Table Of ContentLecture Notes in Computer Science 7801
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
Michel Goemans José Correa (Eds.)
Integer Programming
and Combinatorial
Optimization
16th International Conference, IPCO 2013
Valparaíso, Chile, March 18-20, 2013
Proceedings
1 3
VolumeEditors
MichelGoemans
MassachusettsInstituteofTechnology
DepartmentofMathematics
77MassachusettsAve.
Cambridge,MA02139,USA
E-mail:[email protected]
JoséCorrea
UniversidaddeChile
DepartmentofIndustrialEngineering
Republica701
Santiago,Chile
E-mail:[email protected]
ISSN0302-9743 e-ISSN1611-3349
ISBN978-3-642-36693-2 e-ISBN978-3-642-36694-9
DOI10.1007/978-3-642-36694-9
SpringerHeidelbergDordrechtLondonNewYork
LibraryofCongressControlNumber:2013931229
CRSubjectClassification(1998):G.1.6,F.2.2,G.2.1-3
LNCSSublibrary:SL1–TheoreticalComputerScienceandGeneralIssues
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Preface
This volume contains the 33 extended abstracts presented at IPCO 2013, the
16thConferenceonIntegerProgrammingandCombinatorialOptimization,held
duringMarch18–20,2013,inValpara´ıso,Chile.IPCOconferencesaresponsored
bytheMathematicalOptimizationSociety.ThefirstIPCOconferencetookplace
attheUniversityofWaterlooinMay1990.Itisheldeveryyear,exceptforthose
in which the International Symposium on Mathematical Programming is held.
TheconferencehadaProgramCommitteeconsistingof14membersandwas
chaired by Michel Goemans. In response to the Call for Papers, we received 98
extendedabstracts,ofwhichthree gotwithdrawnpriorto the decisionprogress.
Each submission was reviewed by at least three Program Committee members.
Once the reviews were available,the decisions were made in late November and
early December through conference calls and electronic discussions using the
EasyChair conference management system. We had many high-quality submis-
sions and ended up selecting 33 extended abstracts. This number is dictated by
thefactthattheconferencehasasingle-streamofnon-parallelsessions,asisthe
tradition at IPCO. We expect the full versions of the papers contained in this
volume to be submitted for publication in refereed journals.
This year, IPCO was followed by a Summer School during March 21–23,
2013,withlecturesbySamuelFiorinionextendedformulationsincombinatorial
optimization, and by Franc¸ois Margoton recent developments in cutting planes
formixedintegerprogramming.Forthefirsttime,therewasalsoaPosterSession
held on the first evening of the conference.
We would like to thank:
– All authors who submitted extended abstracts of their researchto IPCO
– ThemembersoftheProgramCommittee,whograciouslygaveplentyoftheir
time and energy to select the accepted extended abstracts
– The reviewers whose expertise was instrumental in guiding our decisions
– The members of the Local OrganizingCommittee (chaired by Jos´eCorrea),
who made this conference possible.
January 2013 Michel Goemans
Jos´e Correa
Organization
Program Committee
Chandra Chekuri University of Illinois, USA
Bill Cook University of Pittsburgh, USA
Jos´e Correa Universidad de Chile, Chile
Jesu´s De Loera University of California, Davis, USA
Michel Goemans MIT, USA
Volker Kaibel University of Magdeburg, Germany
Jon Lee University of Michigan, USA
Franc¸ois Margot CMU, USA
Thomas McCormick UBC, Canada
Andreas Schulz MIT, USA
David Shmoys Cornell University, USA
Zolt´an Szigeti Grenoble INP, France
Robert Weismantel ETH, Switzerland
Giacomo Zambelli London School of Economics and Political
Science, UK
Additional Reviewers
Aissi, Hassene Goyal, Vineet
Andrews, Matthew Guin˜ez, Flavio
Averkov,Gennadiy Gunluk, Oktay
Baes, Michel Gusfield, Dan
Bansal, Nikhil Harvey, Nick
Bley, Andreas Hemmecke, Raymond
Bonami, Pierre Homen-De-Mello, Tito
Burer, Samuel Hosten, Serkan
Bu¨sing, Christina Huh, Tim
Cheriyan, Joseph Husfeldt, Thore
Cheung, Wang Chi Im, Sungjin
Chudnovsky, Maria Iwata, Satoru
Dey, Santanu Kiraly, Tamas
Ene, Alina Kiraly, Zoltan
Felsner, Stefan Kleinberg, Bobby
Fischetti, Matteo Kobayashi,Yusuke
Fukunaga, Takuro Koenemann, Jochen
Gaspers, Serge Kolliopoulos, Stavro
Geelen, Jim Kucukyavuz, Simge
Goundan, Pranava Laraki, Rida
VIII Organization
Luebbecke, Marco Rothvoss, Thomas
Luedtke, James Segev, Danny
Mastrolilli, Monaldo Sidiropoulos, Anastasios
Mehta, Aranyak Singh, Mohit
Mittal, Shashi Soto, Jose
Mueller, Dirk Stier-Moses, Nicolas
Nagarajan,Viswanath Sviridenko, Maxim
Natarajan, Karthik Telha, Claudio
Olver, Neil Tulsiani, Madhur
Ordonez, Fernando Van Vyve, Mathieu
Orlin, James van Zuylen, Anke
Pap, Gyula Vegh, Laci
Peis, Britta Vegh, Laszlo
Pferschy, Ulrich Verschae, Jose
Pfetsch, Marco Vygen, Jens
Pruhs, Kirk Weismantel, Robert
Pˆecher,Arnaud Woeginger, Gerhard J.
