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Real-Time Scheduling with a Budget

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Automata, Languages and Programming (ICALP 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2719))

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Abstract

Suppose that we are given a set of jobs, where each job has a processing time, a non-negative weight, and a set of possible time intervals in which it can be processed. In addition, each job has a processing cost. Our goal is to schedule a feasible subset of the jobs on a single machine, such that the total weight is maximized, and the cost of the schedule is within a given budget. We refer to this problem as budgeted real-time scheduling (BRS). Indeed, the special case where the budget is unbounded is the well-known real-time scheduling problem. The second problem that we consider is budgeted real-time scheduling with overlaps (BRSO), in which several jobs may be processed simultaneously, and the goal is to maximize the time in which the machine is utilized. Our two variants of the real-time scheduling problem have important applications, in vehicle scheduling, linear combinatorial auctions and QoS management for Internet connections. These problems are the focus of this paper.

Both BRS and BRSO are strongly NP-hard, even with unbounded budget. Our main results are (2 + ε)-approximation algorithms for these problems. This ratio coincides with the best known approximation factor for the (unbudgeted) real-time scheduling problem, and is slightly weaker than the best known approximation factor of e/(e − 1) for the (unbudgeted) real-time scheduling with overlaps, presented in this paper. We show that better ratios (or simpler approximation algorithms) can be derived for some special cases, including instances with unit-costs and the budgeted job interval selection problem (JISP). Budgeted JISP is shown to be APX-hard even when overlaps are allowed and with unbounded budget. Finally, our results can be extended to instances with multiple machines.

On leave from the Computer Science Dept., Technion, Haifa 32000, Israel.

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Author information

Authors and Affiliations

  1. Computer Science Dept., Technion, Haifa, 32000, Israel

    Joseph Seffi Naor

  2. Lucent Technologies, Bell Labs, 600 Mountain Ave., Murray Hill, NJ, 07974

    Hadas Shachnai

  3. Dept. of Computer Science and Eng., Univ. of Washington, Box 352350, Seattle, WA, 98195

    Tami Tamir

Authors
  1. Joseph Seffi Naor
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  2. Hadas Shachnai
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  3. Tami Tamir
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Editor information

Editors and Affiliations

  1. Dept. of Mathematics and Computer Science, Technische Universiteit Eindhoven, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands

    Jos C. M. Baeten

  2. School of Industrial and Systems Engineering, Georgia Institute of Technology, 765 Ferst Drive, Atlanta, GA, 30332-0205, USA

    Jan Karel Lenstra

  3. Department of Information Technology, Uppsala University, P.O. Box 337, 75105, Uppsala, Sweden

    Joachim Parrow

  4. Faculty of Electrical Engineering, Mathematics and Computer Science, University of Twente, P.O. Box 217, 7500 AE, Enschede, The Netherlands

    Gerhard J. Woeginger

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© 2003 Springer-Verlag Berlin Heidelberg

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Naor, J.S., Shachnai, H., Tamir, T. (2003). Real-Time Scheduling with a Budget. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds) Automata, Languages and Programming. ICALP 2003. Lecture Notes in Computer Science, vol 2719. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45061-0_86

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  • DOI: https://doi.org/10.1007/3-540-45061-0_86

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  • Print ISBN: 978-3-540-40493-4

  • Online ISBN: 978-3-540-45061-0

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