Online interval scheduling on two related machines: the power of lookahead

Nicolas Pinson, Frits C.R. Spieksma (Corresponding author)

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We consider an online interval scheduling problem on two related machines. If one machine is at least as twice as fast as the other machine, we say the machines are distinct; otherwise the machines are said to be similar. Each job j∈ J is characterized by a length pj, and an arrival time tj; the question is to determine whether there exists a feasible schedule such that each job starts processing at its arrival time. For the case of unit-length jobs, we prove that when the two machines are distinct, there is an amount of lookahead allowing an online algorithm to solve the problem. When the two machines are similar, we show that no finite amount of lookahead is sufficient to solve the problem in an online fashion. We extend these results to jobs having arbitrary lengths, and consider an extension focused on minimizing total waiting time.

Original languageEnglish
Pages (from-to)224-253
Number of pages30
JournalJournal of Combinatorial Optimization
Issue number1
Early online date9 Jan 2019
Publication statusPublished - 15 Jul 2019


  • Competitive ratio
  • Interval scheduling
  • Lookahead
  • Online algorithms


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