Scheduling Fully Parallel Jobs with Integer Parallel Units

  • Vincent Chau
  • Minming Li
  • Kai Wang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10185)


We consider the following scheduling problem. We have m identical machines, where each machine can accomplish one unit of work at each time unit. We have a set of n jobs, where each job j has \(s_j\) units of workload, and each unit workload could be executed on any machine at any time unit. A job is said completed when its whole workload has been executed. The objective is to find a schedule that minimizes the total weighted completion time \(\sum w_j C_j\), where \(w_j\) is the weight of job j and \(C_j\) is the completion time of job j. We first give a PTAS of this problem when m is constant. Then we study the approximation ratio of a greedy algorithm, Largest-Ratio-First algorithm. Any permutation is a possible outcome of this algorithm when \(w_j = s_j\) for each job j, and for this special case we show that the approximation ratio depends on the instance size, i.e. n and m. Finally, when jobs have arbitrary weights, we prove that the upper bound of the approximation ratio is \(1 + \frac{m-1}{m+2}\).



We gratefully thank Gruia Cǎlinescu for our helpful discussions introducing the idea of the PTAS.


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of Computer ScienceCity University of Hong KongHong Kong SARChina

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