Approximation and Online Algorithms: 9th International Workshop, WAOA 2011, Saarbrücken, Germany, September 8-9, 2011, Revised Selected Papers PDF
Preview Approximation and Online Algorithms: 9th International Workshop, WAOA 2011, Saarbrücken, Germany, September 8-9, 2011, Revised Selected Papers
Lecture Notes in Computer Science 7164 CommencedPublicationin1973 FoundingandFormerSeriesEditors: GerhardGoos,JurisHartmanis,andJanvanLeeuwen EditorialBoard DavidHutchison LancasterUniversity,UK TakeoKanade CarnegieMellonUniversity,Pittsburgh,PA,USA JosefKittler UniversityofSurrey,Guildford,UK JonM.Kleinberg CornellUniversity,Ithaca,NY,USA AlfredKobsa UniversityofCalifornia,Irvine,CA,USA FriedemannMattern ETHZurich,Switzerland JohnC.Mitchell StanfordUniversity,CA,USA MoniNaor WeizmannInstituteofScience,Rehovot,Israel OscarNierstrasz UniversityofBern,Switzerland C.PanduRangan IndianInstituteofTechnology,Madras,India BernhardSteffen TUDortmundUniversity,Germany MadhuSudan MicrosoftResearch,Cambridge,MA,USA DemetriTerzopoulos UniversityofCalifornia,LosAngeles,CA,USA DougTygar UniversityofCalifornia,Berkeley,CA,USA GerhardWeikum MaxPlanckInstituteforInformatics,Saarbruecken,Germany Roberto Solis-Oba Giuseppe Persiano (Eds.) Approximation and Online Algorithms 9th International Workshop, WAOA 2011 Saarbrücken, Germany, September 8-9, 2011 Revised Selected Papers 1 3 VolumeEditors RobertoSolis-Oba TheUniversityofWesternOntario DepartmentofComputerScience London,ON,N6A5B7,Canada E-mail:[email protected] GiuseppePersiano UniversitàdiSalerno DipartimentodiInformatica"RenatoM.Capocelli" ViaPonteDonMelillo,84081Fisciano(SA),Italy E-mail:[email protected] ISSN0302-9743 e-ISSN1611-3349 ISBN978-3-642-29115-9 e-ISBN978-3-642-29116-6 DOI10.1007/978-3-642-29116-6 SpringerHeidelbergDordrechtLondonNewYork LibraryofCongressControlNumber:2012934372 CRSubjectClassification(1998):F.2.2,G.2.1-2,G.1.2,G.1.6,I.3.5,E.1 LNCSSublibrary:SL1–TheoreticalComputerScienceandGeneralIssues ©Springer-VerlagBerlinHeidelberg2012 Thisworkissubjecttocopyright.Allrightsarereserved,whetherthewholeorpartofthematerialis concerned,specificallytherightsoftranslation,reprinting,re-useofillustrations,recitation,broadcasting, reproductiononmicrofilmsorinanyotherway,andstorageindatabanks.Duplicationofthispublication orpartsthereofispermittedonlyundertheprovisionsoftheGermanCopyrightLawofSeptember9,1965, initscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpringer.Violationsareliable toprosecutionundertheGermanCopyrightLaw. Theuseofgeneraldescriptivenames,registerednames,trademarks,etc.inthispublicationdoesnotimply, evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevantprotectivelaws andregulationsandthereforefreeforgeneraluse. Typesetting:Camera-readybyauthor,dataconversionbyScientificPublishingServices,Chennai,India Printedonacid-freepaper SpringerispartofSpringerScience+BusinessMedia(www.springer.com) Preface The9thWorkshoponApproximationandOnlineAlgorithms(WAOA2011)took place in Saarbru¨cken, Germany, September 8–9, 2011. The workshop was part of the ALGO 2011 event that also hosted ESA 2011, WABI 2011, IPEC 2011, ALGOSENSORS2011,andATMOS2011.ThepreviousWAOAworkshopswere heldinBudapest(2003),Rome(2004),PalmadeMallorca(2005),Zurich(2006), Eilat (2007), Karlsruhe (2008), Copenhagen (2009), and Liverpool (2010). The proceedingsofthesepreviousWAOAworkshopshaveappearedasLNCSvolumes 2909, 3351,3879, 4368, 4927, 5426, 5893,and 6534, respectively. The Workshop on Approximation and Online Algorithms focuses on the de- sign and analysis of algorithms for online and computationally hard problems. Both kinds of problems have a large number of applications in a wide variety of fields.TopicsofinterestforWAOA2011were:algorithmicgametheory,approx- imation classes, coloring and partitioning, competitive