Phase transitions of the typical algorithmic complexity of the random satisfiability problem studied with linear programming

Here we study linear programming applied to the random K-SAT problem, a fundamental problem in computational complexity. The K-SAT problem is to decide whether a Boolean formula with N variables and structured as a conjunction of M clauses, each being a disjunction of K variables or their negations...

Celý popis

Uloženo v:

Podrobná bibliografie
Vydáno v:	PloS one Ročník 14; číslo 4; s. e0215309
Hlavní autoři:	Schawe, Hendrik, Bleim, Roman, Hartmann, Alexander K.
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	United States Public Library of Science 19.04.2019 Public Library of Science (PLoS)
Témata:	Algorithms Boolean algebra Complexity Computational mathematics Computer applications Computer science Computer Simulation Configurations Critical phenomena Disjunction Hardness Hardness (Materials) Integer programming Linear programming Models, Theoretical Optimization Percolation Phase Transition Phase transitions Phase transitions (Physics) Physicists Programming, Linear Solution space Statistical mechanics Statistical physics Surface hardness Theory Variables Germany
ISSN:	1932-6203, 1932-6203
On-line přístup:	Získat plný text
Tagy:	Přidat tag Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!

Abstract	Here we study linear programming applied to the random K-SAT problem, a fundamental problem in computational complexity. The K-SAT problem is to decide whether a Boolean formula with N variables and structured as a conjunction of M clauses, each being a disjunction of K variables or their negations is satisfiable or not. The ensemble of random K-SAT attracted considerable interest from physicists because for a specific ratio αs = M/N it undergoes in the limit of large N a sharp phase transition from a satisfiable to an unsatisfiable phase. In this study we will concentrate on finding for linear programming algorithms "easy-hard" transitions between phases of different typical hardness of the problems on either side. Linear programming is widely applied to solve practical optimization problems, but has been only rarely considered in the physics community. This is a deficit, because those typically studied types of algorithms work in the space of feasible {0, 1}N configurations while linear programming operates outside the space of valid configurations hence gives a very different perspective on the typical-case hardness of a problem. Here, we demonstrate that the technique leads to one simple-to-understand transition for the well known 2-SAT problem. On the other hand we detect multiple transitions in 3-SAT and 4-SAT. We demonstrate that, in contrast to the previous work on vertex cover and therefore somewhat surprisingly, the hardness transitions are not driven by changes of any of various standard percolation or solution space properties of the problem instances. Thus, here a more complex yet undetected property must be related to the easy-hard transition.
AbstractList	Here we study linear programming applied to the random K-SAT problem, a fundamental problem in computational complexity. The K-SAT problem is to decide whether a Boolean formula with N variables and structured as a conjunction of M clauses, each being a disjunction of K variables or their negations is satisfiable or not. The ensemble of random K-SAT attracted considerable interest from physicists because for a specific ratio αs = M/N it undergoes in the limit of large N a sharp phase transition from a satisfiable to an unsatisfiable phase. In this study we will concentrate on finding for linear programming algorithms “easy-hard” transitions between phases of different typical hardness of the problems on either side. Linear programming is widely applied to solve practical optimization problems, but has been only rarely considered in the physics community. This is a deficit, because those typically studied types of algorithms work in the space of feasible {0, 1}N configurations while linear programming operates outside the space of valid configurations hence gives a very different perspective on the typical-case hardness of a problem. Here, we demonstrate that the technique leads to one simple-to-understand transition for the well known 2-SAT problem. On the other hand we detect multiple transitions in 3-SAT and 4-SAT. We demonstrate that, in contrast to the previous work on vertex cover and therefore somewhat surprisingly, the hardness transitions are not driven by changes of any of various standard percolation or solution space properties of the problem instances. Thus, here a more complex yet undetected property must be related to the easy-hard transition. Here we study linear programming applied to the random K-SAT problem, a fundamental problem in computational complexity. The K-SAT problem is to decide whether a Boolean formula with N variables and structured as a conjunction of M clauses, each being a disjunction of K variables or their negations is satisfiable or not. The ensemble of random K-SAT attracted considerable interest from physicists because for a specific ratio [alpha].sub.s = M/N it undergoes in the limit of large N a sharp phase transition from a satisfiable to an unsatisfiable phase. In this study we will concentrate on finding for linear programming algorithms "easy-hard" transitions between phases of different typical hardness of the problems on either side. Linear programming is widely applied to solve practical optimization problems, but has been only rarely considered in the physics community. This is a deficit, because those typically studied types of algorithms work in the space of feasible {0, 1}.sup.N configurations while linear programming operates outside the space of valid configurations hence gives a very different perspective on the typical-case hardness of a problem. Here, we demonstrate that the technique leads to one simple-to-understand transition for the well known 2-SAT problem. On the other hand we detect multiple transitions in 3-SAT and 4-SAT. We demonstrate that, in contrast to the previous work on vertex cover and therefore somewhat surprisingly, the hardness transitions are not driven by changes of any of various standard percolation or solution space properties of the problem instances. Thus, here a more complex yet undetected property must be related to the easy-hard transition. Here we study linear programming applied to the random K-SAT problem, a fundamental problem in computational complexity. The K-SAT problem is to decide whether a Boolean formula with N variables and structured as a conjunction of M clauses, each being a disjunction of K variables or their negations is satisfiable or not. The ensemble of random K-SAT attracted considerable interest from physicists because for a specific ratio αs = M/N it undergoes in the limit of large N a sharp phase transition from a satisfiable to an unsatisfiable phase. In this study we will concentrate on finding for linear programming algorithms "easy-hard" transitions between phases of different typical hardness of the problems on either side. Linear programming is widely applied to solve practical optimization problems, but has been only rarely considered in the physics community. This is a deficit, because those typically studied types of algorithms work in the space of feasible {0, 1}N configurations while linear programming operates outside the space of valid configurations hence gives a very different perspective on the typical-case hardness of a problem. Here, we demonstrate that the technique leads to one simple-to-understand transition for the well known 2-SAT problem. On the other hand we detect multiple transitions in 3-SAT and 4-SAT. We demonstrate that, in contrast to the previous work on vertex cover and therefore somewhat surprisingly, the hardness transitions are not driven by changes of any of various standard percolation or solution space properties of the problem instances. Thus, here a more complex yet undetected property must be related to the easy-hard transition.Here we study linear programming applied to the random K-SAT problem, a fundamental problem in computational complexity. The K-SAT problem is to decide whether a Boolean formula with N variables and structured as a conjunction of M clauses, each being a disjunction of K variables or their negations is satisfiable or not. The ensemble of random K-SAT attracted considerable interest from physicists because for a specific ratio αs = M/N it undergoes in the limit of large N a sharp phase transition from a satisfiable to an unsatisfiable phase. In this study we will concentrate on finding for linear programming algorithms "easy-hard" transitions between phases of different typical hardness of the problems on either side. Linear programming is widely applied to solve practical optimization problems, but has been only rarely considered in the physics community. This is a deficit, because those typically studied types of algorithms work in the space of feasible {0, 1}N configurations while linear programming operates outside the space of valid configurations hence gives a very different perspective on the typical-case hardness of a problem. Here, we demonstrate that the technique leads to one simple-to-understand transition for the well known 2-SAT problem. On the other hand we detect multiple transitions in 3-SAT and 4-SAT. We demonstrate that, in contrast to the previous work on vertex cover and therefore somewhat surprisingly, the hardness transitions are not driven by changes of any of various standard percolation or solution space properties of the problem instances. Thus, here a more complex yet undetected property must be related to the easy-hard transition.
