Approximation schemes for scheduling

Noga Alon*, Yossi Azar, Gerhard J. Woeginger, Tal Yadid

*Corresponding author for this work

Research output: Contribution to conferencePaperpeer-review


We consider the classic scheduling/load balancing problems where there are m identical machines and n jobs, and each job should be assigned to some machine. Traditionally, the assignment of jobs to machines is measured by the makespan (maximum load) i.e., the L norm of the assignment. An ε-approximation scheme was given by Hochbaum and Shmoys for minimizing the L norm. In several applications, such as in storage allocation, a more appropriate measure is the sum of the squares of the loads (which is equivalent to the L2 norm). This problem was considered in [4, 5, 13] who showed how to approximate the optimum value by a factor of about 1.04. In fact, a more general measure, which is the Lp norm (for any p≥1) can also be approximated to some constant which may be as large as 3/2. We improve these results by providing an ε-approximation scheme for the general Lp norm (and in particular for the L2 norm). We also consider the case of restricted assignment of unit jobs where we show how to find in polynomial time, a solution which is optimal for all norms.

Original languageEnglish
Number of pages8
StatePublished - 1997
EventProceedings of the 1996 8th Annual ACM-SIAM Symposium on Discrete Algorithms - New Orleans, LA, USA
Duration: 5 Jan 19977 Jan 1997


ConferenceProceedings of the 1996 8th Annual ACM-SIAM Symposium on Discrete Algorithms
CityNew Orleans, LA, USA


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