analysis, computational finance, cuts and connectivity, geometric problems, inapproximability results, mechanism design, network design, packing and covering, paradigms for design andanalysisofapproximationandonlinealgorithms,parameterizedcomplexity, randomization techniques and scheduling problems. In response to the call for papers, we received 48 submissions. Each submis- sionwasreviewedbyatleastthreereferees.Thesubmissionsweremainlyjudged on originality, technical quality, and relevance to the topics of the conference. Basedonthereviews,theProgramCommitteeselected21papers.Inadditionto the presentations of the 21 accepted papers, Klaus Jansen from the University of Kiel gave an invited talk on “Approximation Algorithms for Scheduling and Packing Problems.” We are grateful to Andrei Voronkov for providing the EasyChair conference system, which was used to manage the electronic submissions and the review process. It made our task much easier. We would also like to thank all the authors who submitted papers to WAOA 2011 as well as the local organizers of ALGO 2011. November 2011 Roberto Solis-Oba Giuseppe Persiano Organization Program Co-chairs Roberto Solis-Oba University of Western Ontario, Canada Giuseppe Persiano Universit`a di Salerno, Italy Program Committee Vincenzo Auletta Universit`a di Salerno, Italy Evripidis Bampis University of Evry, France Ioannis Caragiannis University of Patras, Greece Jose Correa Universidad de Chile, Chile Khaled Elbassioni Max Planck Institut fu¨r Informatik, Germany Rudolf Fleischer Fudan University, China Thomas Erlebach University of Leicester, UK Klaus Jansen University of Kiel, Germany Christos Kaklamanis University of Patras, Greece Jochen Ko¨nemann University of Waterloo, Canada Alejandro Lo´pez-Ortiz University of Waterloo, Canada Monaldo Mastrolilli IDSIA Lugano, Switzerland Julian Mestre University of Sydney, Australia Giuseppe Persiano (Co-chair), Universita` di Salerno, Italy Hadas Shachnai Technion, Israel Roberto Solis-Oba (Co-chair), University of Western Ontario, Canada Clifford Stein Columbia University, USA Denis Trystram Grenoble Institute of Technology, France Carmine Ventre University of Liverpool, UK Additional Referees Markus Bl¨aser Masud Hasan Marin Bougeret Chien-Chung Huang Stefan Canzar Sungjin Im Johanne Cohen Shahin Kamali Reza Dorrigiv Panagiotis Kanellopoulos Ioannis Emiris Nikos Karanikolas Leah Epstein Kim Klein Cristina Fernandes Ephraim Korach Diodato Ferraioli Stefan Kraft Robert Fraser Ariel Kulik Konstantinos Georgiou Maria Kyropoulou VIII Organization Bundit Laekhanukit Dror Rawitz Dimitris Letsios David Rizzuto Giorgio Lucarelli Christina Robenek Hamid Mahini Alejandro Salinger Bodo Manthey Guido Schaefer Nicole Megow Ilka Schnoor Nikolaus Mutsanas Martin Skutella Rajiv Raman Gwen Spencer Aris Pagourtzis Ola Svensson Konstantinos Panagiotou Chaitanya Swamy Paolo Penna Tami Tamir Matthias Poloczek Marc Uetz Lars Pra¨del Anke Van Zuylen Kirk Pruhs Jose Verschae Claude-Guy Quimper Haifeng Xu Lisa Zhang Table of Contents Approximation Algorithms for Scheduling and Packing Problems....... 1 Klaus Jansen Approximating Subset k-Connectivity Problems ..................... 9 Zeev Nutov Learning in Stochastic Machine Scheduling.......................... 21 Sebastia´n Marba´n, Cyriel Rutten, and Tjark Vredeveld An Online Algorithm Optimally Self-tuning to Congestion for Power Management Problems ........................................... 35 Wolfgang Bein, Naoki Hatta, Nelson Hernandez-Cons, Hiro Ito, Shoji Kasahara, and Jun Kawahara Single Approximation for Biobjective Max TSP...................... 49 Cristina Bazgan, Laurent Gourv`es, J´eroˆme Monnot, and Fanny Pascual ParameterizedApproximation Algorithms for Hitting Set ........... 