Smoothed performance guarantees for local search

We study popular local search and greedy algorithms for standard machine scheduling problems. The performance guarantee of these algorithms is well understood, but the worst-case lower bounds seem somewhat contrived and it is questionable whether they arise in practical applications. To find out how...

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Vydáno v:Mathematical programming Ročník 146; číslo 1-2; s. 185 - 218
Hlavní autoři: Brunsch, Tobias, Röglin, Heiko, Rutten, Cyriel, Vredeveld, Tjark
Médium: Journal Article
Jazyk:angličtina
Vydáno: Berlin/Heidelberg Springer Berlin Heidelberg 01.08.2014
Springer Nature B.V
Témata:
Algorithms
Analysis
Approximation
Calculus of Variations and Optimal Control; Optimization
Combinatorics
Data smoothing
Full Length Paper
Games
Guarantees
Job shops
Lower bounds
Mathematical analysis
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematical programming
Mathematics
Mathematics and Statistics
Mathematics of Computing
Noise
Numerical Analysis
Schedules
Scheduling
Searching
Studies
Texts
Theoretical
68Q25
68W40
68W25
68Q87
90B35
ISSN:0025-5610, 1436-4646
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Popis
Shrnutí:We study popular local search and greedy algorithms for standard machine scheduling problems. The performance guarantee of these algorithms is well understood, but the worst-case lower bounds seem somewhat contrived and it is questionable whether they arise in practical applications. To find out how robust these bounds are, we study the algorithms in the framework of smoothed analysis, in which instances are subject to some degree of random noise. While the lower bounds for all scheduling variants with restricted machines are rather robust, we find out that the bounds are fragile for unrestricted machines. In particular, we show that the smoothed performance guarantee of the jump and the lex-jump algorithm are (in contrast to the worst case) independent of the number of machines. They are  and  , respectively, where  is a parameter measuring the magnitude of the perturbation. The latter immediately implies that also the smoothed price of anarchy is  for routing games on parallel links. Additionally, we show that for unrestricted machines also the greedy list scheduling algorithm has an approximation guarantee of   .
Bibliografie:SourceType-Scholarly Journals-1
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ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-013-0683-7