Strengthening convex relaxations of 0/1-sets using Boolean formulas

In convex integer programming, various procedures have been developed to strengthen convex relaxations of sets of integer points. On the one hand, there exist several general-purpose methods that strengthen relaxations without specific knowledge of the set S of feasible integer points, such as popul...

Celý popis

Uloženo v:

Podrobná bibliografie
Vydáno v:	Mathematical programming Ročník 190; číslo 1-2; s. 467 - 482
Hlavní autoři:	Fiorini, Samuel, Huynh, Tony, Weltge, Stefan
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Berlin/Heidelberg Springer Berlin Heidelberg 01.11.2021 Springer Nature B.V
Témata:	Boolean Boolean algebra Calculus of Variations and Optimal Control; Optimization Combinatorial analysis Combinatorics Full Length Paper Hierarchies Integer programming Linear programming Mathematical and Computational Physics Mathematical Methods in Physics Mathematics Mathematics and Statistics Mathematics of Computing Numerical Analysis Optimization Theoretical 90Cxx 68Q06 52Bxx
ISSN:	0025-5610, 1436-4646
On-line přístup:	Získat plný text
Tagy:	Přidat tag Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!

Abstract	In convex integer programming, various procedures have been developed to strengthen convex relaxations of sets of integer points. On the one hand, there exist several general-purpose methods that strengthen relaxations without specific knowledge of the set S of feasible integer points, such as popular linear programming or semi-definite programming hierarchies. On the other hand, various methods have been designed for obtaining strengthened relaxations for very specific sets S that arise in combinatorial optimization. We propose a new efficient method that interpolates between these two approaches. Our procedure strengthens any convex set containing a set S ⊆ { 0 , 1 } n by exploiting certain additional information about S . Namely, the required extra information will be in the form of a Boolean formula ϕ defining the target set S . The new relaxation is obtained by “feeding” the convex set into the formula ϕ . We analyze various aspects regarding the strength of our procedure. As one application, interpreting an iterated application of our procedure as a hierarchy, our findings simplify, improve, and extend previous results by Bienstock and Zuckerberg on covering problems.
AbstractList	In convex integer programming, various procedures have been developed to strengthen convex relaxations of sets of integer points. On the one hand, there exist several general-purpose methods that strengthen relaxations without specific knowledge of the set S of feasible integer points, such as popular linear programming or semi-definite programming hierarchies. On the other hand, various methods have been designed for obtaining strengthened relaxations for very specific sets S that arise in combinatorial optimization. We propose a new efficient method that interpolates between these two approaches. Our procedure strengthens any convex set containing a set $$ S \subseteq \{0,1\}^n $$ S⊆0,1n by exploiting certain additional information about S. Namely, the required extra information will be in the form of a Boolean formula $$\phi $$ ϕ defining the target set S. The new relaxation is obtained by “feeding” the convex set into the formula $$\phi $$ ϕ. We analyze various aspects regarding the strength of our procedure. As one application, interpreting an iterated application of our procedure as a hierarchy, our findings simplify, improve, and extend previous results by Bienstock and Zuckerberg on covering problems. In convex integer programming, various procedures have been developed to strengthen convex relaxations of sets of integer points. On the one hand, there exist several general-purpose methods that strengthen relaxations without specific knowledge of the set S of feasible integer points, such as popular linear programming or semi-definite programming hierarchies. On the other hand, various methods have been designed for obtaining strengthened relaxations for very specific sets S that arise in combinatorial optimization. We propose a new efficient method that interpolates between these two approaches. Our procedure strengthens any convex set containing a set S ⊆ { 0 , 1 } n by exploiting certain additional information about S . Namely, the required extra information will be in the form of a Boolean formula ϕ defining the target set S . The new relaxation is obtained by “feeding” the convex set into the formula ϕ . We analyze various aspects regarding the strength of our procedure. As one application, interpreting an iterated application of our procedure as a hierarchy, our findings simplify, improve, and extend previous results by Bienstock and Zuckerberg on covering problems. In convex integer programming, various procedures have been developed to strengthen convex relaxations of sets of integer points. On the one hand, there exist several general-purpose methods that strengthen relaxations without specific knowledge of the set S of feasible integer points, such as popular linear programming or semi-definite programming hierarchies. On the other hand, various methods have been designed for obtaining strengthened relaxations for very specific sets S that arise in combinatorial optimization. We propose a new efficient method that interpolates between these two approaches. Our procedure strengthens any convex set containing a set S ⊆ { 0 , 1 } n by exploiting certain additional information about S. Namely, the required extra information will be in the form of a Boolean formula ϕ defining the target set S. The new relaxation is obtained by "feeding" the convex set into the formula