Advertisement

Scheduling Jobs with Multiple Non-uniform Tasks

  • Venkatesan T. Chakaravarthy
  • Anamitra Roy Choudhury
  • Sambuddha Roy
  • Yogish Sabharwal
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8097)

Abstract

This paper considers the problem of maximizing the throughput of jobs wherein each job consists of multiple tasks. Consider a system offering a uniform capacity of a resource (say unit bandwidth). We are given a set of jobs, each consisting of a sequence of at most r tasks. Each task is associated with a window (specified by a release time and a deadline) within which it can be scheduled; each task also has a processing time and a bandwidth requirement. Each job has a profit associated with it. A feasible solution must choose a subset of jobs and schedule all the tasks for these jobs such that at any point of time, the total bandwidth requirement does not exceed the capacity of the resource; furthermore, the schedule must obey the precedence constraints (tasks of a job must be scheduled in order of the input sequence). The goal is to compute the feasible solution having maximum profit.

Prior work has studied the problem without the notion of windows; furthermore, the algorithms presented therein require that the bandwidths of all the tasks of a job are uniform. Under these two restrictions, O(r)-approximation algorithms are known. Our main result presents an O(r)-approximation algorithm for the general case wherein tasks can have windows and bandwidths of tasks within the same job may be non-uniform.

Keywords

Feasible Solution Approximation Algorithm Precedence Constraint Bandwidth Requirement Bandwidth Constraint 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Bafna, V., Narayanan, B., Ravi, R.: Nonoverlapping local alignments (weighted independent sets of axis-parallel rectangles). Discrete Applied Math. 71(1-3), 41–53 (1996)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Bar-Noy, A., Bar-Yehuda, R., Freund, A., Naor, J., Schieber, B.: A unified approach to approximating resource allocation and scheduling. J. of the ACM 48(5), 1069–1090 (2001)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Bar-Yehuda, R., Halldórsson, M., Naor, J., Shachnai, H., Shapira, I.: Scheduling split intervals. SIAM Journal of Computing 36(1), 1–15 (2006)zbMATHCrossRefGoogle Scholar
  4. 4.
    Bar-Yehuda, R., Rawitz, D.: Using fractional primal-dual to schedule split intervals with demands. In: Brodal, G.S., Leonardi, S. (eds.) ESA 2005. LNCS, vol. 3669, pp. 714–725. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  5. 5.
    Berman, P., DasGupta, B., Muthukrishnan, S.: Simple approximation algorithm for nonoverlapping local alignments. In: SODA (2002)Google Scholar
  6. 6.
    Bonsma, P., Schulz, J., Wiese, A.: A constant factor approximation algorithm for unsplittable flow on paths. In: FOCS (2011)Google Scholar
  7. 7.
    Calinescu, G., Chakrabarti, A., Karloff, H., Rabani, Y.: Improved approximation algorithms for resource allocation. In: Cook, W.J., Schulz, A.S. (eds.) IPCO 2002. LNCS, vol. 2337, pp. 401–414. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  8. 8.
    Chakrabarti, A., Chekuri, C., Gupta, A., Kumar, A.: Approximation algorithms for the unsplittable flow problem. Algorithmica 47(1), 53–78 (2007)MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Chekuri, C., Khanna, S.: On multidimensional packing problems. SIAM J. Comput. 33(4), 837–851 (2004)MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    Grötschel, M., Lovász, L., Schrijver, A.: Geometric Algorithms And Combinatorial Optimization. Springer (1993)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Venkatesan T. Chakaravarthy
    • 1
  • Anamitra Roy Choudhury
    • 1
  • Sambuddha Roy
    • 1
  • Yogish Sabharwal
    • 1
  1. 1.IBM Research - IndiaNew DelhiIndia

Personalised recommendations