63 Ljiljana Brankovic and Henning Fernau Approximation Algorithms for the Maximum Leaf Spanning Tree Problem on Acyclic Digraphs...................................... 77 Nadine Schwartges, Joachim Spoerhase, and Alexander Wolff Optimization over Integers with Robustness in Cost and Few Constraints ..................................................... 89 Kai-Simon Goetzmann, Sebastian Stiller, and Claudio Telha A Lower Bound on Deterministic Online Algorithms for Scheduling on Related Machines without Preemption.............................. 102 Toma´ˇs Ebenlendr and Jiˇr´ı Sgall Scheduling Jobs on Identical and Uniform ProcessorsRevisited ........ 109 Klaus Jansen and Christina Robenek Approximation Algorithms for Fragmenting a Graph against a Stochastically-Located Threat ..................................... 123 David B. Shmoys and Gwen Spencer Non-clairvoyant Weighted Flow Time Scheduling on Different Multi-processor Models ........................................... 137 Jianqiao Zhu, Ho-Leung Chan, and Tak-Wah Lam X Table of Contents A New Perspective on List Update: Probabilistic Locality and Working Set............................................................. 150 Reza Dorrigiv and Alejandro Lo´pez-Ortiz OnlineMin: A Fast Strongly Competitive Randomized Paging Algorithm....................................................... 164 Gerth Stølting Brodal, Gabriel Moruz, and Andrei Negoescu Faster and Simpler Approximation of Stable Matchings ............... 176 Katarzyna Paluch Simpler 3/4-ApproximationAlgorithms for MAX SAT................ 188 Anke van Zuylen On Online Algorithms with Advice for the k-Server Problem .......... 198 Marc P. Renault and Adi Ros´en Improved Lower Bound for Online Strip Packing (Extended Abstract) ............................................. 211 Rolf Harren and Walter Kern Competitive Router Scheduling with Structured Data ................ 219 Yishay Mansour, Boaz Patt-Shamir, and Dror Rawitz Approximation with a Fixed Number of Solutions of Some Biobjective Maximization Problems........................................... 233 Cristina Bazgan, Laurent Gourv`es, and J´eroˆme Monnot Generalized Maximum Flows over Time............................. 247 Martin Groß and Martin Skutella The Price of Anarchy for Minsum Related Machine Scheduling ........ 261 Ruben Hoeksma and Marc Uetz Author Index.................................................. 275 Approximation Algorithms for Scheduling and Packing Problems Klaus Jansen(cid:2) Institut fu¨r Informatik, Christian-Albrechts-Universit¨at zu Kiel, 24098 Kiel, Germany [email protected] Abstract. Inthispaperwepresentanoverviewaboutnewapproxima- tion results for several optimization problems. During the last years we have worked on the design of approximation algorithms with a smaller approximation ratio and on the design of efficient polynomial time ap- proximation schemes with afaster runningtime. Wepresented approxi- mationalgorithmswithasmallerratioforschedulingwithfixedjobsand fortwodimensionalstrippacking.Ontheotherhand,wedevelopedeffi- cientapproximationschemeswithanimprovedrunningtimeformultiple knapsack and scheduling independent jobs on uniform processors. 1 Introduction In the first part of the paper we focus on approximation algorithms with good performanceguarantees.LetA(I)betheobjectivevalue(e.g.theschedulelength ortotalprofit)generatedbyapolynomialtimealgorithmA,andOPT(I)bethe optimalvalueforaninstanceI.TheapproximationratioR ofAissup A(I) A I OPT(I) andsup OPT(I) foraminimizationproblemandmaximizationproblem,respec- I A(I) tively. The goal in both cases is to find an algorithm with minimum ratio R . A In the second part we focus on the running time of approximation schemes. A problem admits a polynomial-time approximation scheme (PTAS) if there is a family of algorithms {A |ε>0} such that for any ε>0 and any instance I, ε