Scheduling with Outliers
In classical scheduling problems, we are given jobs and machines, and have to schedule all the jobs to minimize some objective function. What if each job has a specified profit, and we are no longer required to process all jobs? Instead, we can schedule any subset of jobs whose total profit is at least a (hard) target profit requirement, while still trying to approximately minimize the objective function.
We refer to this class of problems as scheduling with outliers. This model was initiated by Charikar and Khuller (SODA ’06) for minimum max-response time in broadcast scheduling. In this paper, we consider three other well-studied scheduling objectives: the generalized assignment problem, average weighted completion time, and average flow time, for which LP-based approximation algorithms are provided. Our main results are:
For the minimum average flow time problem on identical machines, we give an LP-based logarithmic approximation algorithm for the unit profits case, and complement this result by presenting a matching integrality gap.
For the average weighted completion time problem on unrelated machines, we give a constant-factor approximation. The algorithm is based on randomized rounding of the time-indexed LP relaxation strengthened by knapsack-cover inequalities.
For the generalized assignment problem with outliers, we outline a simple reduction to GAP without outliers to obtain an algorithm whose makespan is within 3 times the optimum makespan, and whose cost is at most (1 + ε) times the optimal cost.
- Scheduling with Outliers
- Book Title
- Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
- Book Subtitle
- 12th International Workshop, APPROX 2009, and 13th International Workshop, RANDOM 2009, Berkeley, CA, USA, August 21-23, 2009. Proceedings
- pp 149-162
- Print ISBN
- Online ISBN
- Series Title
- Lecture Notes in Computer Science
- Series Volume
- Series ISSN
- Springer Berlin Heidelberg
- Copyright Holder
- Springer-Verlag Berlin Heidelberg
- Additional Links
- Industry Sectors
- eBook Packages
- Editor Affiliations
- 16. Dept. of Applied Math and Computer Science, The Weizmann Institute of Science
- 17. Institute for Computer Science and Applied Mathematics, University of Kiel
- 18. Technion, Computer Science Department
- 19. University of Geneva, Centre Universitaire d’Informatique
- Author Affiliations
- 20. Department of Computer Science, Carnegie Mellon University, USA
- 21. Department of Computer Science and Engineering, Indian Institute of Technology, New Delhi, India, 110016
- 22. Sloan School of Management, Massachusetts Institute of Technology, USA
To view the rest of this content please follow the download PDF link above.