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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| Vydané v: | Mathematical programming Ročník 146; číslo 1-2; s. 185 - 218 |
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| Hlavní autori: | , , , |
| Médium: | Journal Article |
| Jazyk: | English |
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Berlin/Heidelberg
Springer Berlin Heidelberg
01.08.2014
Springer Nature B.V |
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| ISSN: | 0025-5610, 1436-4646 |
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| Abstract | 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
. |
|---|---|
| AbstractList | 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
. (ProQuest: ... denotes formulae and/or non-USASCII text omitted; see image).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 ... (ProQuest: ... denotes formulae and/or non-USASCII text omitted; see image) 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 ...[PUBLICATION ABSTRACT] |
| Author | Rutten, Cyriel Röglin, Heiko Vredeveld, Tjark Brunsch, Tobias |
| Author_xml | – sequence: 1 givenname: Tobias surname: Brunsch fullname: Brunsch, Tobias organization: Department of Computer Science, University of Bonn – sequence: 2 givenname: Heiko surname: Röglin fullname: Röglin, Heiko organization: Department of Computer Science, University of Bonn – sequence: 3 givenname: Cyriel surname: Rutten fullname: Rutten, Cyriel organization: Department of Quantitative Economics, Maastricht University – sequence: 4 givenname: Tjark surname: Vredeveld fullname: Vredeveld, Tjark email: t.vredeveld@maastrichtuniversity.nl organization: Department of Quantitative Economics, Maastricht University |
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| Cites_doi | 10.1007/11671541_2 10.1016/j.tcs.2006.05.010 10.1016/j.ejor.2005.03.023 10.1145/990308.990310 10.1145/1867719.1867721 10.1016/S0167-5060(08)70356-X 10.1145/258128.258201 10.1145/1219944.1219949 10.1016/j.orl.2012.04.002 10.1016/j.ijpe.2008.09.003 10.1017/CBO9780511800481.022 10.1002/j.1538-7305.1966.tb01709.x 10.1080/01621459.1963.10500830 10.1002/nav.20286 10.1007/BF01930985 10.1287/moor.1050.0170 10.1145/1562764.1562785 10.1137/0209007 10.1137/0217033 10.1287/ijoc.1050.0152 10.1016/j.jcss.2004.04.004 10.1002/nav.20202 |
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| References | Vöcking, B.: Selfish load balancing. In: Nisan, N., Roughgarden, T., Tardos, E., Vazirani, V. (eds.) Algorithmic Game Theory, chapter 20. Cambridge University Press, New York (2007) AwerbuchBAzarYRichterYTsurDTradeoffs in worst-case equilibriaTheor. Comput. Sci.200636120020910.1016/j.tcs.2006.05.0101097.680122252578 GrahamRLBounds for certain multiprocessing anomaliesBell Syst. Tech. J.1966451563158110.1002/j.1538-7305.1966.tb01709.x RuttenCRecaldeDSchuurmanPVredeveldTPerformance guarantees of jump neighborhoods on restricted related parallel machinesOper. Res. Lett.20124028729110.1016/j.orl.2012.04.0021247.901622930031 Angel, E.: A survey of approximation results for local search algorithms. In: Bampis, E., Jansen, K., Kenyon, C. (eds.) Efficient Approximation and Online Algorithms, Volume 3484 of LNCS, pp. 30–73. Springer, Heidelberg (2006) GareyMRJohnsonDSComputers and Intractibility: A Guide to the Theory of NP-Completeness1979New YorkW.H. Freeman & Co.0411.68039 ChoYSahniSBounds for list schedules on uniform processorsSIAM J. Comput.198099110310.1137/02090070446.68025557828 LiCLScheduling unit-length jobs with machine eligibility