., Mt minimizing Pt i=1 iMi. This problem is APXhard, even in the case of bipartite graphs [Marx 2009]. This special case is closely related to the classic open shop scheduling problem. We give a 1.8298approximation algorithm for BPSMS improving the previously best ratio known of 2 [BarNoy et al. 1998]. The algorithm combines a configuration LP with greedy methods, using nonstandard randomized rounding on the LP fractions. We also give an efficient combinatorial 1.8886approximation algorithm for the case of simple graphs, which gives an improved 1.79568 + O(log d/d)approximation