A polynomial oracle-time algorithm for convex integer minimization
In this paper we consider the solution of certain convex integer minimization problems via greedy augmentation procedures. We show that a greedy augmentation procedure that employs only directions from certain Graver bases needs only polynomially many augmentation steps to solve the given problem. W...
Saved in:
| Published in: | Mathematical programming Vol. 126; no. 1; pp. 97 - 117 |
|---|---|
| Main Authors: | , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Berlin/Heidelberg
Springer-Verlag
01.01.2011
Springer Springer Nature B.V |
| Subjects: | |
| ISSN: | 0025-5610, 1436-4646 |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Abstract | In this paper we consider the solution of certain convex integer minimization problems via greedy augmentation procedures. We show that a greedy augmentation procedure that employs only directions from certain Graver bases needs only polynomially many augmentation steps to solve the given problem. We extend these results to convex
N
-fold integer minimization problems and to convex 2-stage stochastic integer minimization problems. Finally, we present some applications of convex
N
-fold integer minimization problems for which our approach provides polynomial time solution algorithms. |
|---|---|
| AbstractList | In this paper we consider the solution of certain convex integer minimization problems via greedy augmentation procedures. We show that a greedy augmentation procedure that employs only directions from certain Graver bases needs only polynomially many augmentation steps to solve the given problem. We extend these results to convex N-fold integer minimization problems and to convex 2-stage stochastic integer minimization problems. Finally, we present some applications of convex N-fold integer minimization problems for which our approach provides polynomial time solution algorithms.[PUBLICATION ABSTRACT] In this paper we consider the solution of certain convex integer minimization problems via greedy augmentation procedures. We show that a greedy augmentation procedure that employs only directions from certain Graver bases needs only polynomially many augmentation steps to solve the given problem. We extend these results to convex N-fold integer minimization problems and to convex 2-stage stochastic integer minimization problems. Finally, we present some applications of convex N-fold integer minimization problems for which our approach provides polynomial time solution algorithms. In this paper we consider the solution of certain convex integer minimization problems via greedy augmentation procedures. We show that a greedy augmentation procedure that employs only directions from certain Graver bases needs only polynomially many augmentation steps to solve the given problem. We extend these results to convex N -fold integer minimization problems and to convex 2-stage stochastic integer minimization problems. Finally, we present some applications of convex N -fold integer minimization problems for which our approach provides polynomial time solution algorithms. |
| Author | Hemmecke, Raymond Onn, Shmuel Weismantel, Robert |
| Author_xml | – sequence: 1 givenname: Raymond surname: Hemmecke fullname: Hemmecke, Raymond email: raymond@hemmecke.de organization: Fakultät für Mathematik, Otto-von-Guericke-Universität Magdeburg – sequence: 2 givenname: Shmuel surname: Onn fullname: Onn, Shmuel organization: Davidson Faculty of IE & M, Technion - Israel Institute of Technology – sequence: 3 givenname: Robert surname: Weismantel fullname: Weismantel, Robert organization: Fakultät für Mathematik, Otto-von-Guericke-Universität Magdeburg |
| BackLink | http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=23790115$$DView record in Pascal Francis |