ϕ . We analyze various aspects regarding the strength of our procedure. As one application, interpreting an iterated application of our procedure as a hierarchy, our findings simplify, improve, and extend previous results by Bienstock and Zuckerberg on covering problems.In convex integer programming, various procedures have been developed to strengthen convex relaxations of sets of integer points. On the one hand, there exist several general-purpose methods that strengthen relaxations without specific knowledge of the set S of feasible integer points, such as popular linear programming or semi-definite programming hierarchies. On the other hand, various methods have been designed for obtaining strengthened relaxations for very specific sets S that arise in combinatorial optimization. We propose a new efficient method that interpolates between these two approaches. Our procedure strengthens any convex set containing a set S ⊆ { 0 , 1 } n by exploiting certain additional information about S. Namely, the required extra information will be in the form of a Boolean formula ϕ defining the target set S. The new relaxation is obtained by "feeding" the convex set into the formula ϕ . We analyze various aspects regarding the strength of our procedure. As one application, interpreting an iterated application of our procedure as a hierarchy, our findings simplify, improve, and extend previous results by Bienstock and Zuckerberg on covering problems. In convex integer programming, various procedures have been developed to strengthen convex relaxations of sets of integer points. On the one hand, there exist several general-purpose methods that strengthen relaxations without specific knowledge of the set S of feasible integer points, such as popular linear programming or semi-definite programming hierarchies. On the other hand, various methods have been designed for obtaining strengthened relaxations for very specific sets S that arise in combinatorial optimization. We propose a new efficient method that interpolates between these two approaches. Our procedure strengthens any convex set containing a set S⊆{0,1}n by exploiting certain additional information about S. Namely, the required extra information will be in the form of a Boolean formula ϕ defining the target set S. The new relaxation is obtained by “feeding” the convex set into the formula ϕ. We analyze various aspects regarding the strength of our procedure. As one application, interpreting an iterated application of our procedure as a hierarchy, our findings simplify, improve, and extend previous results by Bienstock and Zuckerberg on covering problems. In convex integer programming, various procedures have been developed to strengthen convex relaxations of sets of integer points. On the one hand, there exist several general-purpose methods that strengthen relaxations without specific knowledge of the set S of feasible integer points, such as popular linear programming or semi-definite programming hierarchies. On the other hand, various methods have been designed for obtaining strengthened relaxations for very specific sets S that arise in combinatorial optimization. We propose a new efficient method that interpolates between these two approaches. Our procedure strengthens any convex set containing a set $$ S \subseteq \{0,1\}^n $$ S ⊆ { 0 , 1 } n by exploiting certain additional information about S . Namely, the required extra information will be in the form of a Boolean formula $$\phi $$ ϕ defining the target set S . The new relaxation is obtained by “feeding” the convex set into the formula $$\phi $$ ϕ . We analyze various aspects regarding the strength of our procedure. As one application, interpreting an iterated application of our procedure as a hierarchy, our findings simplify, improve, and extend previous results by Bienstock and Zuckerberg on covering problems.
Author	Huynh, Tony Fiorini, Samuel Weltge, Stefan
Author_xml	– sequence: 1 givenname: Samuel surname: Fiorini fullname: Fiorini, Samuel organization: Université libre de Bruxelles – sequence: 2 givenname: Tony surname: Huynh fullname: Huynh, Tony organization: Monash University – sequence: 3 givenname: Stefan surname: Weltge fullname: Weltge, Stefan email: weltge@tum.de organization: Technical University of Munich
BookMark	eNp9kUtvFDEQhC0URDaBP8BpJC5cnLTf3gsSrIAgReJA7pbt6dlMNGsHeyaPf4-TjUDkkFMf_FV1ueuIHKSckJD3DE4YgDmtDBgYChwoMCU5vX1FVkwKTaWW-oCsALiiSjM4JEe1XgEAE9a-IYdCGqOVkCuy-TUXTNv5EtOYtl3M6QbvuoKTv_PzmFPt8tDBKaMV59ot9QH6kvOEPnVDLrtl8vUteT34qeK7p3lMLr59vdic0fOf339sPp_TqJiZqbSyH4LoAw5BCtMHjyoY1WsFEH3odbTaWIV8jaqP6EMYGFcoddQ8rpU4Jp_2ttdL2GEj0lz85K7LuPPl3mU_uv9f0njptvnGWaWgHaQZfHwyKPn3gnV2u7FGnCafMC_VcbU2ljMmTEM_PEOv8lJS-12jLAjJpOSN4nsqllxrweFvGAbuoSK3r8i1itxjRe62iewzURznx1u30OP0slTspbXtSVss_1K9oPoD-HSoRQ
CitedBy_id	crossref_primary_10_1016_j_orl_2024_107156 crossref_primary_10_1109_LCSYS_2025_3585953 crossref_primary_10_1007_s10107_021_01705_3
Cites_doi	10.1007/978-3-319-33461-5_25 10.1007/978-3-319-59250-3_33 10.1287/moor.2017.0880 10.1016/j.ipl.2005.09.008 10.1109/FOCS.2015.73 10.1137/0403036 10.1137/0801013 10.1016/S0167-6377(98)00025-X 10.1007/978-3-642-15369-3_28 10.1007/11830924_38 10.1007/3-540-45535-3_23 10.1007/s10107-017-1134-7 10.1109/FOCS.2016.67 10.1145/3127497 10.1016/S0167-5060(08)70342-X 10.1016/0012-365X(73)90167-2 10.1007/s004930050057 10.1007/s10107-012-0574-3 10.1016/0020-0190(83)90011-X 10.1137/S1052623402420346 10.1145/2716307 10.1137/0403021 10.1137/1.9781611975031.53 10.1137/1.9781611974782.153 10.1145/146637.146684 10.1007/s10107-005-0598-z 10.1016/j.ipl.2012.02.009
ContentType	Journal Article
Copyright	The Author(s) 2020 The Author(s) 2020. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. The Author(s) 2020.