Ravi, R. Zenklusen, Rico
Richard, Jean-Philippe Zwick, Uri
Romeijn, Zedwin
Table of Contents
On the Structure of Reduced Kernel Lattice Bases ................... 1
Karen Aardal and Frederik von Heymann
All-or-Nothing Generalized Assignment with Application to Scheduling
Advertising Campaigns ........................................... 13
Ron Adany, Moran Feldman, Elad Haramaty, Rohit Khandekar,
Baruch Schieber, Roy Schwartz, Hadas Shachnai, and Tami Tamir
Constant Integrality Gap LP Formulations of Unsplittable Flow
on a Path....................................................... 25
Aris Anagnostopoulos, Fabrizio Grandoni, Stefano Leonardi, and
Andreas Wiese
Intersection Cuts for Mixed Integer Conic Quadratic Sets ............. 37
Kent Andersen and Anders Nedergaard Jensen
Content Placement via the Exponential Potential Function Method .... 49
David Applegate, Aaron Archer, Vijay Gopalakrishnan,
Seungjoon Lee, and K.K. Ramakrishnan
Equivariant Perturbation in Gomory and Johnson’s Infinite Group
Problem: II. The Unimodular Two-Dimensional Case ................. 62
Amitabh Basu, Robert Hildebrand, and Matthias K¨oppe
Blocking Optimal Arborescences ................................... 74
Attila Bern´ath and Gyula Pap
Minimum Clique Cover in Claw-Free Perfect Graphs and the Weak
Edmonds-JohnsonProperty ....................................... 86
Flavia Bonomo, Gianpaolo Oriolo, Claudia Snels, and
Gautier Stauffer
A Complexity and Approximability Study of the Bilevel Knapsack
Problem ........................................................ 98
Alberto Caprara, Margarida Carvalho, Andrea Lodi, and
Gerhard J. Woeginger
Matroid and Knapsack Center Problems ............................ 110
Danny Z. Chen, Jian Li, Hongyu Liang, and Haitao Wang
Cut-Generating Functions......................................... 123
Michele Conforti, G´erard Cornu´ejols, Aris Daniilidis,
Claude Lemar´echal, and J´eroˆme Malick
X Table of Contents
Reverse Chv´atal-Gomory Rank .................................... 133
Michele Conforti, Alberto Del Pia, Marco Di Summa,
Yuri Faenza, and Roland Grappe
On Some Generalizations of the Split Closure........................ 145
Sanjeeb Dash, Oktay Gu¨nlu¨k, and Diego Alejandro Mora´n Ramirez
Packing Interdiction and Partial Covering Problems .................. 157
Michael Dinitz and Anupam Gupta
On Valid Inequalities for Quadratic Programming with Continuous
Variables and Binary Indicators.................................... 169
Hongbo Dong and Jeff Linderoth
An Improved Integrality Gap for Asymmetric TSP Paths ............. 181
Zachary Friggstad, Anupam Gupta, and Mohit Singh
SingleCommodity-FlowAlgorithmsforLiftsofGraphicandCo-graphic
Matroids........................................................ 193
Bertrand Guenin and Leanne Stuive
A Stochastic Probing Problem with Applications..................... 205
Anupam Gupta and Viswanath Nagarajan
Thrifty Algorithms for Multistage Robust Optimization............... 217
Anupam Gupta, Viswanath Nagarajan, and Vijay V. Vazirani
Shallow-Light Steiner Arborescences with Vertex Delays .............. 229
Stephan Held and Daniel Rotter
Two Dimensional Optimal Mechanism Design for a Sequencing
Problem ........................................................ 242
Ruben Hoeksma and Marc Uetz
Advances on Matroid Secretary Problems: Free Order Model and
Laminar Case ................................................... 254
Patrick Jaillet, Jos´e A. Soto, and Rico Zenklusen
A Polynomial-Time Algorithm to Check Closedness of Simple Second
Order Mixed-Integer Sets ......................................... 266
Diego Alejandro Mora´n Ram´ırez and Santanu S. Dey
The Complexity of Scheduling for p-Norms of Flow and Stretch
