Algorithm Engineering: Bridging the Gap between Algorithm Theory and Practice

527 Pages·2010·3.37 MB·English

by  Matthias Müller-Hannemann

Lecture Notes in Computer Science 5971
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
Matthias Müller-Hannemann
Stefan Schirra (Eds.)
Algorithm
Engineering
Bridging the Gap
between Algorithm Theory and Practice
1 3
VolumeEditors
MatthiasMüller-Hannemann
Martin-Luther-UniversitätHalle-Wittenberg,InstitutfürInformatik
Von-Seckendorff-Platz1,06120Halle,Germany
E-mail:[email protected]
StefanSchirra
Otto-von-GuerickeUniversitätMagdeburg,FakultätfürInformatik
Universitätsplatz2,39106Magdeburg,Germany
E-mail:[email protected]
LibraryofCongressControlNumber:2010931447
CRSubjectClassification(1998):F.2,D.2,G.1-2,G.4,E.1,I.3.5,I.6
LNCSSublibrary:SL1–TheoreticalComputerScienceandGeneralIssues
ISSN 0302-9743
ISBN-10 3-642-14865-4SpringerBerlinHeidelbergNewYork
ISBN-13 978-3-642-14865-1SpringerBerlinHeidelbergNewYork
Thisworkissubjecttocopyright.Allrightsarereserved,whetherthewholeorpartofthematerialis
concerned,specificallytherightsoftranslation,reprinting,re-useofillustrations,recitation,broadcasting,
reproductiononmicrofilmsorinanyotherway,andstorageindatabanks.Duplicationofthispublication
orpartsthereofispermittedonlyundertheprovisionsoftheGermanCopyrightLawofSeptember9,1965,
initscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpringer.Violationsareliable
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Preface
Thesystematicdevelopmentofefficientalgorithmshasbecomeakeytechnology
for all kinds of ambitious and innovative computer applications. With major
parts of algorithmic theory and algorithmic practice developing in different di-
rections since the 1970sa groupof leading researchersin the field startedabout
15 years ago to coin the new paradigm “Algorithm Engineering”. Its major goal
is to bridge the gap between theory and practice.
This book is a collection of survey articles on different aspects of Algo-
rithmEngineering,writtenbyparticipantsofaGI-Dagstuhlseminarheldduring
September3-8,2006.DorotheaWagnerandPeterSanderscameupwiththeidea
forthe seminar,andapproachedus to organizeit. Ingeneral,the conceptofthe
GI-Dagstuhl seminars is to provide young researchers (mostly PhD students)
with the opportunity to be introduced into a new emerging field of computer
science.Basedonalistoftopicscollectedbytheorganizers,theparticipantspre-
paredoverviewlectures they presentedand discussedwith other participants at
the research seminar in Dagstuhl. Each contribution was elaborated afterwards
and carefully cross-reviewedby all participants.
Chapter 1 gives an introduction into the emerging field of Algorithm Engi-
neering and describes its main ingredients. It also serves as an overview for the
remaining chapters of the book.
The editing process took much longer than expected, partially due to the
fact that several aspects of Algorithm Engineering have never been written up
before, which gave rise to lengthy internal discussions. But for the major part
of the delay, the editors take their responsibility. Since the field of Algorithm
Engineering has developed rapidly since the seminar took place, we made an
effort to keep the contents up to date. Ideally, our book will be used as an
introductiontothefield.Althoughithasnotbeenwrittenasatextbook,itmay
well serve as accompanying material and as a reference in class.
Asthisbookprojectnowcomestoanend,weareindebtedtomanypeopleand
institutions. First of all, we would like to thank the Gesellschaft für Informatik
e.V.(GI)fortheirgeneroussupportoftheGI-Dagstuhlseminar,fundingthestay
of all participants at Schloss Dagstuhl. We thank the Schloss Dagstuhl Leibniz-
Zentrum für Informatik GmbH for their excellent workshop facilities and its
hospitality, which provided the basis for a successful seminar. Alfred Hofmann
andhisteammadeitpossibletosmoothlypublishthisvolumeintheLNCSseries
of Springer. Special thanks go to Annabell Berger, Holger Blaar, and Kathleen
Kletsch for their help in the editing process.