Copyright_xml	– notice: The Author(s) 2020 – notice: The Author(s) 2020. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. – notice: The Author(s) 2020.
DBID	C6C AAYXX CITATION 7SC 8FD JQ2 L7M L~C L~D 7X8 5PM
DOI	10.1007/s10107-020-01542-w
DatabaseName	Springer Nature OA Free Journals CrossRef Computer and Information Systems Abstracts Technology Research Database ProQuest Computer Science Collection Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional MEDLINE - Academic PubMed Central (Full Participant titles)
DatabaseTitle	CrossRef Computer and Information Systems Abstracts Technology Research Database Computer and Information Systems Abstracts – Academic Advanced Technologies Database with Aerospace ProQuest Computer Science Collection Computer and Information Systems Abstracts Professional MEDLINE - Academic
DatabaseTitleList	MEDLINE - Academic Computer and Information Systems Abstracts CrossRef
Database_xml	– sequence: 1 dbid: 7X8 name: MEDLINE - Academic url: https://search.proquest.com/medline sourceTypes: Aggregation Database
DeliveryMethod	fulltext_linktorsrc
Discipline	Engineering Mathematics
EISSN	1436-4646
EndPage	482
ExternalDocumentID	PMC8550646 10_1007_s10107_020_01542_w
GrantInformation_xml	– fundername: European Research Council grantid: 615640-ForEFront funderid: http://dx.doi.org/10.13039/501100000781 – fundername: National Science Foundation grantid: CCF-1740425 funderid: http://dx.doi.org/10.13039/100000001 – fundername: ; grantid: 615640-ForEFront – fundername: ; grantid: CCF-1740425
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 C6C 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 7SC 8FD JQ2 L7M L~C L~D 7X8 5PM
ID	FETCH-LOGICAL-c517t-484dfb3dbefb437dbae5b75d6500cabd6c86785e29e5dceabbf125e46c62c953
IEDL.DBID	RSV
ISICitedReferencesCount	5
ISICitedReferencesURI	http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000548756000001&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	Tue Nov 04 01:48:19 EST 2025 Fri Sep 05 07:25:49 EDT 2025 Thu Sep 25 00:52:26 EDT 2025 Sat Nov 29 03:34:02 EST 2025 Tue Nov 18 20:53:24 EST 2025 Fri Feb 21 02:47:09 EST 2025
IsDoiOpenAccess	true
IsOpenAccess	true
IsPeerReviewed	true
IsScholarly	true
Issue	1-2
Keywords	90Cxx 68Q06 52Bxx
Language	English
License	Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
LinkModel	DirectLink
MergedId	FETCHMERGED-LOGICAL-c517t-484dfb3dbefb437dbae5b75d6500cabd6c86785e29e5dceabbf125e46c62c953
Notes	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 content type line 23
OpenAccessLink	https://link.springer.com/10.1007/s10107-020-01542-w
PMID	34776534
PQID	2580341442
PQPubID	25307
PageCount	16
ParticipantIDs	pubmedcentral_primary_oai_pubmedcentral_nih_gov_8550646 proquest_miscellaneous_2597821137 proquest_journals_2580341442 crossref_primary_10_1007_s10107_020_01542_w crossref_citationtrail_10_1007_s10107_020_01542_w springer_journals_10_1007_s10107_020_01542_w
PublicationCentury	2000
PublicationDate	2021-11-01
PublicationDateYYYYMMDD	2021-11-01
PublicationDate_xml	– month: 11 year: 2021 text: 2021-11-01 day: 01
PublicationDecade	2020
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	2021
Publisher	Springer Berlin Heidelberg Springer Nature B.V
Publisher_xml	– name: Springer Berlin Heidelberg – name: Springer Nature B.V
