Abstract
We study the scheduling problem of makespan minimization with machine conflicts that arise in various settings, e.g., shared resources for pre- and post-processing of tasks or spatial restrictions. In this context, each job has a blocking time before and after its processing time, i.e., three parameters. Given a set of jobs, a set of machines, and a graph representing machine conflicts, the problem SchedulingWithMachineConflicts (smc), asks for a conflict-free schedule of minimum makespan in which the blocking times of no two jobs intersect on conflicting machines. We show that, unless P = NP, smc on m machines does not allow for a O(m1-e) -approximation algorithm for any e> 0, even in the case of identical jobs and every choice of fixed positive parameters, including the unit case. Complementary, we provide approximation algorithms when a suitable collection of independent sets is given. Finally, we present polynomial time algorithms to solve the problem for the case of unit jobs smc-Unit on special graph classes. As our main result, we solve smc-Unit for bipartite graphs by using structural insights for conflict graphs of star forests. As the set of active machines at each point in time induces a bipartite graph, the insights yield a local optimality criterion.
Original language | English |
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Title of host publication | Approximation and Online Algorithms - 20th International Workshop, WAOA 2022, Proceedings |
Editors | Parinya Chalermsook, Bundit Laekhanukit |
Publisher | Springer Verlag |
Pages | 36-60 |
Number of pages | 25 |
Volume | 13538 LNCS |
ISBN (Print) | 9783031183669 |
DOIs | |
Publication status | Published - 1 Jan 2022 |
Event | 20th International Workshop on Approximation and Online Algorithms - Potsdam, Germany Duration: 8 Sept 2022 → 9 Sept 2022 Conference number: 20 |
Publication series
Series | Lecture Notes in Computer Science |
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Volume | 13538 |
ISSN | 0302-9743 |
Workshop
Workshop | 20th International Workshop on Approximation and Online Algorithms |
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Abbreviated title | WAOA 2022 |
Country/Territory | Germany |
City | Potsdam |
Period | 8/09/22 → 9/09/22 |
Keywords
- Approximation algorithm
- Bipartite graph
- Inapproximability
- Machine conflict
- NP-hard
- Scheduling
- Star forest