March 2010 Matthias Müller-Hannemann
Stefan Schirra
List of Contributors
Editors
Matthias Müller-Hannemann Stefan Schirra
Martin-Luther-Universität Otto-von-Guericke Universität
Halle-Wittenberg Magdeburg
Institut für Informatik Fakultät für Informatik
Von-Seckendorff-Platz 1 Universitätsplatz 2
06120 Halle, Germany 39106 Magdeburg, Germany
[email protected] [email protected]
Authors
Heiner Ackermann Daniel Delling
Fraunhofer Institute for Microsoft Research Silicon Valley
Industrial Mathematics 1065 La Avenida
Fraunhofer-Platz 1 Montain View, CA 94043,USA
67663 Kaiserslautern,Germany [email protected]
[email protected]
Roman Dementiev
Deepak Ajwani
Universität Karlsruhe (TH)
Aarhus University
Department of Computer Science,
MADALGO - Center for Massive
Algorithmics II
Data Algorithmics
Am Fasanengarten 5
IT-parken, Aabogade 34
76131 Karlsruhe, Germany
8200 Aarhus N, Denmark
[email protected]
[email protected]
Markus Geyer
Eric Berberich Universität Tübingen
Max-Planck-Institut für Informatik Wilhelm-Schickard-Institut für
Algorithms and Complexity Informatik, Paralleles Rechnen
Campus E1 4 Sand 14
66123 Saarbrücken,Germany 72076 Tübingen, Germany
[email protected] [email protected]
VIII List of Contributors
Matthias Hagen Maria Kandyba
Bauhaus Universität Weimar Technische Universität Dortmund
Faculty of Media, Web Technology Fakultät für Informatik
and Information Systems Group Lehrstuhl für Algorithm Engineering
Bauhausstr. 11 Otto-Hahn-Str. 14
99423 Weimar, Germany 44227 Dortmund, Germany
[email protected] [email protected]
Sabine Helwig Sascha Meinert
Universität Erlangen-Nürnberg Karlsruhe Institute of Technology
Department of Computer Science (KIT)
Hardware-Software-Co-Design Institute of Theoretical Informatics,
Am Weichselgarten 3 Algorithmics I
91058 Erlangen, Germany Am Fasanengarten 5
[email protected] 76131 Karlsruhe, Germany
[email protected]
Benjamin Hiller
Konrad-Zuse-Zentrumfür Henning Meyerhenke
Informationstechnik Berlin (ZIB) Universität Paderborn
Department Optimization Department of Computer Science
Takustr. 7 Fürstenallee 11
14195 Berlin-Dahlem, Germany 33102 Paderborn, Germany
[email protected] [email protected]
Roberto Hoffmann Marc Mörig
Martin-Luther-Universität Otto-von-Guericke Universität
Halle-Wittenberg Magdeburg
Institut für Informatik Fakultät für Informatik
Von-Seckendorff-Platz 1 Universitätsplatz 2
06120 Halle, Germany 39106 Magdeburg, Germany
[email protected] [email protected]
Falk Hüffner Hannes Moser
Humboldt-Universität zu Berlin Friedrich-Schiller-UniversitätJena
Institut für Informatik Institut für Informatik
Rudower Chaussee 25 Ernst-Abbe-Platz 2
12489 Berlin, Germany 07743 Jena, Germany
[email protected] [email protected]
List of Contributors IX
Matthias Müller-Hannemann Anna Schulze
Martin-Luther-Universität Universität zu Köln
Halle-Wittenberg Zentrum für Angewandte Informatik
Institut für Informatik (ZAIK)
Von-Seckendorff-Platz 1 Gyrhofstr. 8c
06120 Halle, Germany 50931 Köln, Germany
[email protected] [email protected]
Heiko Röglin Nils Schweer
Maastricht University Technische Universität Braunschweig
Department of Quantitative Institute of Operating Systems
Economics and Computer Networks
6200MD Maastricht,The Netherlands Mühlenpfordtstr. 23
[email protected] 38106 Braunschweig,Germany
[email protected]
Ivo Rössling
Otto-von-GuerickeUniversität Johannes Singler
Magdeburg Universität Karlsruhe (TH)
Fakultät für Informatik Department of Computer Science,
Universitätsplatz 2 Algorithmics II
39106 Magdeburg, Germany Am Fasanengarten 5
[email protected] 76131 Karlsruhe, Germany
[email protected]
Ulf Schellbach
Technische Universität Ilmenau Tobias Tscheuschner
Institut für Theoretische Informatik Universität Paderborn
Helmholtzplatz 1 Department of Computer Science
98684 Ilmenau, Germany Fürstenallee 11
[email protected] 33102 Paderborn, Germany
[email protected]
Stefan Schirra
Otto-von-GuerickeUniversität Maik Weinard
Magdeburg Johann Wolfgang Goethe-Universität
Fakultät für Informatik Frankfurt am Main
Universitätsplatz 2 Theoretische Informatik
39106 Magdeburg, Germany Robert-Mayer-Str.11-15
[email protected] 60325 Frankfurt am Main, Germany
[email protected]
Sven Scholz
Freie Universität Berlin
Institut für Informatik
Takustr. 9
14195 Berlin, Germany
[email protected]
Contents
Chapter 1. Foundations of Algorithm Engineering
M. Müller-Hannemann, S. Schirra ............................... 1
1.1 Introduction ................................................. 1
1.1.1 Classical Algorithmics .................................. 1
1.1.2 The New Paradigm: Algorithm Engineering................ 2
1.1.3 Towards a Definition of Algorithm Engineering............. 4
1.1.4 Methodology........................................... 5
1.1.5 Visibility of Algorithm Engineering ....................... 6
1.2 Building Blocks of Algorithm Engineering ....................... 7