References	BienstockDZuckerbergMSubset algebra lift operators for 0–1 integer programmingSIAM J. Optim.20041516395211297610.1137/S1052623402420346MR 2112976 Singh, M., Talwar, K.: Improving integrality gaps via Chvátal-Gomory rounding. In: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, 13th International Workshop, APPROX 2010, and 14th International Workshop, RANDOM 2010, Barcelona, Spain, September 1-3, 2010. Proceedings, pp. 366–379 (2010) WegenerIRelating monotone formula size and monotone depth of Boolean functionsInf. Process. Lett.1983161414269400810.1016/0020-0190(83)90011-X Benchetrit, Y., Fiorini, S., Huynh, T., Weltge, S.: Characterizing Polytopes Contained in the 0/1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0/1$$\end{document}-Cube with Bounded Chvátal-Gomory Rank. Mathematics of Operations Research (2018) Rothvoß, T.: The matching polytope has exponential extension complexity. J. ACM 64, no. 6, Art. 41, 19 (2017). MR 3713797 Göös, M., Jain, R., Watson, T.: Extension complexity of independent set polytopes. In: Proc. FOCS 2016, (2016) Fiorini, S., Groß, M., Könemann, J., Sanità, L.: Approximating weighted tree augmentation via Chvátal-Gomory cuts. In: Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 817–831. SIAM, Philadelphia, PA (2018). MR 3775841 RazRWigdersonAviMonotone circuits for matching require linear depthJ. Assoc. Comput. Mach.1992393736744117796010.1145/146637.146684MR 1177960 Hoory, S., Magen, A., Pitassi, T.: Monotone circuits for the majority function. In: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, 9th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2006 and 10th International Workshop on Randomization and Computation, RANDOM 2006, Barcelona, Spain, August 28-30 2006, Proceedings, pp. 410–425 (2006) Schrijver, A.: Combinatorial optimization. Polyhedra and efficiency. Vol. A, Algorithms and Combinatorics, vol. 24, Springer-Verlag, Berlin, 2003, Paths, flows, matchings, Chapters 1–38. MR 1956924 (2004b:90004a) RothvoßTSome 0/1 polytopes need exponential size extended formulationsMath. Program. A2013142255268312707410.1007/s10107-012-0574-3 LovászLSchrijverACones of matrices and set-functions and 0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0$$\end{document}-1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1$$\end{document} optimizationSIAM J. Optim.199112166190109842510.1137/0801013MR 1098425 Averkov, G., Kaibel, V., Weltge, S.: Maximum semidefinite and linear extension complexity of families of polytopes. Math. Program. 167(2), Ser. A, pp. 381–394 (2018). MR 3755737 Mastrolilli, M: High degree sum of squares proofs, Bienstock-Zuckerberg hierarchy and CG cuts. In: Integer Programming and Combinatorial Optimization - 19th International Conference, IPCO 2017, Waterloo, ON, Canada, June 26-28, 2017, Proceedings, pp. 405–416 (2017) Lasserre, J. B.: An explicit exact SDP relaxation for nonlinear 0-1 programs. Integer programming and combinatorial optimization (Utrecht, 2001), Lecture Notes in Comput. Sci., vol. 2081, pp. 293–303. Springer, Berlin (2001). MR 2041934 Bazzi, A., Fiorini, S., Huang, S., Svensson, O.: Small extended formulation for knapsack cover inequalities from monotone circuits. In: Proceedings of the 28th Annual ACM-SIAM Symposium on Discrete Algorithms 2017, (2017) EisenbrandFOn the membership problem for the elementary closure of a polyhedronCombinatorica1999192297300172304510.1007/s004930050057 Bazzi, A., Fiorini, S., Pokutta, S., Svensson, O.: No small linear program approximates vertex cover within a factor 2–e. In: 2015 IEEE 56th Annual Symposium on Foundations of Computer Science (FOCS), pp. 1123–1142 (2015) Cornuéjols, G., Lee, D.: On some polytopes contained in the 0,1 hypercube that have a small Chvátal rank. In: International Conference on Integer Programming and Combinatorial Optimization, pp. 300–311. Springer (2016) SheraliHDAdamsWPA