Scheduling with conflicts: Online and offline algorithms

Guy Even*, Magnús M. Halldórsson, Lotem Kaplan, Dana Ron

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

45 Citations (Scopus)


We consider the following problem of scheduling with conflicts (swc): Find a minimum makespan schedule on identical machines where conflicting jobs cannot be scheduled concurrently. We study the problem when conflicts between jobs are modeled by general graphs. Our first main positive result is an exact algorithm for two machines and job sizes in {1,2}. For jobs sizes in {1,2,3}, we can obtain a {4}{3} -approximation, which improves on the {3}{2} -approximation that was previously known for this case. Our main negative result is that for jobs sizes in {1,2,3,4}, the problem is APX-hard. Our second contribution is the initiation of the study of an online model for swc, where we present the first results in this model. Specifically, we prove a lower bound of 2-\frac{1}{m} on the competitive ratio of any deterministic online algorithm for m machines and unit jobs, and an upper bound of 2 when the algorithm is not restricted computationally. For three machines we can show that an efficient greedy algorithm achieves this bound. For two machines we present a more complex algorithm that achieves a competitive ratio of 2-\frac{1}{7} when the number of jobs is known in advance to the algorithm.

Original languageEnglish
Pages (from-to)199-224
Number of pages26
JournalJournal of Scheduling
Issue number2
Publication statusPublished - Apr 2009

Other keywords

  • Approximation algorithms
  • Mutual exclusion scheduling
  • Online algorithms
  • Scheduling with conflicts


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