On the Configuration-LP for Scheduling on Unrelated Machines
| dc.contributor.author | Verschae, José | |
| dc.contributor.author | Wiese, Andreas | |
| dc.date.accessioned | 2021-12-17T10:08:45Z | |
| dc.date.available | 2021-12-17T10:08:45Z | |
| dc.date.issued | 2010 | |
| dc.description.abstract | One of the most important open problems in machine scheduling is the problem of scheduling a set of jobs on unrelated machines to minimize the makespan. The best known approximation algorithm for this problem guarantees an approximation factor of 2. It is known to be NP-hard to approximate with a better ratio than 3/2. Closing this gap has been open for over 20 years. The best known approximation factors are achieved by LP-based algorithms. The strongest known linear program formulation for the problem is the configuration-LP. We show that the configuration-LP has an integrality gap of 2 even for the special case of unrelated graph balancing, where each job can be assigned to at most two machines. In particular, our result implies that a large family of cuts does not help to diminish the integrality gap of the canonical assignment-LP. Also, we present cases of the problem which can be approximated with a better factor than 2. They constitute valuable insights for constructing an NP-hardness reduction which improves the known lowerbound. Very recently Svensson [22] studied the restricted assignment case, where each job can only be assigned to a given set of machines on which it has the same processing time. He shows that in this setting the configuration-LP has an integrality gap of 33/17≈1.94. Hence, our result imply that the unrelated graph balancing case is significantly more complex than the restricted assignment case. Then we turn to another objective function: maximizing the minimum machine load. For the case that every job can be assigned to at most two machines we give a purely combinatorial 2-approximation which is best possible, unless P=NP. This improves on the computationally costly LP-based (2 +ε)-approximation algorithm by Chakrabarty et al. [7]. | en |
| dc.identifier.issn | 2197-8085 | |
| dc.identifier.uri | https://depositonce.tu-berlin.de/handle/11303/15678 | |
| dc.identifier.uri | http://dx.doi.org/10.14279/depositonce-14451 | |
| dc.language.iso | en | en |
| dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | en |
| dc.subject.ddc | 510 Mathematik | en |
| dc.subject.other | scheduling | en |
| dc.subject.other | unrelated machines | en |
| dc.subject.other | configuration-LP | en |
| dc.subject.other | MaxMin-allocation problem | en |
| dc.subject.other | integrality gap | en |
| dc.title | On the Configuration-LP for Scheduling on Unrelated Machines | en |
| dc.type | Research Paper | en |
| dc.type.version | submittedVersion | en |
| tub.accessrights.dnb | free | en |
| tub.affiliation | Fak. 2 Mathematik und Naturwissenschaften::Inst. Mathematik | de |
| tub.affiliation.faculty | Fak. 2 Mathematik und Naturwissenschaften | de |
| tub.affiliation.institute | Inst. Mathematik | de |
| tub.publisher.universityorinstitution | Technische Universität Berlin | en |
| tub.series.issuenumber | 2010, 25 | en |
| tub.series.name | Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin | en |
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