Audience	Academic
Author	Hartmann, Alexander K. Schawe, Hendrik Bleim, Roman
AuthorAffiliation	Scuola Internazionale Superiore di Studi Avanzati, ITALY Institut für Physik, Universität Oldenburg, Oldenburg, Germany
AuthorAffiliation_xml	– name: Institut für Physik, Universität Oldenburg, Oldenburg, Germany – name: Scuola Internazionale Superiore di Studi Avanzati, ITALY
Author_xml	– sequence: 1 givenname: Hendrik orcidid: 0000-0002-8197-1372 surname: Schawe fullname: Schawe, Hendrik – sequence: 2 givenname: Roman surname: Bleim fullname: Bleim, Roman – sequence: 3 givenname: Alexander K. surname: Hartmann fullname: Hartmann, Alexander K.
BackLink	https://www.ncbi.nlm.nih.gov/pubmed/31002678$$D View this record in MEDLINE/PubMed
BookMark	eNqNk12L1DAUhousuB_6D0QLgujFjE3SNq0XwrL4MbCw4tdtOE3SToa0qUmqO-CPN93pLNNlEelFyjnPe07y5uQ0OupMJ6PoKUqWiFD0ZmMG24Fe9iG8TDDKSFI-iE5QSfAixwk5Ovg_jk6d2yRJRoo8fxQdE5QkOKfFSfTn8xqcjL2FzimvTOdiU8d-HULbXnHQMejGWOXXreIxN22v5bXy2z0VdMK0sQOvXK2gUnpM9tZUWoawH4SSIv4d9LFWnQQ75hoLbau65nH0sAbt5JNpPYu-f3j_7eLT4vLq4-ri_HLB8xL7RVqkEnCdSVpVJRAsMpEhSvO6pjUgkHVBMeZSCJIA1KgqZJLmOadZwQuBREnOoue7ur02jk3GOYYxQsGEFKWBWO0IYWDDeqtasFtmQLGbgLENA-sV15KhPCEkA0w4hhTRsuCiKGiZIVIVRIg81Ho3dRuqVgouu-CunhWdZzq1Zo35xfKUpnmGQ4FXUwFrfg7SedYqx6XW0Ekz7PZdZuEOR_TFHfT-001UA-EAqqtN6MvHouw8K3CYEorHfS_vocInZLj7MGW1CvGZ4PVMEBgvr30Dg3Ns9fXL_7NXP-bsywN2LUH7tTN6uBnPOfjs0Olbi_fjHYB0B3BrnLOyvkVQwsZXtLeLja-ITa8oyN7ekXHlYWwfHFH63-K_eGolKQ
CitedBy_id	crossref_primary_10_1007_s12065_024_00936_5 crossref_primary_10_1109_ACCESS_2019_2947992 crossref_primary_10_1038_s41598_020_74366_5 crossref_primary_10_3390_math11040984 crossref_primary_10_1109_ACCESS_2021_3068998
Cites_doi	10.1088/0305-4470/37/6/008 10.1103/PhysRevE.93.052211 10.1016/0041-5553(80)90061-0 10.1145/362248.362272 10.1016/0167-6377(88)90044-2 10.1016/S0304-3975(01)00149-9 10.1103/PhysRevLett.86.1658 10.1103/PhysRevE.66.056126 10.1145/321033.321034 10.1103/PhysRevLett.86.1654 10.1038/nphys2105 10.1137/0203021 10.1103/PhysRevE.76.031131 10.1103/PhysRevE.78.040101 10.1016/S0004-3702(96)00030-6 10.1093/acprof:oso/9780199233212.001.0001 10.1006/jcss.1996.0081 10.1016/S0378-4371(02)00516-2 10.1007/s10107-003-0440-4 10.1145/368273.368557 10.1016/S0377-2217(99)00015-6 10.1214/aos/1176344552 10.1103/PhysRevLett.84.6118 10.1088/0305-4470/36/43/028 10.1023/A:1022886412117 10.1016/S0304-3975(01)00159-1 10.1103/PhysRevE.86.041128 10.1073/pnas.0703685104 10.1103/PhysRevE.82.056702 10.1142/9019 10.1126/science.1073287 10.1007/s10051-001-8683-4 10.1002/3527606734 10.1145/800057.808695 10.1093/acprof:oso/9780198570837.001.0001 10.1145/800157.805047 10.1088/0305-4470/34/22/303 10.1209/0295-5075/113/30004 10.1002/rsa.20061 10.1002/rsa.20057
ContentType	Journal Article
Copyright	COPYRIGHT 2019 Public Library of Science 2019 Schawe et al. This is an open access article distributed under the terms of the Creative Commons Attribution License: http://creativecommons.org/licenses/by/4.0/ (the “License”), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. 2019 Schawe et al 2019 Schawe et al
Copyright_xml	– notice: COPYRIGHT 2019 Public Library of Science – notice: 2019 Schawe et al. This is an open access article distributed under the terms of the Creative Commons Attribution License: http://creativecommons.org/licenses/by/4.0/ (the “License”), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. – notice: 2019 Schawe et al 2019 Schawe et al
DBID	AAYXX CITATION CGR CUY CVF ECM EIF NPM IOV ISR 3V. 7QG 7QL 7QO 7RV 7SN 7SS 7T5 7TG 7TM 7U9 7X2 7X7 7XB 88E 8AO 8C1 8FD 8FE 8FG 8FH 8FI 8FJ 8FK ABJCF ABUWG AEUYN AFKRA ARAPS ATCPS AZQEC BBNVY BENPR BGLVJ BHPHI C1K CCPQU D1I DWQXO FR3 FYUFA GHDGH GNUQQ H94 HCIFZ K9. KB. KB0 KL. L6V LK8 M0K M0S M1P M7N M7P M7S NAPCQ P5Z P62 P64 PATMY PDBOC PHGZM PHGZT PIMPY PJZUB PKEHL PPXIY PQEST PQGLB PQQKQ PQUKI PRINS PTHSS PYCSY RC3 7X8 5PM DOA
DOI	10.1371/journal.pone.0215309
DatabaseName	CrossRef Medline MEDLINE MEDLINE (Ovid) MEDLINE MEDLINE PubMed Gale In Context: Opposing Viewpoints Gale In Context: Science ProQuest Central (Corporate) Animal Behavior Abstracts Bacteriology Abstracts (Microbiology B) Biotechnology Research Abstracts Nursing & Allied Health Database Ecology Abstracts Entomology Abstracts (Full archive) Immunology Abstracts Meteorological & Geoastrophysical Abstracts Nucleic Acids Abstracts Virology and AIDS Abstracts Agricultural Science Collection Health & Medical Collection (ProQuest) ProQuest Central (purchase pre-March 2016) Medical Database (Alumni Edition) ProQuest Pharma Collection Public Health Database Technology Research Database ProQuest SciTech Collection ProQuest Technology Collection ProQuest Natural Science Collection Hospital Premium Collection Hospital Premium Collection (Alumni Edition) ProQuest Central (Alumni) (purchase pre-March 2016) Materials Science & Engineering Collection ProQuest Central (Alumni) ProQuest One Sustainability ProQuest Central UK/Ireland ProQuest SciTech Premium Collection Technology Collection Advanced Technologies & Aerospace Collection Agricultural & Environmental Science Collection ProQuest Central Essentials ProQuest SciTech Premium Collection Natural Science Collection Biological Science Collection ProQuest Central ProQuest Technology Collection Natural Science Collection Environmental Sciences and Pollution Management ProQuest One Community College ProQuest Materials Science Collection ProQuest Central Korea Engineering Research Database Proquest Health Research Premium Collection Health Research Premium Collection (Alumni) ProQuest Central Student AIDS and Cancer Research Abstracts SciTech Collection (ProQuest) ProQuest Health & Medical Complete (Alumni) Materials Science Database Nursing & Allied Health Database (Alumni Edition) Meteorological & Geoastrophysical Abstracts - Academic ProQuest Engineering Collection ProQuest Biological Science Collection Agricultural Science Database Health & Medical Collection (Alumni Edition) Medical Database Algology Mycology and Protozoology Abstracts (Microbiology C) Biological Science Database Engineering Database Nursing & Allied Health Premium Advanced Technologies & Aerospace Database ProQuest Advanced Technologies & Aerospace Collection Biotechnology and BioEngineering Abstracts Environmental Science Database Materials Science Collection ProQuest One Academic ProQuest One Academic (New) ProQuest - Publicly Available Content Database ProQuest Health & Medical Research Collection ProQuest One Academic Middle East (New) ProQuest One Health & Nursing 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 Environmental Science Collection Genetics Abstracts MEDLINE - Academic PubMed Central (Full Participant titles) DOAJ: Directory of Open Access Journal (DOAJ)
DatabaseTitle	CrossRef MEDLINE Medline Complete MEDLINE with Full Text PubMed MEDLINE (Ovid) Agricultural Science Database Publicly Available Content Database ProQuest Central Student ProQuest Advanced Technologies & Aerospace Collection ProQuest Central Essentials Nucleic Acids Abstracts SciTech Premium Collection ProQuest Central China Environmental Sciences and Pollution Management ProQuest One Applied & Life Sciences ProQuest One Sustainability Health Research Premium Collection Meteorological & Geoastrophysical Abstracts Natural Science Collection Health & Medical Research Collection Biological Science Collection ProQuest Central (New) ProQuest Medical Library (Alumni) Engineering Collection Advanced Technologies & Aerospace Collection Engineering Database Virology and AIDS Abstracts ProQuest Biological Science Collection ProQuest One Academic Eastern Edition Agricultural Science Collection ProQuest Hospital Collection ProQuest Technology Collection Health Research Premium Collection (Alumni) Biological Science Database Ecology Abstracts ProQuest Hospital Collection (Alumni) Biotechnology and BioEngineering Abstracts Environmental Science Collection Entomology Abstracts Nursing & Allied Health Premium ProQuest Health & Medical Complete ProQuest One Academic UKI Edition Environmental Science Database ProQuest Nursing & Allied Health Source (Alumni) Engineering Research Database ProQuest One Academic Meteorological & Geoastrophysical Abstracts - Academic ProQuest One Academic (New) Technology Collection Technology Research Database ProQuest One Academic Middle East (New) Materials Science Collection ProQuest Health & Medical Complete (Alumni) ProQuest Central (Alumni Edition) ProQuest One Community College ProQuest One Health & Nursing ProQuest Natural Science Collection ProQuest Pharma Collection ProQuest Central ProQuest Health & Medical Research Collection Genetics Abstracts ProQuest Engineering Collection Biotechnology Research Abstracts Health and Medicine Complete (Alumni Edition) ProQuest Central Korea Bacteriology Abstracts (Microbiology B) Algology Mycology and Protozoology Abstracts (Microbiology C) Agricultural & Environmental Science Collection AIDS and Cancer Research Abstracts Materials Science Database ProQuest Materials Science Collection ProQuest Public Health ProQuest Nursing & Allied Health Source ProQuest SciTech Collection Advanced Technologies & Aerospace Database ProQuest Medical Library Animal Behavior Abstracts Materials Science & Engineering Collection Immunology Abstracts ProQuest Central (Alumni) MEDLINE - Academic
DatabaseTitleList	Agricultural Science Database MEDLINE MEDLINE - Academic
Database_xml	– sequence: 1 dbid: DOA name: DOAJ Directory of Open Access Journals url: https://www.doaj.org/ sourceTypes: Open Website – sequence: 2 dbid: NPM name: PubMed url: http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed sourceTypes: Index Database – sequence: 3 dbid: PIMPY name: Publicly Available Content Database url: http://search.proquest.com/publiccontent sourceTypes: Aggregation Database
DeliveryMethod	fulltext_linktorsrc
Discipline	Sciences (General) Computer Science
DocumentTitleAlternate	Phase transitions of the complexity of the random satisfiability problem studied with linear programming
EISSN	1932-6203