| BookMark | eNp9kU1rFEEQhhtJwE30B3gbBPHUsWqmP2aPMcQkEPBizk1tT03s0NO9ds-K8dc760aEgJ7q8jwvVfWeiKOUEwvxBuEMAeyHioBgJcBaQmuNtC_EClVnpDLKHIkVQKulNggvxUmtDwCAXd-vxMfzZpvjY8pToNjkQj6ynMPEDcX7XML8dWrGXBqf03f-0YQ08z2XZgopTOEnzSGnV-J4pFj59dM8FXefLr9cXMvbz1c3F-e30ivVzdL0CnHUjHowm27cECv2OFhGGDaDVZbX2jONWttuULRR1CvSOOh2PRhoqTsV7w-525K_7bjObgrVc4yUOO-q6xcTbWf0Qr59Rj7kXUnLcq5v0SrTglmgd08QVU9xLJR8qG5bwkTl0bWdXQPiPsweOF9yrYVH58P8-_C5UIgOwe0bcIcG3NKA2zfg7GLiM_NP-P-c9uDUhU3Lq_-u_m_pF4LImcg |
| CODEN | MHPGA4 |
| CitedBy_id | crossref_primary_10_1016_j_disopt_2014_07_003 crossref_primary_10_1365_s13291_012_0055_x crossref_primary_10_1287_ijoc_2024_0574 crossref_primary_10_3389_fcomp_2023_1286657 crossref_primary_10_1007_s00026_015_0297_2 crossref_primary_10_1137_20M1330658 crossref_primary_10_1515_advgeom_2016_0020 crossref_primary_10_1137_151002915 crossref_primary_10_1016_j_orl_2020_04_004 crossref_primary_10_1007_s10107_013_0638_z crossref_primary_10_1137_21M1419994 crossref_primary_10_1016_j_disopt_2021_100629 crossref_primary_10_1007_s11590_010_0231_9 crossref_primary_10_1016_j_disopt_2024_100862 crossref_primary_10_1007_s10107_011_0447_1 crossref_primary_10_1016_j_disopt_2019_100566 crossref_primary_10_1137_22M1489988 crossref_primary_10_3389_fcomp_2023_1286860 crossref_primary_10_1007_s10107_010_0383_5 crossref_primary_10_1017_S0962492913000032 crossref_primary_10_1007_s10107_012_0545_8 crossref_primary_10_1016_j_laa_2014_01_007 crossref_primary_10_1137_151004227 crossref_primary_10_1134_S199047892001007X crossref_primary_10_1137_140976868 crossref_primary_10_1007_s10107_011_0490_y crossref_primary_10_1016_j_orl_2014_10_002 crossref_primary_10_1016_j_jsc_2015_09_003 crossref_primary_10_1007_s10107_012_0605_0 crossref_primary_10_1016_j_disopt_2017_08_004 crossref_primary_10_1016_j_disc_2018_09_021 |
| Cites_doi | 10.1007/s10107-002-0322-1 10.1137/040610623 10.1016/j.orl.2004.09.003 10.1007/s10107-003-0385-7 10.1016/j.jcta.2006.06.001 10.1137/S0097539702403803 10.1007/BF01681344 10.1007/BF01737559 10.1007/978-3-662-04331-8_29 10.1007/s10208-005-0174-1 10.1016/j.orl.2003.11.007 |
| ContentType | Journal Article |
| Copyright | Springer and Mathematical Programming Society 2009 2015 INIST-CNRS Springer and Mathematical Optimization Society 2011 |
| Copyright_xml | – notice: Springer and Mathematical Programming Society 2009 – notice: 2015 INIST-CNRS – notice: Springer and Mathematical Optimization Society 2011 |
| DBID | AAYXX CITATION IQODW 3V. 7SC 7WY 7WZ 7XB 87Z 88I 8AL 8AO 8FD 8FE 8FG 8FK 8FL ABJCF ABUWG AFKRA ARAPS AZQEC BENPR BEZIV BGLVJ CCPQU DWQXO FRNLG F~G GNUQQ HCIFZ JQ2 K60 K6~ K7- L.- L.0 L6V L7M L~C L~D M0C M0N M2P M7S P5Z P62 PHGZM PHGZT PKEHL PQBIZ PQBZA PQEST PQGLB PQQKQ PQUKI PRINS PTHSS Q9U |
| DOI | 10.1007/s10107-009-0276-7 |
| DatabaseName | CrossRef Pascal-Francis ProQuest Central (Corporate) Computer and Information Systems Abstracts ABI/INFORM Collection ABI/INFORM Global (PDF only) ProQuest Central (purchase pre-March 2016) ABI/INFORM Collection Science Database (Alumni Edition) Computing Database (Alumni Edition) ProQuest Pharma Collection Technology Research Database ProQuest SciTech Collection ProQuest Technology Collection ProQuest Central (Alumni) (purchase pre-March 2016) ABI/INFORM Collection (Alumni) Materials Science & Engineering Collection ProQuest Central ProQuest Central UK/Ireland Advanced Technologies & Computer Science Collection ProQuest Central Essentials ProQuest Central Business Premium Collection ProQuest Technology Collection ProQuest One Community College ProQuest Central Korea Business Premium Collection (Alumni) ABI/INFORM Global (Corporate) ProQuest Central Student SciTech Premium Collection ProQuest Computer Science Collection ProQuest Business Collection (Alumni Edition) ProQuest Business Collection Computer Science Database ABI/INFORM Professional