restrictionsEur. J. Oper. Res.20061741325132810.1016/j.ejor.2005.03.0231102.90023 HoeferM.SouzaA.Tradeoffs and average-case equilibria in selfish routingACM Trans. Comput. Theory2010212 LeungJYTLiCLScheduling with processing set restrictions: a surveyInt. J. Prod. Econ.200811625126210.1016/j.ijpe.2008.09.003 BeierRVöckingBRandom knapsack in expected polynomial timeJ. Comput. Syst. Sci.200469330632910.1016/j.jcss.2004.04.0041062.90037 Englert, M., Röglin, H., Vöcking, B.: Worst case and probabilistic analysis of the 2-opt algorithm for the TSP. In: Proceedings of the 18th ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 1295–13004 (2007) SpielmanDATengSHSmoothed analysis of algorithms: why the simplex algorithm usually takes polynomial timeJ. ACM200451338546310.1145/990308.9903101192.901202145860 CzumajA.VöckingB.Tight bounds for worst-case equilibriaACM Trans. Algorithms2007314 SchäferGSivadasanNTopology matters: smoothed competitiveness of metrical task systemsTheor. Comput. Sci.20053411–3314 Michiels, W.P.A.J., Aarts, E.H.L., Korst, J.H.M.: Theoretical Aspects of Local Search. Springer, Heidelberg (2007) AspnesJAzarYFiatAPlotkinSAWaartsOOn-line routing of virtual circuits with applications to load balancing and machine schedulingJ. ACM199744348650410.1145/258128.2582010890.680141470153 SchuurmanPVredeveldTPerformance guarantees of local search for multiprocessor schedulingInf. J. Comput.2007191526310.1287/ijoc.1050.01521241.900572300584 HoeffdingWProbability inequalities for sums of bounded random variablesJ. Am. Stat. Assoc.196358301133010.1080/01621459.1963.105008300127.10602144363 BecchettiLLeonardiSMarchetti-SpaccamelaASchäferGVredeveldTAverage case and smoothed competitive analysis for the multi-level feedback algorithmMath. Oper. Res.20063138510810.1287/moor.1050.01701278.901432205520 OuJLeungJY-TLiCLScheduling parallel machines with inclusive set restrictionsNaval Res. Logist.200855432833810.1002/nav.202861153.904322404209 SpielmanDATengSHSmoothed analysis: an attempt to explain the behavior of algorithms in practiceCommun. ACM20095210768410.1145/1562764.1562785 FinnGHorowitzEA linear time approximation algorithm for multiprocessor schedulingBIT19791931232010.1007/BF019309850413.68038548611 HochbaumDSShmoysDBA polynomial approximation scheme for machine scheduling on uniform processors: using the dual approximation approachSIAM J. Comput.19881753955110.1137/02170330647.68040941944 GrahamRLLawlerELLenstraJKRinnooy KanAHGOptimization and approximation in deterministic sequencing and scheduling: a surveyAnn. Discret. Math.1979528732610.1016/S0167-5060(08)70356-X0411.90044558574 GlassCAKellererHParallel machine scheduling with job assignment restrictionsNaval Res. Logist.200754325025710.1002/nav.202021149.900582296798 683_CR7 683_CR8 JYT Leung (683_CR17) 2008; 116 DA Spielman (683_CR24) 2004; 51 G Finn (683_CR9) 1979; 19 B Awerbuch (683_CR3) 2006; 361 MR Garey (683_CR10) 1979 RL Graham (683_CR13) 1979; 5 683_CR1 R Beier (683_CR5) 2004; 69 DS Hochbaum (683_CR14) 1988; 17 J Aspnes (683_CR2) 1997; 44 683_CR19 CA Glass (683_CR11) 2007; 54 P Schuurman (683_CR23) 2007; 19 RL Graham (683_CR12) 1966; 45 683_CR15 L Becchetti (683_CR4) 2006; 31 Y Cho (683_CR6) 1980; 9 J Ou (683_CR20) 2008; 55 C Rutten (683_CR21) 2012; 40 DA Spielman (683_CR25) 2009; 52 G Schäfer (683_CR22) 2005; 341 CL Li (683_CR18) 2006; 174 W Hoeffding (683_CR16) 1963; 58 683_CR26 |