ExternalDocumentID	2211678414 oai_doaj_org_article_160335a23c2a41798cd8879513b83dd6 PMC6474652 A582932726 31002678 10_1371_journal_pone_0215309
Genre	Research Support, Non-U.S. Gov't Journal Article
GeographicLocations	Germany
GeographicLocations_xml	– name: Germany
GrantInformation_xml	– fundername: ; grantid: HA 3169/8-1
GroupedDBID	--- 123 29O 2WC 53G 5VS 7RV 7X2 7X7 7XC 88E 8AO 8C1 8CJ 8FE 8FG 8FH 8FI 8FJ A8Z AAFWJ AAUCC AAWOE AAYXX ABDBF ABIVO ABJCF ABUWG ACCTH ACGFO ACIHN ACIWK ACPRK ACUHS ADBBV AEAQA AENEX AEUYN AFFHD AFKRA AFPKN AFRAH AHMBA ALMA_UNASSIGNED_HOLDINGS AOIJS APEBS ARAPS ATCPS BAIFH BAWUL BBNVY BBTPI BCNDV BENPR BGLVJ BHPHI BKEYQ BPHCQ BVXVI BWKFM CCPQU CITATION CS3 D1I D1J D1K DIK DU5 E3Z EAP EAS EBD EMOBN ESX EX3 F5P FPL FYUFA GROUPED_DOAJ GX1 HCIFZ HH5 HMCUK HYE IAO IEA IGS IHR IHW INH INR IOV IPY ISE ISR ITC K6- KB. KQ8 L6V LK5 LK8 M0K M1P M48 M7P M7R M7S M~E NAPCQ O5R O5S OK1 OVT P2P P62 PATMY PDBOC PHGZM PHGZT PIMPY PJZUB PPXIY PQGLB PQQKQ PROAC PSQYO PTHSS PV9 PYCSY RNS RPM RZL SV3 TR2 UKHRP WOQ WOW ~02 ~KM 3V. ADRAZ ALIPV BBORY CGR CUY CVF ECM EIF IPNFZ NPM RIG 7QG 7QL 7QO 7SN 7SS 7T5 7TG 7TM 7U9 7XB 8FD 8FK AZQEC C1K DWQXO ESTFP FR3 GNUQQ H94 K9. KL. M7N P64 PKEHL PQEST PQUKI PRINS RC3 7X8 5PM AAPBV ABPTK
ID	FETCH-LOGICAL-c692t-484ea2f5e7bb9a32d5d51776ff7fa1aef8722cedd30aaf1b8e0466c758c8d1d93
IEDL.DBID	DOA
ISICitedReferencesCount	8
ISICitedReferencesURI	http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000465019900015&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN	1932-6203
IngestDate	Sun Sep 03 00:14:13 EDT 2023 Fri Oct 03 12:53:28 EDT 2025 Tue Nov 04 01:47:52 EST 2025 Sun Nov 09 14:34:35 EST 2025 Tue Oct 07 07:57:53 EDT 2025 Sat Nov 29 12:57:06 EST 2025 Sat Nov 29 10:07:46 EST 2025 Wed Nov 26 10:00:06 EST 2025 Wed Nov 26 09:34:22 EST 2025 Thu May 22 21:31:16 EDT 2025 Wed Feb 19 02:31:05 EST 2025 Sat Nov 29 02:20:53 EST 2025 Tue Nov 18 22:35:27 EST 2025
IsDoiOpenAccess	true
IsOpenAccess	true
IsPeerReviewed	true
IsScholarly	true
Issue	4
Language	English
License	This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Creative Commons Attribution License
LinkModel	DirectLink
MergedId	FETCHMERGED-LOGICAL-c692t-484ea2f5e7bb9a32d5d51776ff7fa1aef8722cedd30aaf1b8e0466c758c8d1d93
Notes	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 content type line 23 Competing Interests: The authors have declared that no competing interests exist.
ORCID	0000-0002-8197-1372
OpenAccessLink	https://doaj.org/article/160335a23c2a41798cd8879513b83dd6
PMID	31002678
PQID	2211678414
PQPubID	1436336
PageCount	e0215309
ParticipantIDs	plos_journals_2211678414 doaj_primary_oai_doaj_org_article_160335a23c2a41798cd8879513b83dd6 pubmedcentral_primary_oai_pubmedcentral_nih_gov_6474652 proquest_miscellaneous_2211953102 proquest_journals_2211678414 gale_infotracmisc_A582932726 gale_infotracacademiconefile_A582932726 gale_incontextgauss_ISR_A582932726 gale_incontextgauss_IOV_A582932726 gale_healthsolutions_A582932726 pubmed_primary_31002678 crossref_primary_10_1371_journal_pone_0215309 crossref_citationtrail_10_1371_journal_pone_0215309
PublicationCentury	2000
PublicationDate	2019-04-19
PublicationDateYYYYMMDD	2019-04-19
PublicationDate_xml	– month: 04 year: 2019 text: 2019-04-19 day: 19
PublicationDecade	2010
PublicationPlace	United States
PublicationPlace_xml	– name: United States – name: San Francisco – name: San Francisco, CA USA
PublicationTitle	PloS one
PublicationTitleAlternate	PLoS One
PublicationYear	2019
Publisher	Public Library of Science Public Library of Science (PLoS)
Publisher_xml	– name: Public Library of Science – name: Public Library of Science (PLoS)
References	A Montanari (ref44) 2004; 37 M Mézard (ref9) 2002; 297 M Mézard (ref49) 2003; 111 S Cocco (ref12) 2001; 86 M Varga (ref19) 2016; 93 D Applegate (ref23) 2003; 97 M Bauer (ref26) 2001; 24 A Braunstein (ref46) 2005; 27 F Krzakała (ref11) 2007; 104 G Biroli (ref10) 2002; 306 MR Garey (ref1) 1979 AK Hartmann (ref5) 2005 A Goerdt (ref39) 1996; 53 C Moore (ref7) 2011 M Molloy (ref47) 2005; 27 Y Nesterov (ref29) 1994; vol. 13 D Achlioptas (ref48) 2001; 265 A Mann (ref21) 2010; 82 ref8 M Weigt (ref18) 2001; 86 ref3 LG Khachiyan (ref27) 1980; 20 JN Hooker (ref41) 1988; 7 H Schawe (ref25) 2016; 113 B Efron (ref33) 1979; 7 ref37 ref36 A Atamtürk (ref42) 2000; 121 J Hopcroft (ref50) 1973; 16 J Ardelius (ref51) 2008; 78 RM Karp (ref4) 1972 ref38 L Zdeborová (ref15) 2007; 76 AK Hartmann (ref35) 2015 OC Martin (ref13) 2001; 265 T Dewenter (ref24) 2012; 86 AP Young (ref34) 2015 M Leone (ref40) 2001; 34 M Davis (ref31) 1962; 5 M Weigt (ref16) 2000; 84 TH Cormen (ref22) 2009 CH Papadimitriou (ref2) 1998 AK Hartmann (ref17) 2003; 36 M Ercsey-Ravasz (ref20) 2011; 7 M Mézard (ref45) 2002; 66 ref28 S Joy (ref43) 1997 S Sahni (ref32) 1974; 3 IP Gent (ref14) 1996; 88 M Davis (ref30) 1960; 7 M Mézard (ref6) 2009