A producesa(1+ε)-approximatesolutionintime polynomialinthe sizeofthe ε input. Two important restricted classes of approximation schemes were defined to reduce the running time. An efficient polynomial-time approximationscheme (EPTAS)isaPTASwithrunningtime ofthe formf(1/(cid:3))poly(|I|),while afully timepolynomialtimeapproximationscheme(FPTAS)runsintimepoly(|I|,1/(cid:3)). There is an interesting connection to parameterized complexity, i.e. to fixed parametertractable(FPT)algorithmsandtothecomplexityclassW[1].Infact, if the standard parametrization of an optimization problem is W[1]-hard, then theoptimizationproblemdoesnothaveanEPTAS,unlessFPT=W[1][2,4].For asurveyontheconnectionbetweenapproximationalgorithmsandparameterized complexity we refer to [31]. (cid:2) Research supported by theDeutscheForschungsgemeinschaft (DFG). R.Solis-ObaandG.Persiano(Eds.):WAOA2011,LNCS7164,pp.1–8,2012. (cid:2)c Springer-VerlagBerlinHeidelberg2012 2 K. Jansen 2 Scheduling with Fixed Jobs In parallel machine scheduling, an important issue is the scenario where either some jobs are already fixed in the system [33] or intervals of non-availability of some machines must be taken into account [21]. The first problem occurs when high-priority jobs are already scheduled in the system while the latter problem is due to regular maintenance of machines. Both models are relevant for turnaround scheduling [32] and distributed computing where machines are donated on a volunteer basis. The problem can be defined as follows: an instance consists of a set M = {M ,...,M } of m identical machines and a set J = {J ,...,J } of n jobs 1 m 1 n with non-negative processingtimes p ,...,p ∈N. The firstk jobs are fixed via 1 n a list (m ,s ),...,(m ,s ) giving a machine index m ∈ M and starting time 1 1 k k j s ≥ 0 for the corresponding job J , for j = 1,...,k. We suppose that these j j fixedjobs donotoverlap.Aschedule isanon-preemptiveassignmentofthe jobs tomachinesandstartingtimessuchthatthefirstk jobsareassignedasencoded in the instance and all jobs do not intersect. For the problem with fixed jobs, the objective is to minimize the makespan (the maximum completion time C = s + p ) among all jobs including the j j j fixed ones; i.e. C = max C . In the setting with non-availability, max j=1,...,n j our goal is to find a schedule with minimum makespan among all non-fixed jobs; i.e. C = max C . Both problems generalize the well-known max j=k+1,...,n j problem P||C (scheduling jobs on parallel identical machines to minimize max makespan) [18] and hence are strongly NP-hard. Interestingly, the second vari- ant is harder to approximate. 2.1 Related Results SchedulingwithfixedjobswasstudiedbyScharbrodt,StegerandWeisser[34,33]. They mainly studied the problem for a constant number m of processors. For thisstronglyNP-hardproblem(whichconsequentlydoesnotadmitanFPTAS) they presented a polynomial time approximation scheme (PTAS). They also found approximation algorithms for an arbitrary number m of processors with ratios 3 [34] and 2 + (cid:3) [33]. Furthermore, they [33] proved that there is no approximation algorithm with ratio 3/2−(cid:3) for scheduling with fixed jobs for any (cid:3)∈(0,1/2], unless P = NP. 2.2 New Results Diedrich and Jansen [9] presented a 3/2+(cid:3)-approximation for both variants. However, the algorithm used on a large number of enumeration steps and in- volveduptom1/(cid:4)1/(cid:2)2 callstoasubroutinethatapproximatelysolvesamaximiza- tion problem, the Multiple Subset Sum Problem (MSSP), for a fixed accuracy (cid:3)>0. Let T (n,(cid:3)) be the running time of this subroutine. MSSP Recently,wepresentedimprovedalgorithmsforschedulingwithfixedjobsand scheduling with non-availability constraints. These algorithms achieve exactly
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