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Online Splitting Interval Scheduling on m Identical Machines

  • Feifeng Zheng
  • Bo Liu
  • Yinfeng Xu
  • E. Zhang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6124)

Abstract

This paper investigates online scheduling on m identical machines with splitting intervals, i.e., intervals can be split into pieces arbitrarily and processed simultaneously on different machines. The objective is to maximize the throughput, i.e., the total length of satisfied intervals. Intervals arrive over time and the knowledge of them becomes known upon their arrivals. The decision on splitting and assignment for each interval is made irrecoverably upon its arrival. We first show that any non-split online algorithms cannot have bounded competitive ratios if the ratio of longest to shortest interval length is unbounded. Our main result is giving an online algorithm ES (for Equivalent Split) which has competitive ratio of 2 and \(\frac{2m-1}{m-1}\) for m = 2 and m ≥ 3, respectively. We further present a lower bound of \(\frac{m}{m-1}\), implying that ES is optimal as m = 2.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Feifeng Zheng
    • 1
    • 2
    • 3
    • 4
  • Bo Liu
    • 1
  • Yinfeng Xu
    • 1
    • 2
    • 3
    • 4
  • E. Zhang
    • 5
  1. 1.School of ManagementXi’an JiaoTong UniversityXi’anChina
  2. 2.Ministry of Education Key Lab for Intelligent Networks and Network SecurityXi’anChina
  3. 3.Ministry of Education Key Lab for Process Control and Efficiency EngineeringXi’anChina
  4. 4.State Key Lab for Manufacturing Systems EngineeringXi’anChina
  5. 5.School of Information Management and EngineeringShanghai University of Finance and EconomicsShanghaiChina

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