References_xml	– ident: ref37 – volume: 37 start-page: 2073 issue: 6 year: 2004 ident: ref44 article-title: Instability of one-step replica-symmetry-broken phase in satisfiability problems publication-title: Journal of Physics A: Mathematical and General doi: 10.1088/0305-4470/37/6/008 – volume: 93 start-page: 052211 issue: 5 year: 2016 ident: ref19 article-title: Order-to-chaos transition in the hardness of random Boolean satisfiability problems publication-title: Physical Review E doi: 10.1103/PhysRevE.93.052211 – volume: 20 start-page: 53 issue: 1 year: 1980 ident: ref27 article-title: Polynomial algorithms in linear programming publication-title: USSR Computational Mathematics and Mathematical Physics doi: 10.1016/0041-5553(80)90061-0 – volume: 16 start-page: 372 issue: 6 year: 1973 ident: ref50 article-title: Algorithm 447: Efficient Algorithms for Graph Manipulation publication-title: Commun ACM doi: 10.1145/362248.362272 – volume: 7 start-page: 1 issue: 1 year: 1988 ident: ref41 article-title: Resolution vs. cutting plane solution of inference problems: Some computational experience publication-title: Operations Research Letters doi: 10.1016/0167-6377(88)90044-2 – volume: 265 start-page: 3 issue: 1 year: 2001 ident: ref13 article-title: Statistical mechanics methods and phase transitions in optimization problems publication-title: Theoretical computer science doi: 10.1016/S0304-3975(01)00149-9 – volume: 86 start-page: 1658 year: 2001 ident: ref18 article-title: The typical-case complexity of a vertex-covering algorithm on finite-connectivity random graphs publication-title: Phys Rev Lett doi: 10.1103/PhysRevLett.86.1658 – volume: 66 start-page: 056126 year: 2002 ident: ref45 article-title: Random K-satisfiability problem: From an analytic solution to an efficient algorithm publication-title: Phys Rev E doi: 10.1103/PhysRevE.66.056126 – volume: 7 start-page: 201 issue: 3 year: 1960 ident: ref30 article-title: A Computing Procedure for Quantification Theory publication-title: J ACM doi: 10.1145/321033.321034 – year: 1997 ident: ref43 article-title: Satisfiability Problem: Theory and Applications. vol. 35 of DIMACS Series on Discrete Mathematics and Theoretical Computer Science – volume: 86 start-page: 1654 year: 2001 ident: ref12 article-title: Trajectories in phase diagrams, growth processes, and computational complexity: How search algorithms solve the 3-satisfiability problem publication-title: Phys Rev Lett doi: 10.1103/PhysRevLett.86.1654 – volume: 7 start-page: 966 issue: 12 year: 2011 ident: ref20 article-title: Optimization hardness as transient chaos in an analog approach to constraint satisfaction publication-title: Nature Physics doi: 10.1038/nphys2105 – volume: 3 start-page: 262 issue: 4 year: 1974 ident: ref32 article-title: Computationally Related Problems publication-title: SIAM Journal on Computing doi: 10.1137/0203021 – volume: 76 start-page: 031131 year: 2007 ident: ref15 article-title: Phase transitions in the coloring of random graphs publication-title: Phys Rev E doi: 10.1103/PhysRevE.76.031131 – ident: ref36 – volume: 78 start-page: 040101 year: 2008 ident: ref51 article-title: Exhaustive enumeration unveils clustering and freezing in the random 3-satisfiability problem publication-title: Phys Rev E doi: 10.1103/PhysRevE.78.040101 – volume: 88 start-page: 349 issue: 1–2 year: 1996 ident: ref14 article-title: The TSP phase transition publication-title: Artificial Intelligence doi: 10.1016/S0004-3702(96)00030-6 – year: 2011 ident: ref7 article-title: The Nature of Computation doi: 10.1093/acprof:oso/9780199233212.001.0001 – year: 2009 ident: ref22 article-title: Introduction to algorithms – volume: 53 start-page: 469 issue: 3 year: 1996 ident: ref39 article-title: A Threshold for Unsatisfiability publication-title: Journal of Computer and System Sciences doi: 10.1006/jcss.1996.0081 – volume: 306 start-page: 381 issue: 0 year: 2002 ident: ref10 article-title: Phase transitions and complexity in computer science: an overview of the statistical physics approach to the random satisfiability problem publication-title: Physica A: Statistical Mechanics and its Applications doi: 10.1016/S0378-4371(02)00516-2 – volume: 97 start-page: 91 issue: 1-2 year: 2003 ident: ref23 article-title: Implementing the Dantzig-Fulkerson-Johnson algorithm for large traveling salesman problems publication-title: Mathematical programming doi: 10.1007/s10107-003-0440-4 – volume: 5 start-page: 394 issue: 7 year: 1962 ident: ref31 article-title: A Machine Program for Theorem-proving publication-title: Commun ACM doi: 10.1145/368273.368557 – volume: 121 start-page: 40 issue: 1 year: 2000 ident: ref42 article-title: Conflict graphs in solving integer programming problems publication-title: European Journal of Operational Research doi: 10.1016/S0377-2217(99)00015-6 – volume: 7 start-page: 1 issue: 1 year: 1979 ident: ref33 article-title: Bootstrap Methods: Another Look at the Jackknife publication-title: Ann Statist doi: 10.1214/aos/1176344552 – volume: 84 start-page: 6118 year: 2000 ident: ref16 article-title: Number of Guards Needed by a Museum: A Phase Transition in Vertex Covering of Random Graphs publication-title: Phys Rev Lett doi: 10.1103/PhysRevLett.84.6118 – year: 