hierarchy of relaxations between the continuous and convex hull representations for zero-one programming problemsSIAM J. Discrete Math.199033411430106198110.1137/0403036MR 1061981 KlabjanDNemhauserGLToveyCThe complexity of cover inequality separationOper. Res. Lett.1998233540166424110.1016/S0167-6377(98)00025-X ChvátalVEdmonds polytopes and a hierarchy of combinatorial problemsDiscrete Math.1973430533731308010.1016/0012-365X(73)90167-2MR 0313080 Balas, E.: Disjunctive programming. Ann. Discrete Math. 5, 3–51 (1979). Discrete optimization (Proceedings of the Advanced Research Institute on Discrete Optimization and Systems Applications, Banff, Alta., 1977), II. MR 558566 HrubešPavelOn the nonnegative rank of distance matricesInf. Process. Lett.201211211457461290514810.1016/j.ipl.2012.02.009MR 2905148 KarchmerMWigdersonAMonotone circuits for connectivity require super-logarithmic depthSIAM J. Discrete Math.19903255265103929610.1137/0403021 Weltge, S.: Sizes of linear descriptions in combinatorial optimization. dissertation, Otto-von-Guericke-Universität Magdeburg, (2016) BienstockDZuckerbergMApproximate fixed-rank closures of covering problemsMath. Program. Ser. A2006105927218592610.1007/s10107-005-0598-z BeimelAWeinrebEMonotone circuits for monotone weighted threshold functionsInf. Process. Lett.20069711218218406710.1016/j.ipl.2005.09.008 Fiorini, S., Massar, S., Pokutta, S., Tiwary, H. R., de Wolf, R.: Exponential lower bounds for polytopes in combinatorial optimization. J. ACM 62(2), 1–23 (2015) Bienstock, D., Zuckerberg, M.: Simpler derivation of bounded pitch inequalities for set covering, and minimum knapsack sets, arXiv:1806.07435 (2018) 1542_CR20 1542_CR22 1542_CR25 F Eisenbrand (1542_CR12) 1999; 19 D Klabjan (1542_CR19) 1998; 23 T Rothvoß (1542_CR24) 2013; 142 Pavel Hrubeš (1542_CR17) 2012; 112 D Bienstock (1542_CR8) 2006; 105 1542_CR26 V Chvátal (1542_CR10) 1973; 4 1542_CR28 1542_CR9 1542_CR30 I Wegener (1542_CR29) 1983; 16 1542_CR4 1542_CR11 L Lovász (1542_CR21) 1991; 1 1542_CR6 1542_CR13 1542_CR14 R Raz (1542_CR23) 1992; 39 1542_CR1 1542_CR2 1542_CR3 A Beimel (1542_CR5) 2006; 97 D Bienstock (1542_CR7) 2004; 15 1542_CR15 1542_CR16 M Karchmer (1542_CR18) 1990; 3 HD Sherali (1542_CR27) 1990; 3
References_xml	– reference: Schrijver, A.: Combinatorial optimization. Polyhedra and efficiency. Vol. A, Algorithms and Combinatorics, vol. 24, Springer-Verlag, Berlin, 2003, Paths, flows, matchings, Chapters 1–38. MR 1956924 (2004b:90004a) – reference: SheraliHDAdamsWPA hierarchy of relaxations between the continuous and convex hull representations for zero-one programming problemsSIAM J. Discrete Math.199033411430106198110.1137/0403036MR 1061981 – reference: KlabjanDNemhauserGLToveyCThe complexity of cover inequality separationOper. Res. Lett.1998233540166424110.1016/S0167-6377(98)00025-X – reference: BeimelAWeinrebEMonotone circuits for monotone weighted threshold functionsInf. Process. Lett.20069711218218406710.1016/j.ipl.2005.09.008 – reference: Singh, M., Talwar, K.: Improving integrality gaps via Chvátal-Gomory rounding. In: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, 13th International Workshop, APPROX 2010, and 14th International Workshop, RANDOM 2010, Barcelona, Spain, September 1-3, 2010. Proceedings, pp. 366–379 (2010) – reference: ChvátalVEdmonds polytopes and a hierarchy of combinatorial problemsDiscrete Math.1973430533731308010.1016/0012-365X(73)90167-2MR 0313080 – reference: Mastrolilli, M: High degree sum of squares proofs, Bienstock-Zuckerberg hierarchy and CG cuts. In: Integer Programming and Combinatorial