Advanced ABI/INFORM Professional Standard ProQuest Engineering Collection Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional ABI/INFORM Global Computing Database Science Database (ProQuest) Engineering Database Advanced Technologies & Aerospace Database ProQuest Advanced Technologies & Aerospace Collection ProQuest Central Premium ProQuest One Academic (New) ProQuest One Academic Middle East (New) ProQuest One Business ProQuest One Business (Alumni) ProQuest One Academic Eastern Edition (DO NOT USE) ProQuest One Applied & Life Sciences ProQuest One Academic (retired) ProQuest One Academic UKI Edition ProQuest Central China Engineering Collection ProQuest Central Basic |
| DatabaseTitle | CrossRef ProQuest Business Collection (Alumni Edition) Computer Science Database ProQuest Central Student ProQuest Advanced Technologies & Aerospace Collection ProQuest Central Essentials ProQuest Computer Science Collection Computer and Information Systems Abstracts SciTech Premium Collection ProQuest Central China ABI/INFORM Complete ProQuest One Applied & Life Sciences ProQuest Central (New) Engineering Collection Advanced Technologies & Aerospace Collection Business Premium Collection ABI/INFORM Global Engineering Database ProQuest Science Journals (Alumni Edition) ProQuest One Academic Eastern Edition ProQuest Technology Collection ProQuest Business Collection ProQuest One Academic UKI Edition ProQuest One Academic ProQuest One Academic (New) ABI/INFORM Global (Corporate) ProQuest One Business Technology Collection Technology Research Database Computer and Information Systems Abstracts – Academic ProQuest One Academic Middle East (New) ProQuest Central (Alumni Edition) ProQuest One Community College ProQuest Pharma Collection ProQuest Central ABI/INFORM Professional Advanced ProQuest Engineering Collection ABI/INFORM Professional Standard ProQuest Central Korea Advanced Technologies Database with Aerospace ABI/INFORM Complete (Alumni Edition) ProQuest Computing ABI/INFORM Global (Alumni Edition) ProQuest Central Basic ProQuest Science Journals ProQuest Computing (Alumni Edition) ProQuest SciTech Collection Computer and Information Systems Abstracts Professional Advanced Technologies & Aerospace Database Materials Science & Engineering Collection ProQuest One Business (Alumni) ProQuest Central (Alumni) Business Premium Collection (Alumni) |
| DatabaseTitleList | ProQuest Business Collection (Alumni Edition) Computer and Information Systems Abstracts |
| Database_xml | – sequence: 1 dbid: BENPR name: ProQuest Central Database Suite (ProQuest) url: https://www.proquest.com/central sourceTypes: Aggregation Database |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Engineering Mathematics Applied Sciences Statistics |
| EISSN | 1436-4646 |
| EndPage | 117 |
| ExternalDocumentID | 2225965101 23790115 10_1007_s10107_009_0276_7 |
| Genre | Feature |
| GroupedDBID | --K --Z -52 -5D -5G -BR -EM -Y2 -~C -~X .4S .86 .DC .VR 06D 0R~ 0VY 199 1B1 1N0 1OL 1SB 203 28- 29M 2J2 2JN 2JY 2KG 2KM 2LR 2P1 2VQ 2~H 30V 3V. 4.4 406 408 409 40D 40E 5GY 5QI 5VS 67Z 6NX 6TJ 78A 7WY 88I 8AO 8FE 8FG 8FL 8TC 8UJ 8VB 95- 95. 95~ 96X AAAVM AABHQ AACDK AAHNG AAIAL AAJBT AAJKR AANZL AARHV AARTL AASML AATNV AATVU AAUYE AAWCG AAYIU AAYQN AAYTO AAYZH ABAKF ABBBX ABBXA ABDBF ABDZT ABECU ABFTV ABHLI ABHQN ABJCF ABJNI ABJOX ABKCH ABKTR ABMNI ABMQK ABNWP ABQBU ABQSL ABSXP ABTEG ABTHY ABTKH ABTMW ABULA ABUWG ABWNU ABXPI ACAOD ACBXY ACDTI ACGFS ACGOD ACHSB ACHXU ACIWK ACKNC ACMDZ ACMLO ACNCT ACOKC ACOMO ACPIV ACUHS ACZOJ ADHHG ADHIR ADIMF ADINQ ADKNI ADKPE ADRFC ADTPH ADURQ ADYFF ADZKW AEBTG AEFIE AEFQL AEGAL AEGNC AEJHL AEJRE AEKMD AEMOZ AEMSY AENEX AEOHA AEPYU AESKC AETLH AEVLU AEXYK AFBBN AFEXP AFFNX AFGCZ AFKRA AFLOW AFQWF AFWTZ AFZKB AGAYW AGDGC AGGDS AGJBK AGMZJ AGQEE AGQMX AGRTI AGWIL AGWZB AGYKE AHAVH AHBYD