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Journal of Scheduling

, Volume 20, Issue 3, pp 279–292 | Cite as

A greedy approximation algorithm for minimum-gap scheduling

  • Marek Chrobak
  • Uriel Feige
  • Mohammad Taghi Hajiaghayi
  • Sanjeev Khanna
  • Fei Li
  • Seffi Naor
Article
  • 273 Downloads

Abstract

We consider scheduling of unit-length jobs with release times and deadlines, where the objective is to minimize the number of gaps in the schedule. Polynomial-time algorithms for this problem are known, yet they are rather inefficient, with the best algorithm running in time \(O(n^4)\) and requiring \(O(n^3)\) memory. We present a greedy algorithm that approximates the optimum solution within a factor of 2 and show that our analysis is tight. Our algorithm runs in time \(O(n^2 \log n)\) and needs only O(n) memory. In fact, the running time is \(O(n (g^*+1)\log n)\), where \(g^*\) is the minimum number of gaps.

Keywords

Scheduling Approximation algorithms Greedy algorithms 

Notes

Acknowledgments

Marek Chrobak has been supported by the National Science Foundation grants CCF-1217314, CCF-1536026, and OISE-1157129. Mohammad Taghi Hajiaghayi has been supported in part by the National Science Foundation CAREER award 1053605, Office of Naval Research YIP award N000141110662, and a University of Maryland Research and Scholarship Award (RASA). Fei Li has been supported by the National Science Foundation grants CCF-0915681 and CCF-1216993.

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Marek Chrobak
    • 1
  • Uriel Feige
    • 2
  • Mohammad Taghi Hajiaghayi
    • 3
  • Sanjeev Khanna
    • 4
  • Fei Li
    • 5
  • Seffi Naor
    • 6
  1. 1.Department of Computer Science and EngineeringUniversity of CaliforniaRiversideUSA
  2. 2.Department of Computer Science and Applied MathematicsThe Weizmann InstituteRehovotIsrael
  3. 3.Computer Science DepartmentUniversity of MarylandCollege ParkUSA
  4. 4.Department of Computer and Information ScienceUniversity of PennsylvaniaPhiladelphiaUSA
  5. 5.Department of Computer ScienceGeorge Mason UniversityFairfaxUSA
  6. 6.Computer Science DepartmentTechnionHaifaIsrael

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