Optimization - 19th International Conference, IPCO 2017, Waterloo, ON, Canada, June 26-28, 2017, Proceedings, pp. 405–416 (2017) – reference: WegenerIRelating monotone formula size and monotone depth of Boolean functionsInf. Process. Lett.1983161414269400810.1016/0020-0190(83)90011-X – reference: Weltge, S.: Sizes of linear descriptions in combinatorial optimization. dissertation, Otto-von-Guericke-Universität Magdeburg, (2016) – reference: BienstockDZuckerbergMApproximate fixed-rank closures of covering problemsMath. Program. Ser. A2006105927218592610.1007/s10107-005-0598-z – reference: EisenbrandFOn the membership problem for the elementary closure of a polyhedronCombinatorica1999192297300172304510.1007/s004930050057 – reference: Averkov, G., Kaibel, V., Weltge, S.: Maximum semidefinite and linear extension complexity of families of polytopes. Math. Program. 167(2), Ser. A, pp. 381–394 (2018). MR 3755737 – reference: Cornuéjols, G., Lee, D.: On some polytopes contained in the 0,1 hypercube that have a small Chvátal rank. In: International Conference on Integer Programming and Combinatorial Optimization, pp. 300–311. Springer (2016) – reference: Balas, E.: Disjunctive programming. Ann. Discrete Math. 5, 3–51 (1979). Discrete optimization (Proceedings of the Advanced Research Institute on Discrete Optimization and Systems Applications, Banff, Alta., 1977), II. MR 558566 – reference: Fiorini, S., Groß, M., Könemann, J., Sanità, L.: Approximating weighted tree augmentation via Chvátal-Gomory cuts. In: Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 817–831. SIAM, Philadelphia, PA (2018). MR 3775841 – reference: Göös, M., Jain, R., Watson, T.: Extension complexity of independent set polytopes. In: Proc. FOCS 2016, (2016) – reference: Bazzi, A., Fiorini, S., Huang, S., Svensson, O.: Small extended formulation for knapsack cover inequalities from monotone circuits. In: Proceedings of the 28th Annual ACM-SIAM Symposium on Discrete Algorithms 2017, (2017) – reference: BienstockDZuckerbergMSubset algebra lift operators for 0–1 integer programmingSIAM J. Optim.20041516395211297610.1137/S1052623402420346MR 2112976 – reference: Bazzi, A., Fiorini, S., Pokutta, S., Svensson, O.: No small linear program approximates vertex cover within a factor 2–e. In: 2015 IEEE 56th Annual Symposium on Foundations of Computer Science (FOCS), pp. 1123–1142 (2015) – reference: Bienstock, D., Zuckerberg, M.: Simpler derivation of bounded pitch inequalities for set covering, and minimum knapsack sets, arXiv:1806.07435 (2018) – reference: RazRWigdersonAviMonotone circuits for matching require linear depthJ. Assoc. Comput. Mach.1992393736744117796010.1145/146637.146684MR 1177960 – reference: LovászLSchrijverACones of matrices and set-functions and 0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0$$\end{document}-1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1$$\end{document} optimizationSIAM J. Optim.199112166190109842510.1137/0801013MR 1098425 – reference: KarchmerMWigdersonAMonotone circuits for connectivity require super-logarithmic depthSIAM J. Discrete Math.19903255265103929610.1137/0403021 – reference: Hoory, S., Magen, A., Pitassi, T.: Monotone circuits for the majority function. In: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, 9th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2006 and 10th International Workshop on Randomization and Computation, RANDOM 2006, Barcelona, Spain, August 28-30 2006, Proceedings, pp. 410–425 (2006) – reference: Benchetrit, Y., Fiorini, S., Huynh, T., Weltge, S.: Characterizing Polytopes Contained in the 