AHKAY AHQJS AHSBF AHYZX AIAKS AIGIU AIIXL AILAN AITGF AJBLW AJRNO AJZVZ AKVCP ALMA_UNASSIGNED_HOLDINGS ALWAN AMKLP AMXSW AMYLF AMYQR AOCGG ARAPS ARCSS ARMRJ ASPBG AVWKF AXYYD AYJHY AZFZN AZQEC B-. B0M BA0 BAPOH BBWZM BDATZ BENPR BEZIV BGLVJ BGNMA BPHCQ BSONS CAG CCPQU COF CS3 CSCUP DDRTE DL5 DNIVK DPUIP DU5 DWQXO EAD EAP EBA EBLON EBR EBS EBU ECS EDO EIOEI EJD EMI EMK EPL ESBYG EST ESX FEDTE FERAY FFXSO FIGPU FINBP FNLPD FRNLG FRRFC FSGXE FWDCC GGCAI GGRSB GJIRD GNUQQ GNWQR GQ6 GQ7 GQ8 GROUPED_ABI_INFORM_COMPLETE GXS H13 HCIFZ HF~ HG5 HG6 HMJXF HQYDN HRMNR HVGLF HZ~ H~9 I-F I09 IAO IHE IJ- IKXTQ ITM IWAJR IXC IZIGR IZQ I~X I~Z J-C J0Z JBSCW JCJTX JZLTJ K1G K60 K6V K6~ K7- KDC KOV KOW L6V LAS LLZTM M0C M0N M2P M4Y M7S MA- N2Q N9A NB0 NDZJH NPVJJ NQ- NQJWS NU0 O9- O93 O9G O9I O9J OAM P19 P2P P62 P9R PF0 PQBIZ PQBZA PQQKQ PROAC PT4 PT5 PTHSS Q2X QOK QOS QWB R4E R89 R9I RHV RIG RNI RNS ROL RPX RPZ RSV RZK S16 S1Z S26 S27 S28 S3B SAP SCLPG SDD SDH SDM SHX SISQX SJYHP SMT SNE SNPRN SNX SOHCF SOJ SPISZ SRMVM SSLCW STPWE SZN T13 T16 TH9 TN5 TSG TSK TSV TUC TUS U2A UG4 UOJIU UTJUX UZXMN VC2 VFIZW W23 W48 WH7 WK8 XPP YLTOR Z45 Z5O Z7R Z7S Z7X Z7Y Z7Z Z81 Z83 Z86 Z88 Z8M Z8N Z8R Z8T Z8W Z92 ZL0 ZMTXR ZWQNP ~02 ~8M ~EX AAPKM AAYXX ABBRH ABDBE ABFSG ABRTQ ACSTC ADHKG ADXHL AEZWR AFDZB AFFHD AFHIU AFOHR AGQPQ AHPBZ AHWEU AIXLP AMVHM ATHPR AYFIA CITATION PHGZM PHGZT PQGLB IQODW 7SC 7XB 8AL 8FD 8FK JQ2 L.- L.0 L7M L~C L~D PKEHL PQEST PQUKI PRINS PUEGO Q9U |
| ID | FETCH-LOGICAL-c443t-68411f5e15d6b3fbae4ec1d7e10dbd747e95ceaf5573d4ab4a84a51d529d602a3 |
| IEDL.DBID | M2P |
| ISICitedReferencesCount | 37 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000286218900004&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 0025-5610 |
| IngestDate | Sun Nov 09 13:33:43 EST 2025 Thu Sep 25 00:41:55 EDT 2025 Mon Jul 21 09:15:08 EDT 2025 Tue Nov 18 22:22:43 EST 2025 Sat Nov 29 05:49:01 EST 2025 Fri Feb 21 02:32:34 EST 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 1 |
| Keywords | 68R 68U 52B 68W 52C 90B 62H 90C 68Q Polytope Statistical analysis Probabilistic approach Minimization Multivariate analysis Convex programming Polynomial time Integer programming Discrete geometry Oracle |
| Language | English |
| License | http://www.springer.com/tdm CC BY 4.0 |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c443t-68411f5e15d6b3fbae4ec1d7e10dbd747e95ceaf5573d4ab4a84a51d529d602a3 |
| Notes | SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 ObjectType-Article-2 content type line 23 |
| PQID | 821746206 |
| PQPubID | 25307 |
| PageCount | 21 |
| ParticipantIDs | proquest_miscellaneous_855717365 proquest_journals_821746206 pascalfrancis_primary_23790115 crossref_citationtrail_10_1007_s10107_009_0276_7 crossref_primary_10_1007_s10107_009_0276_7 springer_journals_10_1007_s10107_009_0276_7 |
| PublicationCentury | 2000 |
| PublicationDate | 2011-01-01 |
| PublicationDateYYYYMMDD | 2011-01-01 |
| PublicationDate_xml | – month: 01 year: 2011 text: 2011-01-01 day: 01 |
| PublicationDecade | 2010 |
| PublicationPlace | Berlin/Heidelberg |
| PublicationPlace_xml | – name: Berlin/Heidelberg – name: Heidelberg |
| PublicationSubtitle | A Publication of the Mathematical Optimization Society |
| PublicationTitle | Mathematical programming |
| PublicationTitleAbbrev | Math. Program |
| PublicationYear | 2011 |
| Publisher | Springer-Verlag Springer Springer Nature B.V |
| Publisher_xml | – name: Springer-Verlag – name: Springer – name: Springer Nature B.V |
