Table Of ContentLecture 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
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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