0/1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0/1$$\end{document}-Cube with Bounded Chvátal-Gomory Rank. Mathematics of Operations Research (2018) – reference: Lasserre, J. B.: An explicit exact SDP relaxation for nonlinear 0-1 programs. Integer programming and combinatorial optimization (Utrecht, 2001), Lecture Notes in Comput. Sci., vol. 2081, pp. 293–303. Springer, Berlin (2001). MR 2041934 – reference: HrubešPavelOn the nonnegative rank of distance matricesInf. Process. Lett.201211211457461290514810.1016/j.ipl.2012.02.009MR 2905148 – reference: Rothvoß, T.: The matching polytope has exponential extension complexity. J. ACM 64, no. 6, Art. 41, 19 (2017). MR 3713797 – reference: Fiorini, S., Massar, S., Pokutta, S., Tiwary, H. R., de Wolf, R.: Exponential lower bounds for polytopes in combinatorial optimization. J. ACM 62(2), 1–23 (2015) – reference: RothvoßTSome 0/1 polytopes need exponential size extended formulationsMath. Program. A2013142255268312707410.1007/s10107-012-0574-3 – ident: 1542_CR11 doi: 10.1007/978-3-319-33461-5_25 – ident: 1542_CR22 doi: 10.1007/978-3-319-59250-3_33 – ident: 1542_CR6 doi: 10.1287/moor.2017.0880 – ident: 1542_CR30 – volume: 97 start-page: 12 issue: 1 year: 2006 ident: 1542_CR5 publication-title: Inf. Process. Lett. doi: 10.1016/j.ipl.2005.09.008 – ident: 1542_CR4 doi: 10.1109/FOCS.2015.73 – ident: 1542_CR9 – volume: 3 start-page: 411 issue: 3 year: 1990 ident: 1542_CR27 publication-title: SIAM J. Discrete Math. doi: 10.1137/0403036 – volume: 1 start-page: 166 issue: 2 year: 1991 ident: 1542_CR21 publication-title: SIAM J. Optim. doi: 10.1137/0801013 – volume: 23 start-page: 35 year: 1998 ident: 1542_CR19 publication-title: Oper. Res. Lett. doi: 10.1016/S0167-6377(98)00025-X – ident: 1542_CR28 doi: 10.1007/978-3-642-15369-3_28 – ident: 1542_CR16 doi: 10.1007/11830924_38 – ident: 1542_CR20 doi: 10.1007/3-540-45535-3_23 – ident: 1542_CR1 doi: 10.1007/s10107-017-1134-7 – ident: 1542_CR15 doi: 10.1109/FOCS.2016.67 – ident: 1542_CR25 doi: 10.1145/3127497 – ident: 1542_CR2 doi: 10.1016/S0167-5060(08)70342-X – volume: 4 start-page: 305 year: 1973 ident: 1542_CR10 publication-title: Discrete Math. doi: 10.1016/0012-365X(73)90167-2 – volume: 19 start-page: 297 issue: 2 year: 1999 ident: 1542_CR12 publication-title: Combinatorica doi: 10.1007/s004930050057 – volume: 142 start-page: 255 year: 2013 ident: 1542_CR24 publication-title: Math. Program. A doi: 10.1007/s10107-012-0574-3 – volume: 16 start-page: 41 issue: 1 year: 1983 ident: 1542_CR29 publication-title: Inf. Process. Lett. doi: 10.1016/0020-0190(83)90011-X – volume: 15 start-page: 63 issue: 1 year: 2004 ident: 1542_CR7 publication-title: SIAM J. Optim. doi: 10.1137/S1052623402420346 – ident: 1542_CR14 doi: 10.1145/2716307 – volume: 3 start-page: 255 year: 1990 ident: 1542_CR18 publication-title: SIAM J. Discrete Math. doi: 10.1137/0403021 – ident: 1542_CR13 doi: 10.1137/1.9781611975031.53 – ident: 1542_CR3 doi: 10.1137/1.9781611974782.153 – volume: 39 start-page: 736 issue: 3 year: 1992 ident: 1542_CR23 publication-title: J. Assoc. Comput. Mach. doi: 10.1145/146637.146684 – volume: 105 start-page: 9 year: 2006 ident: 1542_CR8 publication-title: Math. Program. Ser. A doi: 10.1007/s10107-005-0598-z – volume: 112 start-page: 457 issue: 11 year: 2012 ident: 1542_CR17 publication-title: Inf. Process. Lett. doi: 10.1016/j.ipl.2012.02.009 – ident: 1542_CR26
SSID	ssj0001388
Score	2.3844023
Snippet	In convex integer programming, various procedures have been developed to strengthen convex relaxations of sets of integer points. On the one hand, there exist...
