On the parameterized complexity of interval scheduling with eligible machine sets

Danny Hermelin, Yuval Itzhaki, Hendrik Molter, Dvir Shabtay

Research output: Contribution to journalArticlepeer-review


We provide new parameterized complexity results for INTERVAL SCHEDULING ON ELIGIBLE MACHINES. In this problem, a set of n jobs is given to be processed non-preemptively on a set of m machines. Each job has a processing time, a deadline, a weight, and a set of eligible machines that can process it. The goal is to find a maximum weight subset of jobs that can each be processed on one of its eligible machines such that it completes exactly at its deadline. We focus on two parameters: The number m of machines, and the largest processing time pmax. Our main contribution is showing W[1]-hardness when parameterized by m. This answers Open Problem 8 of Mnich and van Bevern's list of 15 open problems in parameterized complexity of scheduling problems [Computers & Operations Research, 2018]. Furthermore, we show NP-hardness even when pmax=O(1) and present an FPT-algorithm with for the combined parameter m+pmax.

Original languageEnglish
Article number103533
JournalJournal of Computer and System Sciences
StatePublished - 1 Sep 2024


  • Eligible machine sets
  • Fixed-parameter tractability
  • Interval scheduling
  • Just-in-time scheduling
  • W[1]-hardness

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science
  • Computer Networks and Communications
  • Computational Theory and Mathematics
  • Applied Mathematics


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