1998 ident: ref2 article-title: Dover Books on Computer Science Series – volume: 36 start-page: 11069 issue: 43 year: 2003 ident: ref17 article-title: Statistical mechanics of the vertex-cover problem publication-title: Journal of Physics A: Mathematical and General doi: 10.1088/0305-4470/36/43/028 – volume: 111 start-page: 505 issue: 3 year: 2003 ident: ref49 article-title: Two Solutions to Diluted p-Spin Models and XORSAT Problems publication-title: Journal of Statistical Physics doi: 10.1023/A:1022886412117 – volume: 265 start-page: 159 issue: 1-2 year: 2001 ident: ref48 article-title: Lower bounds for random 3-SAT via differential equations publication-title: Theoretical Computer Science doi: 10.1016/S0304-3975(01)00159-1 – volume: 86 start-page: 041128 issue: 4 year: 2012 ident: ref24 article-title: Phase transition for cutting-plane approach to vertex-cover problem publication-title: Physical Review E doi: 10.1103/PhysRevE.86.041128 – volume: vol. 13 year: 1994 ident: ref29 article-title: Interior-point polynomial algorithms in convex programming – volume: 104 start-page: 10318 issue: 25 year: 2007 ident: ref11 article-title: Gibbs states and the set of solutions of random constraint satisfaction problems publication-title: Proceedings of the National Academy of Sciences doi: 10.1073/pnas.0703685104 – volume: 82 start-page: 056702 issue: 5 year: 2010 ident: ref21 article-title: Numerical solution-space analysis of satisfiability problems publication-title: Physical Review E doi: 10.1103/PhysRevE.82.056702 – year: 2015 ident: ref35 article-title: Big Practical Guide to Computer Simulations doi: 10.1142/9019 – volume: 297 start-page: 812 year: 2002 ident: ref9 article-title: Analytic and algorithmic solution of random satisfiability problems publication-title: Science doi: 10.1126/science.1073287 – ident: ref38 – volume: 24 start-page: 339 issue: 3 year: 2001 ident: ref26 article-title: Core percolation in random graphs: a critical phenomena analysis publication-title: The European Physical Journal B-Condensed Matter and Complex Systems doi: 10.1007/s10051-001-8683-4 – year: 1972 ident: ref4 article-title: Reducibility among combinatorial problems – year: 2005 ident: ref5 article-title: Phase Transitions in Combinatorial Optimization Problems doi: 10.1002/3527606734 – ident: ref28 doi: 10.1145/800057.808695 – year: 2009 ident: ref6 article-title: Information, Physics and Computation doi: 10.1093/acprof:oso/9780198570837.001.0001 – year: 1979 ident: ref1 article-title: Computers and intractability – ident: ref3 doi: 10.1145/800157.805047 – volume: 34 start-page: 4615 issue: 22 year: 2001 ident: ref40 article-title: Phase coexistence and finite-size scaling in random combinatorial problems publication-title: Journal of Physics A: Mathematical and General doi: 10.1088/0305-4470/34/22/303 – volume: 113 start-page: 30004 year: 2016 ident: ref25 article-title: Phase transition of Traveling Salesperson problems solved with linear programming and cutting planes publication-title: Eur Phys Lett doi: 10.1209/0295-5075/113/30004 – year: 2015 ident: ref34 article-title: SpringerBriefs in Physics – volume: 27 start-page: 124 issue: 1 year: 2005 ident: ref47 article-title: Cores in random hypergraphs and Boolean formulas publication-title: Random Structures & Algorithms doi: 10.1002/rsa.20061 – ident: ref8 – volume: 27 start-page: 201 issue: 2 year: 2005 ident: ref46 article-title: Survey propagation: An algorithm for satisfiability publication-title: Random Structures & Algorithms doi: 10.1002/rsa.20057
SSID	ssj0053866
Score	2.3373764
Snippet	Here we study linear programming applied to the random K-SAT problem, a fundamental problem in computational complexity. The K-SAT problem is to decide whether...
SourceID	plos doaj pubmedcentral proquest gale pubmed crossref
SourceType	Open Website Open Access Repository Aggregation Database Index Database Enrichment Source
StartPage	e0215309
SubjectTerms	Algorithms Boolean algebra Complexity Computational mathematics Computer applications Computer science Computer Simulation Configurations Critical phenomena Disjunction Hardness Hardness (Materials) Integer programming Linear programming Models, Theoretical Optimization Percolation Phase Transition Phase transitions Phase transitions (Physics) Physicists Programming, Linear Solution space Statistical mechanics Statistical physics Surface hardness Theory Variables