SourceID	pubmedcentral proquest crossref springer
SourceType	Open Access Repository Aggregation Database Enrichment Source Index Database Publisher
StartPage	467
SubjectTerms	Boolean Boolean algebra Calculus of Variations and Optimal Control; Optimization Combinatorial analysis Combinatorics Full Length Paper Hierarchies Integer programming Linear programming Mathematical and Computational Physics Mathematical Methods in Physics Mathematics Mathematics and Statistics Mathematics of Computing Numerical Analysis Optimization Theoretical
Title	Strengthening convex relaxations of 0/1-sets using Boolean formulas
URI	https://link.springer.com/article/10.1007/s10107-020-01542-w https://www.proquest.com/docview/2580341442 https://www.proquest.com/docview/2597821137 https://pubmed.ncbi.nlm.nih.gov/PMC8550646
Volume	190
WOSCitedRecordID	wos000548756000001&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: PRVAVX databaseName: SpringerLINK 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/eLvHCXMwnV1LS8QwEB58HfTgW6wvInjT4LZNmuxRRfGgIiqyt9KkiS5IK3bX3Z9vptt2XVFBjyVpEiaP-ZKZ-QbgQCdtH7NLUxNpQZlJOFV-GNFUW2sM16kuufQer8TNjex02rdVUFhRe7vXJsnypP4U7Objs1qAjlScBXQwDbNO3UlM2HB3_9icv34oZZ2oFdFBFSrzfRuT6miMMb96SH4xk5ba52Lpf-NehsUKbZKT0fJYgSmTrcLCJw5C93XdELcWa3CGVursCSkRXCkpfdKHBANehqOnPZJb0jr2aWF6BUGn-SdymucvJskIwt--A-Pr8HBx_nB2Sas8C1RzX_Qokyy1KkyVsYqFIlWJ4Urw1IG3lk5UGmnpVBo3QdtwJ5FEKetgkWGRjgLd5uEGzGR5ZjaBWJ7aUFjjcI1mosUS6W6DkrsWNVL_aQ_8WtqxrjjIMRXGSzxmT0ZpxU5acSmteODBYfPP64iB49faO_UkxtVuLOKAy5bT1owFHuw3xW4foXEkyUzexzruPu1uw6HwQExMftMrMnFPlmTd55KRG1nhIhZ5cFQvgXHnP49162_Vt2E-QIeaMhByB2Z6b32zC3P6vdct3vZgWnTkXrkTPgDebAUA
linkProvider	Springer Nature
linkToHtml	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1LS8QwEB58gXrwLdZnBG8a3LZJ0z2qKIrrIrqIt9KkySpIK3ZX_flmum3XFRX0WJImYfKYL5mZbwD2VNx0Mbs01YESlOmYU-n6AU2UMVpzlaiCS--uJdrt8P6-eV0GheWVt3tlkixO6k_Bbi4-q3noSMWZR9_GYZJZjYWM-Te3d_X56_phWCVqRXRQhsp838aoOhpizK8ekl_MpIX2OZv_37gXYK5Em-RosDwWYUynSzD7iYPQfl3VxK35MpyglTrtIiWCLSWFT_o7wYCX98HTHskMaRy6NNe9nKDTfJccZ9mTjlOC8LdvwfgKdM5OOyfntMyzQBV3RY-ykCVG-onURjJfJDLWXAqeWPDWULFMAhValca119TcSiSW0lhYpFmgAk81ub8KE2mW6jUghifGF0ZbXKOYaLA4tLfBkNsWFVL_KQfcStqRKjnIMRXGUzRkT0ZpRVZaUSGt6M2B_fqf5wEDx6-1N6tJjMrdmEceDxtWWzPmObBbF9t9hMaRONVZH-vY-7S9DfvCATEy-XWvyMQ9WpI-PhSM3MgKF7DAgYNqCQw7_3ms63-rvgPT552rVtS6aF9uwIyHzjVFUOQmTPRe-noLptRr7zF_2S72wwf75Ab8
linkToPdf	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV3dT9swED_xJQQPfG2IQBmetLfNapPYcfoIhWrTWIU0hHiL4i-GhBJEUuDPx5cmaYvGpInHyI6dXOzc73x3vwP4otK-j9WlqYmUoMyknEo_jKhW1hrDlVYVl97VuRiN4uvr_sVMFn8V7d64JCc5DcjSlJXde227M4lvPh6xBRhUxVlAnxZhmWEgPdrrv6_af7EfxnFTtBWRQp028_cx5lXTFG--jpZ85TKtNNFw8_3vsAUbNQolx5Nlsw0LJtuB9RluQnf1qyV0LT7AAL3X2Q1SJbhWUsWqPxNMhHmeHPmR3JJe16eFKQuCwfQ35CTP70yaEYTFYwfSP8Ll8Oxy8J3W9Reo4r4oKYuZtjLU0ljJQqFlargUXDtQ11Op1JGKnarjJugb7qSTSmkdXDIsUlGg-jzchaUsz8weEMu1DYU1Du8oJnosjZ2VGHM3okJKQOWB30g-UTU3OZbIuEumrMoorcRJK6mklTx58LW9537CzPHP3p3mgyb1Li2SgMc9p8UZCzz43Da7_YVOkzQz-Rj7ODvbWcmh8EDMLYR2VmTonm_Jbv9UTN3IFhexyINvzXKYTv72s-7_X_cjWL04HSbnP0Y_D2AtwJibKleyA0vlw9gcwop6LG-Lh0_V1ngBGSEP4A
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=Strengthening+convex+relaxations+of+0%2F1-sets+using+Boolean+formulas&rft.jtitle=Mathematical+programming&rft.au=Fiorini%2C+Samuel&rft.au=Huynh%2C+Tony&rft.au=Weltge%2C+Stefan&rft.date=2021-11-01&rft.pub=Springer+Berlin+Heidelberg&rft.issn=0025-5610&rft.eissn=1436-4646&rft.volume=190&rft.issue=1-2&rft.spage=467&rft.epage=482&rft_id=info:doi/10.1007%2Fs10107-020-01542-w&rft_id=info%3Apmid%2F34776534&rft.externalDocID=PMC8550646
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