1.2.1 Modeling of Problems................................... 8
1.2.2 Algorithm Design ...................................... 9
1.2.3 Analysis............................................... 9
1.2.4 Realistic Computer Models .............................. 10
1.2.5 Implementation ........................................ 11
1.2.6 Libraries .............................................. 12
1.2.7 Experiments ........................................... 12
1.2.8 Success Stories of Algorithm Engineering .................. 13
1.2.9 Challenges............................................. 15
1.2.10 Further Topics — Not Covered in This Book............... 15
Chapter 2. Modeling
M. Geyer, B. Hiller, S. Meinert ................................. 16
2.1 Introduction ................................................. 16
2.2 Modeling Fundamentals ....................................... 19
2.2.1 Fundamentals.......................................... 19
2.2.2 Problem Analysis....................................... 21
2.2.3 Problem Specification: Examples ......................... 23
2.2.4 Modeling a Solution Approach ........................... 26
2.2.5 Model Assessment...................................... 28
2.2.6 Inherent Difficulties within the Modeling Process ........... 28
2.3 Modeling Frameworks......................................... 30
2.3.1 Graph-Based Models.................................... 31
2.3.2 Mixed Integer Programming ............................. 35
2.3.3 Constraint Programming ................................ 43
2.3.4 Algebraic Modeling Languages ........................... 49
2.3.5 Summary on Modeling Frameworks....................... 53
2.4 Further Issues................................................ 53
2.4.1 Specific Input Characteristics ............................ 55
2.4.2 Problem Decomposition for Complex Applications.......... 55
2.5 Conclusion................................................... 56
XII Contents
Chapter 3. Selected Design Issues
S. Helwig, F. Hüffner, I. Rössling, M. Weinard .................... 58
3.1 Introduction ................................................. 58
3.2 Simplicity ................................................... 60
3.2.1 Advantages for Implementation .......................... 61
3.2.2 How to Achieve Simplicity?.............................. 61
3.2.3 Effects on Analysis ..................................... 65
3.3 Scalability ................................................... 67
3.3.1 Towards a Definition of Scalability........................ 68
3.3.2 Scalability in Parallel Computing......................... 70
3.3.3 Basic Techniques for Designing Scalable Algorithms......... 73
3.3.4 Scalability in Grid Computing and Peer-to-Peer Networks ... 76
3.4 Time-Space Trade-Offs ........................................ 80
3.4.1 Formal Methods........................................ 82
3.4.2 Reuse and Lookup Tables ............................... 84
3.4.3 Time-Space Trade-Offs in Storing Data ................... 89
3.4.4 Preprocessing.......................................... 92
3.4.5 Brute Force Support.................................... 93
3.5 Robustness .................................................. 95
3.5.1 Software Engineering Aspects ............................ 96
3.5.2 Numerical Robustness Issues............................. 108
3.5.3 Robustness in Computational Geometry................... 113
Chapter 4. Analysis of Algorithms
H. Ackermann, H. Röglin, U. Schellbach, N. Schweer ............... 127
4.1 Introduction and Motivation ................................... 127
4.2 Worst-Case and Average-CaseAnalysis.......................... 130
4.2.1 Worst-Case Analysis.................................... 131
4.2.2 Average-CaseAnalysis .................................. 132
4.3 Amortized Analysis ........................................... 134
4.3.1 Aggregate Analysis ..................................... 136
4.3.2 The Accounting Method................................. 136
4.3.3 The Potential Method .................................. 136
4.3.4 Online Algorithms and Data Structures ................... 138
4.4 Smoothed Analysis ........................................... 140
4.4.1 Smoothed Analysis of Binary Optimization Problems ....... 141
4.4.2 Smoothed Analysis of the Simplex Algorithm .............. 151
4.4.3 Conclusions and Open Questions ......................... 158
4.5 Realistic Input Models ........................................ 159
4.5.1 Computational Geometry ............................... 160
4.5.2 Definitions and Notations ............................... 162
4.5.3 Geometric Input Models ................................ 162
4.5.4 Relationships between the Models ........................ 163
4.5.5 Applications ........................................... 164
4.6 Computational Testing ........................................ 168
4.7 Representative Operation Counts............................... 169