(Extended Abstract) ............................................. 278
Benjamin Moseley, Kirk Pruhs, and Cliff Stein
The Euclidean k-Supplier Problem ................................. 290
Viswanath Nagarajan, Baruch Schieber, and Hadas Shachnai
Table of Contents XI
Facial Structure and Representation of Integer Hulls of Convex Sets .... 302
Vishnu Narayanan
An Efficient Polynomial-Time Approximation Scheme for the Joint
Replenishment Problem........................................... 314
Tim Nonner and Maxim Sviridenko
Chain-Constrained Spanning Trees ................................. 324
Neil Olver and Rico Zenklusen
A Simpler Proof for O(Congestion+Dilation) Packet Routing ......... 336
Thomas Rothvoß
0/1 Polytopes with Quadratic Chva´tal Rank ........................ 349
Thomas Rothvoß and Laura Sanit´a
Eight-Fifth Approximation for the Path TSP ........................ 362
Andr´as Seb˝o
Fast Deterministic Algorithms for Matrix Completion Problems........ 375
Tasuku Soma
Approximating the Configuration-LP for Minimizing Weighted Sum
of Completion Times on Unrelated Machines ........................ 387
Maxim Sviridenko and Andreas Wiese
Author Index.................................................. 399
On the Structure of Reduced Kernel Lattice
Bases
Karen Aardal1,2 and Frederik von Heymann1
1 Delft Instituteof Applied Mathematics, TU Delft, The Netherlands
{k.i.aardal,f.j.vonheymann}@tudelft.nl
2 Centrum Wiskundeen Informatica, Amsterdam, The Netherlands
Abstract. Lattice-based reformulation techniques have been used suc-
cessfullyboththeoreticallyandcomputationally.Onesuchreformulation
is obtained from the lattice kerZ(A) = {x ∈ Zn | Ax = 0}. Some of
the hard instances in the literature that have been successfully tackled
by lattice-based techniques, such as market split and certain classes of
knapsack instances, have randomly generated input A. These instances
havebeen posed to stimulate algorithmic research. Sincetheconsidered
instances are very hard even in low dimension, less experience is avail-
able for larger instances. Recently we have studied larger instances and
observed that the LLL-reduced basis of kerZ(A) has a specific sparse
structure. In particular, this translates into a map in which some of
the original variables get a “rich” translation into a new variable space,
whereassomevariablesareonlysubstitutedinthenewspace.Ifanorig-
inal variable is important in the sense of branching or cutting planes,
this variable should be translated in a non-trivial way. In this paper we
partially explain theobtained structureof theLLL-reduced basis in the
case that the input matrix A consists of one row a. Since the input is
randomlygeneratedouranalysiswillbeprobabilistic.Thekeyingredient
is a bound on the probability that the LLL algorithm will interchange
two subsequent basis vectors. It is worth noticing that computational
experiments indicate that the results of this analysis seem to apply in
the same way also in the general case that A consists of multiple rows.
Ouranalysishasyettobeextendedtothisgeneralcase.Alongwithour
analysis we also present some computational indications that illustrate
thattheprobabilisticanalysisconformswellwiththepracticalbehavior.
1 Introduction
Consider the following integer program:
max{cx|Ax=b, x≥0}, (1)
where A is an integer m×n matrix of full row rank and b an integer m-vector.
Starting with the well-known algorithm of Lenstra [13], several lattice-based
approaches to reformulate the feasible region have been proposed, see, e.g., [1,
3, 5, 11, 16–18]. Here we will consider the reformulation as in [1]:
x:=x0+Qλ, (2)
M.GoemansandJ.Correa(Eds.):IPCO2013,LNCS7801,pp.1–12,2013.
(cid:2)c Springer-VerlagBerlinHeidelberg2013