| References | MärkertA.SchultzR.On deviation measures in stochastic integer programmingOper. Res. Lett.2005334414491099.9003710.1016/j.orl.2004.09.0032146607 GraverJ.E.On the foundation of linear and integer programming IMath. Program.197592072260323.9003510.1007/BF01681344386673 Hemmecke, R.: Test Sets for Integer Programs with Z-convex Objective Function. e-print available from http://front.math.ucdavis.edu/math.CO/0309154, 2003 HemmeckeR.SchultzR.Decomposition of test sets in stochastic integer programmingMath. Program.2003943233411030.9007310.1007/s10107-002-0322-11969115 LouveauxF.V.SchultzR.RuszczynskiA.ShapiroA.Stochastic Integer ProgrammingHandbooks in Operations Research and Management Science, 10: Stochastic Programming2003AmsterdamElsevier Science213266 HoştenS.SullivantS.Finiteness theorems for Markov bases of hierarchical modelsJ. Combinat. Theory Ser. A20071143113211111.6205310.1016/j.jcta.2006.06.001 De LoeraJ.A.OnnS.All linear and integer programs are slim 3-way transportation programsSIAM J. Optim.2006178068211128.9004110.1137/0406106232257210 Sebö, A.: Hilbert bases, Caratheodory’s Theorem and combinatorial optimization. In: Proceedings of the IPCO conference,Waterloo, Canada, pp. 431–455 (1990) De Loera, J.A., Hemmecke, R., Onn, S., Weismantel, R.: N-fold integer programming. Discrete Optim. (to appear) SchultzR.DantzigG.B.HinfangerG.Risk aversion in two-stage stochastic integer programmingStochastic Programming.2006DordrechtKluwer RömischW.SchultzR.GrötschelM.KrumkeS.O.RambauJ.Multistage stochastic integer programming: an introductionOnline Optimization of Large Scale Systems2001BerlinSpringer581600 HemmeckeR.On the positive sum property and the computation of Graver test setsMath. Program.2003962472691059.9010810.1007/s10107-003-0385-71993048 BirgeJ.R.LouveauxF.V.Intorduction to Stochastic Programming1997New YorkSpringer AhujaR.K.MagnantiT.L.OrlinJ.B.Network Flows: Theory, Algorithms, and Applications1993New JerseyPrentice-Hall, Inc. AschenbrennerM.HemmeckeR.Finiteness theorems in stochastic integer programmingFound. Comput. Math.200771832271183.9031310.1007/s10208-005-0174-12324416 De LoeraJ.A.OnnS.The complexity of three-way statistical tablesSIAM J. Comput.2004338198361101.6899610.1137/S00975397024038032065334 MurotaK.SaitoH.WeismantelR.Optimality criterion for a class of nonlinear integer programsOper. Res. Lett.2004324684721054.9004910.1016/j.orl.2003.11.0072058308 Schulz, A., Weismantel, R.: An oracle-polynomial time augmentation algorithm for integer programming. In: Proc. of the 10th ACM-SIAM Symposium on Discrete Algorithms, Baltimore, pp. 967–968 (1999) RosenthalR.W.A class of games possessing pure-strategy Nash equilibriaInt. J. Game Theory1973265670259.9005910.1007/BF01737559 276_CR4 R. Hemmecke (276_CR8) 2003; 96 F.V. Louveaux (276_CR12) 2003 R.K. Ahuja (276_CR1) 1993 R. Hemmecke (276_CR10) 2003; 94 J.R. Birge (276_CR3) 1997 J.A. De Loera (276_CR5) 2004; 33 276_CR9 W. Römisch (276_CR15) 2001 R.W. Rosenthal (276_CR16) 1973; 2 J.E. Graver (276_CR7) 1975; 9 M. Aschenbrenner (276_CR2) 2007; 7 S. Hoşten (276_CR11) 2007; 114 276_CR19 276_CR18 A. Märkert (276_CR13) 2005; 33 K. Murota (276_CR14) 2004; 32 R. Schultz (276_CR17) 2006 J.A. De Loera (276_CR6) 2006; 17 |
| References_xml | – reference: BirgeJ.R.LouveauxF.V.Intorduction to Stochastic Programming1997New YorkSpringer – reference: Hemmecke, R.: Test Sets for Integer Programs with Z-convex Objective Function. e-print available from http://front.math.ucdavis.edu/math.CO/0309154, 2003 – reference: MurotaK.SaitoH.WeismantelR.Optimality criterion for a class of nonlinear integer programsOper. Res. Lett.2004324684721054.9004910.1016/j.orl.2003.11.0072058308 – reference: HemmeckeR.On the positive sum property and the computation of Graver test setsMath. Program.2003962472691059.9010810.1007/s10107-003-0385-71993048 – reference: HemmeckeR.SchultzR.Decomposition of test sets in stochastic integer programmingMath. Program.2003943233411030.9007310.1007/s10107-002-0322-11969115 – reference: RosenthalR.W.A class of games possessing pure-strategy Nash equilibriaInt. J. Game Theory1973265670259.9005910.1007/BF01737559 – reference: SchultzR.DantzigG.B.HinfangerG.Risk aversion in two-stage stochastic integer programmingStochastic Programming.2006DordrechtKluwer – reference: Schulz, A., Weismantel, R.: An oracle-polynomial time augmentation algorithm for integer programming. In: Proc. of the 10th ACM-SIAM Symposium on Discrete Algorithms, Baltimore, pp. 967–968 (1999) – reference: GraverJ.E.On the foundation of linear and integer programming IMath. Program.197592072260323.9003510.1007/BF01681344386673 – reference: De Loera, J.A., Hemmecke, R., Onn, S., Weismantel, R.: N-fold integer programming. Discrete Optim. (to appear) – reference: HoştenS.SullivantS.Finiteness theorems for Markov bases of hierarchical modelsJ. Combinat. Theory Ser. A20071143113211111.6205310.1016/j.jcta.2006.06.001 – reference: AschenbrennerM.HemmeckeR.Finiteness theorems in stochastic integer programmingFound. Comput. Math.200771832271183.9031310.1007/s10208-005-0174-12324416 – reference: LouveauxF.V.SchultzR.RuszczynskiA.ShapiroA.Stochastic Integer ProgrammingHandbooks in Operations Research and Management Science, 10: Stochastic Programming2003AmsterdamElsevier Science213266 – reference: AhujaR.K.MagnantiT.L.OrlinJ.B.Network Flows: Theory, Algorithms, and Applications1993New JerseyPrentice-Hall, Inc. – reference: Sebö, A.: Hilbert bases, Caratheodory’s Theorem and combinatorial optimization. In: Proceedings of the IPCO conference,Waterloo, Canada, pp. 431–455 (1990) – reference: De LoeraJ.A.OnnS.All linear and integer programs are slim 3-way transportation programsSIAM J. Optim.2006178068211128.9004110.1137/0406106232257210 – reference: MärkertA.SchultzR.On deviation measures in stochastic integer programmingOper. Res. Lett.2005334414491099.9003710.1016/j.orl.2004.09.0032146607 – reference: RömischW.SchultzR.GrötschelM.KrumkeS.O.RambauJ.Multistage stochastic integer programming: an introductionOnline Optimization of Large Scale Systems2001BerlinSpringer581600 – reference: De LoeraJ.A.OnnS.The complexity of three-way statistical tablesSIAM J. Comput.2004338198361101.6899610.1137/S00975397024038032065334 – volume: 94 start-page: 323 year: 2003 ident: 276_CR10 publication-title: Math. Program. doi: 10.1007/s10107-002-0322-1 – start-page: 213 volume-title: Handbooks in Operations Research and Management Science, 10: Stochastic Programming year: 2003 ident: 276_CR12 – volume: 17 start-page: 806 year: 2006 ident: 276_CR6 publication-title: SIAM J. Optim. doi: 10.1137/040610623 – ident: 276_CR9 – volume: 33 start-page: 441 year: 2005 ident: 276_CR13 publication-title: Oper. Res. Lett. doi: 10.1016/j.orl.2004.09.003 – volume: 96 start-page: 247 year: 2003 ident: 276_CR8 publication-title: Math. Program. doi: 10.1007/s10107-003-0385-7 – volume: 114 start-page: 311 year: 2007 ident: 276_CR11 publication-title: J. Combinat. Theory Ser. A doi: 10.1016/j.jcta.2006.06.001 – volume-title: Stochastic Programming. year: 2006 ident: 276_CR17 – ident: 276_CR4 – volume: 33 start-page: 819 year: 2004 ident: 276_CR5 publication-title: SIAM J. Comput. doi: 10.1137/S0097539702403803 – volume: 9 start-page: 207 year: 1975 ident: 276_CR7 publication-title: Math. Program. doi: 10.1007/BF01681344 – volume: 2 start-page: 65 year: 1973 ident: 276_CR16 publication-title: Int. J. Game Theory doi: 10.1007/BF01737559 – volume-title: Intorduction to Stochastic Programming year: 1997 ident: 276_CR3 – start-page: 581 volume-title: Online Optimization of Large Scale Systems year: 2001 ident: 276_CR15 doi: 10.1007/978-3-662-04331-8_29 – volume: 7 start-page: 183 year: 2007 ident: 276_CR2 publication-title: Found. Comput. Math. doi: 10.1007/s10208-005-0174-1 – volume: 32 start-page: 468 year: 2004 ident: 276_CR14 publication-title: Oper. Res. Lett. doi: 10.1016/j.orl.2003.11.007 – ident: 276_CR18 – volume-title: Network Flows: Theory, Algorithms, and Applications year: 1993 ident: 276_CR1 – ident: 276_CR19 |
