Convex programming for scheduling unrelated parallel machines

Yossi Azar, Amir Epstein

Research output: Contribution to journalConference articlepeer-review

Abstract

We consider the classical problem of scheduling parallel unrelated machines. Each job is to be processed by exactly one machine. Processing job j on machine i requires time Pij. The goal is to find a schedule that minimizes the ℓp norm. Previous work showed a 2-approximation algorithm for the problem with respect to the ℓ norm. For any fixed ℓp norm the previously known approximation algorithm has a performance of θ(p). We provide a 2-approximation algorithm for any fixed ℓp norm (p > 1). This algorithm uses convex programming relaxation. We also give a √2-approximation algorithm for the ℓ 2 norm. This algorithm relies on convex quadratic programming relaxation. To the best of our knowledge, this is the first time that general convex programming techniques (apart from SDPs and CQPs) are used in the area of scheduling. We show for any given ℓp norm a PTAS for any fixed number of machines. We also consider the multidimensional generalization of the problem in which the jobs are d-dimensional. Here the goal is to minimize the ℓp norm of the generalized load vector, which is a matrix where the rows represent the machines and the columns represent the jobs dimension. For this problem we give a (d+l)-approximation algorithm for any fixed ℓp norm (P > 1).

Original languageEnglish
Pages (from-to)331-337
Number of pages7
JournalProceedings of the Annual ACM Symposium on Theory of Computing
DOIs
StatePublished - 2005
Event13th Color Imaging Conference: Color Science, Systems, Technologies, and Applications - Scottsdale, AZ, United States
Duration: 7 Nov 200511 Nov 2005

Keywords

  • Approximation algorithms
  • Convex programming
  • Randomized algorithms
  • Scheduling unrelated parallel machines

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