SummonAdditionalLinks	– databaseName: Biological Science Database dbid: M7P link: http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1bb9MwFLag8MALYwO2wgCDkICHbI2dxMkTGogJJDQqLtPeIseXtlKblKZFTOLHc47jhAVNgMRbVX9OG_vcbB-fj5CnMgwt1ywK5EizIIqkCWSk4wCkxxbaFpFwXASn78XJSXp2lo39hlvt0ypbm-gMta4U7pEfMoYnBmkURi-XXwNkjcLTVU-hcZVcwyoJ3KXujVtLDLqcJP66HBfhoZ-dg2VVmgP0dRzTEC-4I1e1v7PNg-W8qi8LPH_Pn7zgkI63_vdVbpGbPhSlR43sbJMrptwhWy3NA_Vav0O2_aeaPvdFql_cJj_GU_B_dI2ursn6opWlEE3S9fkSJ57K-QR-dD1dzBR1ievmO0T8LQr66WpBa3e5YtYUCz-nnt6G1i67UVPcJaYYCMsV9ZlkC_C1d8iX4zefX78NPJNDoJKMrYMojYxkNjaiKDLJmY51HAqRWCusDKWxqWBMGa35SEobFqmBZXuiYC2jUh3qjN8lgxJmbY9Q8KcylUUhY1jaGmmRLBliuDRjVpnQsCHh7YTmypc5R7aNee7O7gQsd5rhzVEMci8GQxJ0vZZNmY-_4F-hrHRYLNLtvqhWk9zrfI4M3jyWjCsmkegtVTpFbveQFynXOhmSRyhpeXPjtTM1-VGcQhDGBAPEE4fAQh0lZgJN5Kau83cfTv8B9OljD_TMg2wFw6Gkv30B74QFwHrI_R4SzI3qNe-hXrSjUue_pBl6tvJ-efPjrhkfitl9pak2DSYDZzCC2dttVKsbWTyAYvCAIRE9pesNfb-lnE1dnfQkElESs3t__lv3yQ0Igt0JYZjtk8F6tTEPyHX1DeR_9dAZlJ9r1oOu priority: 102 providerName: ProQuest – databaseName: Public Library of Science (PLoS) Journals Open Access dbid: FPL link: http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1Lb9NAEF6hlAMX-uDRQIEFIQEHt_Gu7V0fCyICqSoRj6o3a72PJlJiR3GCqMSPZ8ZeG1y1Am5R9lvLmZ1nZnaGkJcqDB03LArUyLAgipQNVGTiALjH5cblkahnEZydiNNTeX6eTn4Hilcy-FyER56mh8uysIdooTje19tiPEmwhGs8OWk1L8hukvjrcTft7Jmfukt_p4sHy3lZXedoXq2X_MMAjbf_99V3yF3vatLjhjd2yS1b7JHtdowD9VK9R3b9p4q-9k2o39wjPydTsG90jaasqeqipaPgLdL15RIPlqr5RbmaraeLmaZ1Ybr9AR59i4J9plzQqr48MWuagV9SP76GVnX1oqH4LzBFR1etqK8UW4AtvU--jd9_ffch8JMaAp2kbB1EMrKKudiKPE8VZyY2cShE4pxwKlTWScGYtsbwkVIuzKWFsDzREKtoaUKT8gdkUACR9gkFe6mkynMVQ-hqlcNhyOCjyZQ5bUPLhoS3B5hp38Ycp2nMszo3JyCcacibIdUzT_UhCbpdy6aNx1_wb5E3Oiw24a6_gOPNvExnOKGbx4pxzRQOcpPaSJzdHvJccmOSIXmGnJU1N1o7VZIdxxKcLCYYIF7UCGzEUWClz4XaVFX28dPZP4C-fO6BXnmQK4EcWvnbFfCbsMFXD3nQQ4I60b3lfZSDlipVxhim6mQURrCzlY3rl593y_hQrN4rbLlpMCko-xGc3sNGlDrKYoKJwQOGRPSErEf6_koxm9Z90JNIREnMHt38xo_JHXBw6-xfmB6QwXq1sU_Ibf0deH_1tFYevwCvx3IC priority: 102 providerName: Public Library of Science
Title	Phase transitions of the typical algorithmic complexity of the random satisfiability problem studied with linear programming
URI	https://www.ncbi.nlm.nih.gov/pubmed/31002678 https://www.proquest.com/docview/2211678414 https://www.proquest.com/docview/2211953102 https://pubmed.ncbi.nlm.nih.gov/PMC6474652 https://doaj.org/article/160335a23c2a41798cd8879513b83dd6 http://dx.doi.org/10.1371/journal.pone.0215309
Volume	14
WOSCitedRecordID	wos000465019900015&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: PRVAON databaseName: DOAJ Directory of Open Access Journals customDbUrl: eissn: 1932-6203 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0053866 issn: 1932-6203 databaseCode: DOA dateStart: 20060101 isFulltext: true titleUrlDefault: https://www.doaj.org/ providerName: Directory of Open Access Journals – providerCode: PRVHPJ databaseName: ROAD: Directory of Open Access Scholarly Resources (ISSN International Center) customDbUrl: eissn: 1932-6203 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0053866 issn: 1932-6203 databaseCode: M~E dateStart: 20060101 isFulltext: true titleUrlDefault: https://road.issn.org providerName: ISSN International Centre – providerCode: PRVPQU databaseName: Advanced Technologies & Aerospace Database customDbUrl: eissn: 1932-6203 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0053866 issn: 1932-6203 databaseCode: P5Z dateStart: 20061201 isFulltext: true titleUrlDefault: https://search.proquest.com/hightechjournals providerName: ProQuest – providerCode: PRVPQU databaseName: Agricultural Science Database customDbUrl: eissn: 1932-6203 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0053866 issn: 1932-6203 databaseCode: M0K dateStart: 20061201 isFulltext: true titleUrlDefault: https://search.proquest.com/agriculturejournals providerName: ProQuest – providerCode: PRVPQU databaseName: Biological Science Database customDbUrl: eissn: 1932-6203 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0053866 issn: 1932-6203 databaseCode: M7P dateStart: 20061201 isFulltext: true titleUrlDefault: http://search.proquest.com/biologicalscijournals providerName: ProQuest – providerCode: PRVPQU databaseName: Engineering Database customDbUrl: eissn: 1932-6203 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0053866 issn: 1932-6203 databaseCode: M7S dateStart: 20061201 isFulltext: true titleUrlDefault: http://search.proquest.com providerName: ProQuest – providerCode: PRVPQU databaseName: Environmental Science Database customDbUrl: eissn: 1932-6203 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0053866 issn: 1932-6203 databaseCode: PATMY dateStart: 20061201 isFulltext: true titleUrlDefault: http://search.proquest.com/environmentalscience providerName: ProQuest – providerCode: PRVPQU databaseName: Health & Medical Collection customDbUrl: eissn: 1932-6203 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0053866 issn: 1932-6203 databaseCode: 7X7 dateStart: 20061201 isFulltext: true titleUrlDefault: https://search.proquest.com/healthcomplete providerName: ProQuest – providerCode: PRVPQU databaseName: Materials Science Database customDbUrl: eissn: 1932-6203 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0053866 issn: 1932-6203 databaseCode: KB. dateStart: 20061201 isFulltext: true titleUrlDefault: http://search.proquest.com/materialsscijournals providerName: ProQuest – providerCode: PRVPQU databaseName: Nursing & Allied Health Database customDbUrl: eissn: 1932-6203 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0053866 issn: 1932-6203 databaseCode: 7RV dateStart: 20061201 isFulltext: true titleUrlDefault: https://search.proquest.com/nahs providerName: ProQuest – providerCode: PRVPQU databaseName: ProQuest Central customDbUrl: eissn: 1932-6203 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0053866 issn: 1932-6203 databaseCode: BENPR dateStart: 20061201 isFulltext: true titleUrlDefault: https://www.proquest.com/central providerName: ProQuest – providerCode: PRVPQU databaseName: Public Health Database customDbUrl: eissn: 1932-6203 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0053866 issn: 1932-6203 databaseCode: 8C1 dateStart: 20061201 isFulltext: true titleUrlDefault: https://search.proquest.com/publichealth providerName: ProQuest – providerCode: PRVPQU databaseName: Publicly Available Content Database customDbUrl: eissn: 1932-6203 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0053866 issn: 1932-6203 databaseCode: PIMPY dateStart: 20061201 isFulltext: true titleUrlDefault: http://search.proquest.com/publiccontent providerName: ProQuest – providerCode: PRVATS databaseName: Public Library of Science (PLoS) Journals Open Access customDbUrl: eissn: 1932-6203 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0053866 issn: 1932-6203 databaseCode: FPL dateStart: 20060101 isFulltext: true titleUrlDefault: http://www.plos.org/publications/ providerName: Public Library of Science
link	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV3db9MwELdg8MALYnytMIZBSMBDtsb5sPO4TquYtpVog2nsJXJie6vUJlXTISbxx3PnuFGDJo0HXu4h_jlK78535_p8R8gH6fsmUCz0ZF8xLwyl9mSoIg-0x-TK5CG3vQjOjvhoJM7Pk3Sl1RfmhDXlgRvG7WAb5CCSLCiYxG5ZolACG2T7QS4CpWyxbYh6lpupxgbDKo5jd1Eu4P6Ok8v2rCr1Nnq5ABMQVxyRrdffWuW12aSqbws5_86cXHFFwyfksYsh6W7z7evkni6fknW3Smv6yZWS_vyM_E6vwEvRBTqkJjeLVoZCzEcXNzMUD5WTy2o-XlxNxwW16eX6F8TlSxTMU9WU1vYKxLgp6X1DXRMaWtscREXxv1yK4aqcU5fvNQWP-Jx8H-5_2_viuX4LXhEnbOGFItSSmUjzPE9kwFSkIp_z2BhupC-1EZyxQisV9KU0fi40bK7jAnYchVC-SoIXZK0EDm8QCl5PCpnnMoINqJYGWxpDpCUSZgrta9YjwZL5WeGKkWNPjElmT9g4bEoaXmYossyJrEe8dtasKcZxB36Acm2xWErbPgAFy5yCZXcpWI-8Ra3ImnuprUHIdiMBoRLjDBDvLQLLaZSYr3Mpr-s6O_h69g-g05MO6KMDmQrYUUh3RwJ-E5bp6iA3O0gwCkVneAN1eMmVOmMMD9xE6Icwc6nXtw-_a4fxpZiDV-rqusEkYLL7IL2XzTJoOYvHRAxe0CO8s0A6rO-OlOMrW808DnkYR-zV_5DVa_IIAlp72ucnm2RtMb_Wb8jD4ieskvkWuc9PzpCec0sFULHnb5EHg_1RerJlTQjQYXoE9HCwDfS4f4iUp5aeAk2jC5iRHhynP_4AlSh6mA
linkProvider	Directory of Open Access Journals
linkToHtml	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V1Lb9NAEF5VBQkulJZHA4UuCAQc3Mbrx9oHhMqjatQQqtJGvZn1PpJISRziBIjEb-I3MmOvQ40q4NIDt8g7a8XjmW9mvbPzEfJEuK7xFPMd0VTM8X2hHeGrwAHrMakyqc8LLoJum3c60dlZfLRCflRnYbCsssLEAqhVJvEb-S5juGMQ-a7_avLZQdYo3F2tKDRKszjUi6-wZMtftt7C-33K2P67kzcHjmUVcGQYs5njR74WzASap2ksPKYCFbich8ZwI1yhTcQZk1oprymEcdNIwxIylJBXy0i5CpsvAeRfARx3sYSMH3cr5AfsCEN7PM_j7q61hp1JNtY7GFs9LHs8F_4KloBlLFidDLP8okT393rNcwFwf-1_U91NcsOm2nSv9I11sqLHG2StorGgFtU2yLr9ldPntgn3i1vk-1Ef4judYSgvq9poZihky3S2mKBhUzHswUPO-qOBpEVhvv4GK5pKCuapbETz4vDIoGyGvqCWvofmRfWmovgVnGKiL6bUVsqNIJe4TU4vRTF3yOoYrGSTUMgXRCTSVASwdNfCIBk05KhRzIzUrmYN4lUGlEjbxh3ZRIZJsTfJYTlXqjdBs0us2TWIs5w1KduY_EX-NdrmUhabkBcXsmkvsZiWIEO5FwjmSSaQyC6SKkLuetdLI0-psEG20bKT8kTvEkqTvSCCJJNxBhKPCwlsRDLGSqeemOd50vrQ_Qehj8c1oWdWyGSgDins6RJ4JmxwVpPcqkkCnMra8Cb6YaWVPPnlPTCz8q-Lhx8th_GmWL041tm8lIkh2DXh7d0tXXmpWdxgY3CDBuE1J6-pvj4yHvSLPvChz_0wYPf-_Le2ybWDk_ftpN3qHN4n1yHhL3ZD3XiLrM6mc_2AXJVfwBemDwswo-TTZUPAT0c2428
linkToPdf	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V1Lb9NAEF5VASEulJZHA4UuCAQc3MTrxzoHhEpLRNUqRECr3sx6H0mkJA5xAkTil_HrmLHXpkYVcOmBW-SdteLxPL0z8xHyRLiu8RTzHdFWzPF9oR3hq8AB6TGJMonPcyyC02Pe60VnZ53-GvlR9sJgWWVpE3NDrVKJ38hbjOGJQeS7fsvYsoj-QffV7LODCFJ40lrCaRQicqRXXyF9y14eHsC7fspY983H_beORRhwZNhhC8ePfC2YCTRPko7wmApU4HIeGsONcIU2EWdMaqW8thDGTSIN6WQoIcaWkXIVDmIC83-FeyDF2KW-X5WXgB0JQ9uq53G3ZSVjd5ZO9S76WQ9LIM-5whwxoPILjdk4zS4Ken-v3TznDLvr_zMbb5IbNgSne4XObJA1Pd0k6yW8BbXWbpNs2F8ZfW6Hc7-4Rb73h-D36QJdfFHtRlNDIYqmi9UMBZ6K8QAecjGcjCTNC_b1N8h0SirYp9IJzfKmklExJH1FLawPzfKqTkXx6zjFBEDMqa2gm0CMcZucXApj7pDGFCRmi1CII0QkkkQEkNJrYRAkGmLXqMOM1K5mTeKVwhRLO94dUUbGcX5mySHNK9gbowjGVgSbxKl2zYrxJn-hf41yWtHicPL8QjofxNbWxYhc7gWCeZIJBLiLpIoQ0971kshTKmySHZTyuOj0rUxsvBdEEHwyzoDicU6BA0qmKKMDscyy-PDd6T8QfXhfI3pmiUwK7JDCdp3AM-Hgsxrldo0SzKysLW-hTpZcyeJfmgQ7S127ePlRtYw3xarGqU6XBU0HnGAb3t7dQq0rzuLBG4MbNAmvKXyN9fWV6WiYz4cPfe6HAbv357-1Q66B5sfHh72j--Q65AH5Ianb2SaNxXypH5Cr8guowvxhbtco-XTZFuAnUJHryg
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=Phase+transitions+of+the+typical+algorithmic+complexity+of+the+random+satisfiability+problem+studied+with+linear+programming&rft.jtitle=PloS+one&rft.au=Hendrik+Schawe&rft.au=Roman+Bleim&rft.au=Alexander+K+Hartmann&rft.date=2019-04-19&rft.pub=Public+Library+of+Science+%28PLoS%29&rft.eissn=1932-6203&rft.volume=14&rft.issue=4&rft.spage=e0215309&rft_id=info:doi/10.1371%2Fjournal.pone.0215309&rft.externalDBID=DOA&rft.externalDocID=oai_doaj_org_article_160335a23c2a41798cd8879513b83dd6
thumbnail_l	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1932-6203&client=summon
thumbnail_m	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1932-6203&client=summon
thumbnail_s	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1932-6203&client=summon