| References_xml | – reference: Angel, E.: A survey of approximation results for local search algorithms. In: Bampis, E., Jansen, K., Kenyon, C. (eds.) Efficient Approximation and Online Algorithms, Volume 3484 of LNCS, pp. 30–73. Springer, Heidelberg (2006) – reference: BecchettiLLeonardiSMarchetti-SpaccamelaASchäferGVredeveldTAverage case and smoothed competitive analysis for the multi-level feedback algorithmMath. Oper. Res.20063138510810.1287/moor.1050.01701278.901432205520 – reference: LiCLScheduling unit-length jobs with machine eligibility restrictionsEur. J. Oper. Res.20061741325132810.1016/j.ejor.2005.03.0231102.90023 – reference: BeierRVöckingBRandom knapsack in expected polynomial timeJ. Comput. Syst. Sci.200469330632910.1016/j.jcss.2004.04.0041062.90037 – reference: Englert, M., Röglin, H., Vöcking, B.: Worst case and probabilistic analysis of the 2-opt algorithm for the TSP. In: Proceedings of the 18th ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 1295–13004 (2007) – reference: Michiels, W.P.A.J., Aarts, E.H.L., Korst, J.H.M.: Theoretical Aspects of Local Search. Springer, Heidelberg (2007) – reference: AspnesJAzarYFiatAPlotkinSAWaartsOOn-line routing of virtual circuits with applications to load balancing and machine schedulingJ. ACM199744348650410.1145/258128.2582010890.680141470153 – reference: SchäferGSivadasanNTopology matters: smoothed competitiveness of metrical task systemsTheor. Comput. Sci.20053411–3314 – reference: GareyMRJohnsonDSComputers and Intractibility: A Guide to the Theory of NP-Completeness1979New YorkW.H. Freeman & Co.0411.68039 – reference: SchuurmanPVredeveldTPerformance guarantees of local search for multiprocessor schedulingInf. J. Comput.2007191526310.1287/ijoc.1050.01521241.900572300584 – reference: GrahamRLBounds for certain multiprocessing anomaliesBell Syst. Tech. J.1966451563158110.1002/j.1538-7305.1966.tb01709.x – reference: LeungJYTLiCLScheduling with processing set restrictions: a surveyInt. J. Prod. Econ.200811625126210.1016/j.ijpe.2008.09.003 – reference: GlassCAKellererHParallel machine scheduling with job assignment restrictionsNaval Res. Logist.200754325025710.1002/nav.202021149.900582296798 – reference: GrahamRLLawlerELLenstraJKRinnooy KanAHGOptimization and approximation in deterministic sequencing and scheduling: a surveyAnn. Discret. Math.1979528732610.1016/S0167-5060(08)70356-X0411.90044558574 – reference: HochbaumDSShmoysDBA polynomial approximation scheme for machine scheduling on uniform processors: using the dual approximation approachSIAM J. Comput.19881753955110.1137/02170330647.68040941944 – reference: ChoYSahniSBounds for list schedules on uniform processorsSIAM J. Comput.198099110310.1137/02090070446.68025557828 – reference: RuttenCRecaldeDSchuurmanPVredeveldTPerformance guarantees of jump neighborhoods on restricted related parallel machinesOper. Res. Lett.20124028729110.1016/j.orl.2012.04.0021247.901622930031 – reference: SpielmanDATengSHSmoothed analysis: an attempt to explain the behavior of algorithms in practiceCommun. ACM20095210768410.1145/1562764.1562785 – reference: Vöcking, B.: Selfish load balancing. In: Nisan, N., Roughgarden, T., Tardos, E., Vazirani, V. (eds.) Algorithmic Game Theory, chapter 20. Cambridge University Press, New York (2007) – reference: AwerbuchBAzarYRichterYTsurDTradeoffs in worst-case equilibriaTheor. Comput. Sci.200636120020910.1016/j.tcs.2006.05.0101097.680122252578 – reference: HoeffdingWProbability inequalities for sums of bounded random variablesJ. Am. Stat. 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| SubjectTerms | 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 |
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