| SSID | ssj0001388 |
| Score | 2.1903412 |
| Snippet | In this paper we consider the solution of certain convex integer minimization problems via greedy augmentation procedures. We show that a greedy augmentation... |
| SourceID | proquest pascalfrancis crossref springer |
| SourceType | Aggregation Database Index Database Enrichment Source Publisher |
| StartPage | 97 |
| SubjectTerms | Algorithmics. Computability. Computer arithmetics Algorithms Applied sciences Augmentation Calculus of Variations and Optimal Control; Optimization Circuits Combinatorics Computer science; control theory; systems Convex analysis Convex and discrete geometry Exact sciences and technology Full Length Paper Geometry Information retrieval. Graph Integer programming Integers Mathematical analysis Mathematical and Computational Physics Mathematical Methods in Physics Mathematical programming Mathematics Mathematics and Statistics Mathematics of Computing Minimization Multivariate analysis Numerical Analysis Optimization Polynomials Probability and statistics Sciences and techniques of general use Statistics Stochasticity Studies Theorems Theoretical Theoretical computing |
| SummonAdditionalLinks | – databaseName: SpringerLINK Contemporary 1997-Present dbid: RSV link: http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1LT9wwEB4VyoEKtbwqtrQrHziBIsXxM0daFfVSVPESt8ixHVhpX9rsIvj3jLNJlkUFCaRconhGznhsz3g88wEcMCO1dSaNjEEN5trzSIsUfR5Lbey59bnhFdiEOj3V19fpvzqPu2xuuzchyWqlfpLsRsOxWjjMT5SM1Ap8xN1OB7yGs_OrdvmlTOsGpzUYB00o838sljajjbEpUS7FHNBiyeJ8FiSt9p6TL-_q9SZ8rk1NcjzXjS344Ifb8OlJAUJ8-9tWbS134OcxGY_6DyFRGelQN5AsCuDzxPRvRpPe9HZA0MYl1U31e1JVmvATEqqTDOp0zl24PPl98etPVGMsRJZzNo2k5pQWwlPhZM6K3HjuLXXK09jlDn0NnwrrTSGEYo6bnBvNjaBOJKmTcWLYV1gdjoZ-D0jhjEpTaxKVIG-KtgaVReESy6yOlWUdiBthZ7YuQB5wMPrZonRyEFaGwsqCsDLVgcOWZDyvvvFa4-7SCLYUCVMhwVZ0YL8Z0qyeqWWmg08mk1h2gLRfcYqFuIkZ-tEMm-DPU8UkMjhqBnnB4MX-fHtT631Ynx9Xh-c7rE4nM_8D1uzdtFdOupWKPwKyh_Wa priority: 102 providerName: Springer Nature |
| Title | A polynomial oracle-time algorithm for convex integer minimization |
| URI | https://link.springer.com/article/10.1007/s10107-009-0276-7 https://www.proquest.com/docview/821746206 https://www.proquest.com/docview/855717365 |
| Volume | 126 |
| WOSCitedRecordID | wos000286218900004&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVPQU databaseName: ABI/INFORM Collection customDbUrl: eissn: 1436-4646 dateEnd: 20171231 omitProxy: false ssIdentifier: ssj0001388 issn: 0025-5610 databaseCode: 7WY dateStart: 20011001 isFulltext: true titleUrlDefault: https://www.proquest.com/abicomplete providerName: ProQuest – providerCode: PRVPQU databaseName: ABI/INFORM Collection (ProQuest) customDbUrl: eissn: 1436-4646 dateEnd: 20171231 omitProxy: false ssIdentifier: ssj0001388 issn: 0025-5610 databaseCode: M0C dateStart: 20011001 isFulltext: true titleUrlDefault: https://search.proquest.com/abiglobal providerName: ProQuest – providerCode: PRVPQU databaseName: Advanced Technologies & Aerospace Database customDbUrl: eissn: 1436-4646 dateEnd: 20171231 omitProxy: false ssIdentifier: ssj0001388 issn: 0025-5610 databaseCode: P5Z dateStart: 20011001 isFulltext: true titleUrlDefault: https://search.proquest.com/hightechjournals providerName: ProQuest – providerCode: PRVPQU databaseName: Computer Science Database customDbUrl: eissn: 1436-4646 dateEnd: 20171231 omitProxy: false ssIdentifier: ssj0001388 issn: 0025-5610 databaseCode: K7- dateStart: 20011001 isFulltext: true titleUrlDefault: http://search.proquest.com/compscijour providerName: ProQuest – providerCode: PRVPQU databaseName: Engineering Database customDbUrl: eissn: 1436-4646 dateEnd: 20171231 omitProxy: false ssIdentifier: ssj0001388 issn: 0025-5610 databaseCode: M7S dateStart: 20011001 isFulltext: true titleUrlDefault: http://search.proquest.com