Santa Claus Schedules Jobs on Unrelated Machines
2011 (English)In: 43rd ACM Symposium on Theory of Computing, STOC'11, 2011, 617-626 p.Conference paper (Refereed)
One of the classic results in scheduling theory is the 2-approximation algorithm by Lenstra, Shmoys, and Tardos for the problem of scheduling jobs to minimize makespan on unrelated machines, i.e., job j requires time p ij if processed on machine i. More than two decades after its introduction it is still the algorithm of choice even in the restricted model where processing times are of the form pij ∈ pj, ∞. This problem, also known as the restricted assignment problem, is NP-hard to approximate within a factor less than 1.5 which is also the best known lower bound for the general version. Our main result is a polynomial time algorithm that estimates the optimal makespan of the restricted assignment problem within a factor 33/17 + ∈ ∼ 1.9412 + ∈, where ∈ > 0 is an arbitrarily small constant. The result is obtained by upper bounding the integrality gap of a certain strong linear program, known as configuration LP, that was previously successfully used for the related Santa Claus problem. Similar to the strongest analysis for that problem our proof is based on a local search algorithm that will eventually find a schedule of the mentioned approximation guarantee, but is not known to converge in polynomial time.
Place, publisher, year, edition, pages
2011. 617-626 p.
, Proceedings of the Annual ACM Symposium on Theory of Computing, ISSN 07378017
approximation algorithms, linear programming, scheduling
IdentifiersURN: urn:nbn:se:kth:diva-81023DOI: 10.1145/1993636.1993718ISI: 000297656800064ScopusID: 2-s2.0-79959687327ISBN: 978-1-4503-0691-1OAI: oai:DiVA.org:kth-81023DiVA: diva2:497005
43rd ACM Symposium on Theory of Computing, STOC'11. San Jose, CA. 6 June 2011 - 8 June 2011
QC 201202132012-02-102012-02-102012-04-04Bibliographically approved