Skip to main content
Log in

On Approximating a Scheduling Problem

  • Published:
Journal of Combinatorial Optimization Aims and scope Submit manuscript

Abstract

Given a set of communication tasks (best described in terms of a weighted bipartite graph where one set of nodes denotes the senders, the other set the receivers, edges are communication tasks, and the weight of an edge is the time required for transmission), we wish to minimize the total time required for the completion of all communication tasks assuming that tasks can be preempted (that is, each edge can be subdivided into many edges with weights adding up to the edge's original weight) and that preemption comes with a cost. In this paper, we first prove that one cannot approximate this problem within a factor smaller than \(\frac{7}{6}\) unless P=NP. It is known that a simple approximation algorithm achieves within a ratio of two (H. Choi and S.L. Hakimi, Algorithmica, vol. 3, pp. 223–245, 1988). However, our experimental results show that its performance is worse than the originally proposed heuristic algorithm (I.S. Gopal and C.K. Wong, IEEE Transactions on Communications, vol. 33, pp. 497–501, 1985). We devise a more sophisticated algorithm, called the potential function algorithm which, on the one hand, achieves a provable approximation ratio of two, and on the other hand, shows very good experimental performance. Moreover, the way in which our more sophisticated algorithm derives from the simple one, suggests a hierarchy of algorithms, all of which have a worst-case performance at most two, but which we suspect to have increasingly better performance, both in worst case and with actual instances.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • G. Bongiovanni, D. Coppersmith, and C.K. Wong, “An optimal time slot assignment algorithm for an SS/TDMA system wit variable number of transponders,” IEEE Trans. on Communications, vol. 29, pp. 721-726, 1981.

    Google Scholar 

  • H. Choi and S.L. Hakimi, “Data transfers in networks,” Algorithmica, vol. 3, pp. 223-245, 1988.

    Google Scholar 

  • E.G. Coffman, Jr., M.R. Garey, D.S. Johnson, and A.S. Lapaugh, “Scheduling file transfers,” SIAM J. Comput., vol. 14, pp. 744-780, 1985.

    Google Scholar 

  • S. Even, A. Itai, and A. Shamir, “On the complexity of timetable and multicommodity flow problems,” SIAM J. Comput., vol. 5, pp. 691-703, 1976.

    Google Scholar 

  • I.S. Gopal and C.K. Wong, “Minimizing the number of switchings in an SS/TDMA system,” IEEE Trans. on Communications, vol. 33, pp. 497-501, 1985.

    Google Scholar 

  • M. Goudreau, K. Lang, S.B. Rao, T. Suel, and T. Tsantilas, “Towards efficiency and portability: Programming with the BSP model,” in Proc. SPAA, pp. 1-12, 1996.

  • E.L. Lawler and J. Labetoulle, “On preemptive scheduling of unrelated parallel processors by linear programming,” J. ACM, vol. 25, pp. 612-619, 1978.

    Google Scholar 

  • L.G. Valiant, “A bridging model for parallel computation,” Comm. ACM, vol. 33, pp. 103-111, 1990.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Crescenzi, P., Deng, X. & Papadimitriou, C.H. On Approximating a Scheduling Problem. Journal of Combinatorial Optimization 5, 287–297 (2001). https://doi.org/10.1023/A:1011441109660

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1011441109660

Navigation