providerName: ProQuest – providerCode: PRVPQU databaseName: ProQuest Central Database Suite (ProQuest) customDbUrl: eissn: 1436-4646 dateEnd: 20171231 omitProxy: false ssIdentifier: ssj0001388 issn: 0025-5610 databaseCode: BENPR dateStart: 20011001 isFulltext: true titleUrlDefault: https://www.proquest.com/central providerName: ProQuest – providerCode: PRVPQU databaseName: Science Database (ProQuest) customDbUrl: eissn: 1436-4646 dateEnd: 20171231 omitProxy: false ssIdentifier: ssj0001388 issn: 0025-5610 databaseCode: M2P dateStart: 20011001 isFulltext: true titleUrlDefault: https://search.proquest.com/sciencejournals providerName: ProQuest – providerCode: PRVAVX databaseName: SpringerLINK Contemporary 1997-Present customDbUrl: eissn: 1436-4646 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0001388 issn: 0025-5610 databaseCode: RSV dateStart: 19970101 isFulltext: true titleUrlDefault: https://link.springer.com/search?facet-content-type=%22Journal%22 providerName: Springer Nature |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpR1daxQxcLCtDxbxu3i2HnnwSVncfGefpC0tgtxxtH5UX5ZskrWF6915exX99072qz3BvgjLwLKZJJuZJJPMF8ArbpVx3maJtcjBwgSRGJnhmcdRlwbhQmFFnWxCj8fm7CybtLY5VWtW2a2J9ULt5y7ekb81UXZWLFXvFj-SmDQqKlfbDBobsIWCDY0WXSM26Rdiyo3pMrZGMaFTajaeczTe0UXNANMq0Wvb0v2FrXCEyia1xZrs-Ze6tN6Fjh_-Z_8fwYNW_CT7Db88hjth9gS2bwQlxLdRH8m1egoH-2Qxn_6OzsuIh_yCaElMSE_s9Ds2sDq_JCj3ktp6_Repo0-EJYkRSy5bF89n8On46OPh-6TNu5A4IfgqUUZQWspApVcFLwsbRHDU60BTX3g8f4RMumBLKTX3whbCGmEl9ZJlXqXM8h3YnM1n4TmQ0ludZc4yzbBuivIHVWXpmePOpNrxAaTdsOeuDUoec2NM8-twypFSOVIqj5TK9QBe9yiLJiLHbYWHa7TsMRjX0elWDmC3I1fezt4q72k1ANJ_xWkXdSl2FuZXWAR_nmqusII3HUtcV_DP_ry4tblduNdcWcdnDzZXy6vwEu66n6uLajmEDf3l6xC2Do7GkxN8-6AThKP0cFizfYT6FOFEfkN4cvr5DwRvBwo |
| linkProvider | ProQuest |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V1Jb9UwEB6VgkRRxV7xKBQf4AKKGi-xnUNVlaVq1faphyL1FhzbgUpv4yUF-qP4jx1nKw-J3npAyiWKx4njz-Oxx_MNwGtupLbOpJExiGChvYh0kuKax1Ibe2F9bkSdbEINh_r0ND1egt9dLEw4VtnpxFpRu6kNe-SbOtjOksVye_Y9CkmjgnO1y6DRoOLAX_zEFVu5tf8Ru_cNY7ufTj7sRW1SgcgKwatIakFpkXiaOJnzIjdeeEud8jR2uUPj2qeJ9aZIEsWdMLkwWpiEuoSlTsbMcKz3FtwWgVgsnBRkx73ip1zrLkNsMEs6J2oTqUfDnmDwRDAlI7UwDa7OTIk9UjSpNBZs3b_cs_Wst_vgP_tfD-F-a16TnWY8PIIlP3kM9_4gXcS7o56ptnwC73fIbDq6CMHZKIfjAcWi6mzsiRl9xQZV38YE7XpSn87_RWp2DT8ngZFl3IawPoXPN9KkNVieTCf-GZDCGZWm1jDFsG6K9hWVReGY5VbHyvIBxF03Z7YlXQ-5P0bZFV10QEaGyMgCMjI1gLe9yKxhHLmu8MYCdnoJxlUIKk4GsN7BI2u1U5n12BgA6Z-iWgm-IjPx03Msgo2nikus4F0HwasK_vk9z6993Su4u3dydJgd7g8P1mGl2Z4P1wtYrubn_iXcsT-qs3K-UQ8sAl9uGpmXsjteXA |
| linkToPdf | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV3dS9xAEB-sSlFEbVU8tboPfbIEs9nPPPp1tFQPoR_4Fja7GxXO3HGJov-9u_nSK1YohbyE7AzZmdlkZmfnNwCfieJSGxUHSjkLptLSQLLYxTwa69BSbVNFq2YTYjCQl5fxRdPntGhPu7cpybqmwaM05eXB2GQHLwrfsN9i8xv7keCBeAdz1J-j9-H6j9_dpxgTKduerd5RaNOar7GY-jEtjVXhZJTVzS2mvM8_EqbVf6i_8t8zWIXlxgVFh7XNfIAZm3-ExRfAhO7uvENzLdbg6BCNR8NHX8Ds6JzNOLLAN6VHang1mtyU17fI-b6oOsH-gCoECjtBHrXktinzXIdf_dOfx1-DpvdCoCklZcAlxThjFjPDU5KlylKrsREWhyY1LgaxMdNWZYwJYqhKqZJUMWxYFBseRopswGw-yu0moMwoEcdaRSJyvJ2WMOZZZiJNtAyFJj0IW8EnugEm9_0xhskzpLIXVuKElXhhJaIH-x3JuEbleGvw7pQ2O4qICF94y3qw3ao3aVZwkUgfq_Eo5D1A3VO39Hw-ReV2dOeGuMljQbhj8KVV-DODv77P1j-N3oP3Fyf95Ozb4Ps2LNQ72v7agdlycmc_wby-L2-KyW5l-U8kSgFx |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=A+polynomial+oracle-time+algorithm+for+convex+integer+minimization&rft.jtitle=Mathematical+programming&rft.au=Hemmecke%2C+Raymond&rft.au=Onn%2C+Shmuel&rft.au=Weismantel%2C+Robert&rft.date=2011-01-01&rft.pub=Springer+Nature+B.V&rft.issn=0025-5610&rft.eissn=1436-4646&rft.volume=126&rft.issue=1&rft.spage=97&rft_id=info:doi/10.1007%2Fs10107-009-0276-7&rft.externalDocID=2225965101 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0025-5610&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0025-5610&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0025-5610&client=summon |