Interval Selection with Machine-Dependent Intervals

Katerina Böhmová, Yann Disser, Matús Mihalák, Peter Widmayer

Research output: Chapter in Book/Report/Conference proceedingConference article in proceedingAcademicpeer-review


We study an offline interval scheduling problem where every job has exactly one associated interval on every machine. To schedule a set of jobs, exactly one of the intervals associated with each job must be selected, and the intervals selected on the same machine must not intersect. We show that deciding whether all jobs can be scheduled is np-complete already in various simple cases. In particular, by showing the np-completeness for the case when all the intervals associated with the same job end at the same point in time (also known as just-in-time jobs), we solve an open problem posed by sung and vlach (j. Sched., 2005). We also study the related problem of maximizing the number of scheduled jobs. We prove that the problem is np-hard even for two machines and unit-length intervals. We present a 2/3-approximation algorithm for two machines (and intervals of arbitrary lengths).
Original languageEnglish
Title of host publicationProc. 13 th International Symposium on Algorithms and Data Structures (WADS)
PublisherSpringer Verlag
Number of pages12
Publication statusPublished - 2013

Publication series

SeriesLecture Notes in Computer Science

Cite this

Böhmová, K., Disser, Y., Mihalák, M., & Widmayer, P. (2013). Interval Selection with Machine-Dependent Intervals. In Proc. 13 th International Symposium on Algorithms and Data Structures (WADS) (pp. 170-181). Springer Verlag. Lecture Notes in Computer Science, Vol.. 8037