Matchings with Lower Quotas: Algorithms and Complexity

We study a natural generalization of the maximum weight many-to-one matching problem. We are given an undirected bipartite graph G = ( A ∪ ˙ P , E ) with weights on the edges in E , and with lower and upper quotas on the vertices in P . We seek a maximum weight many-to-one matching satisfying two s...

Full description

Saved in:

Bibliographic Details
Published in:	Algorithmica Vol. 80; no. 1; pp. 185 - 208
Main Authors:	Arulselvan, Ashwin, Cseh, Ágnes, Groß, Martin, Manlove, David F., Matuschke, Jannik
Format:	Journal Article
Language:	English
Published:	New York Springer US 01.01.2018 Springer Nature B.V
Subjects:	Algorithm Analysis and Problem Complexity Algorithms Colleges & universities Complexity Computer Science Computer Systems Organization and Communication Networks Data Structures and Information Theory Graph theory Graphs Matching Mathematics of Computing Polynomials Quotas Students Theory of Computation Maximum matching Bounded treewidth Many-to-one matching Inapproximability Project allocation
ISSN:	0178-4617, 1432-0541
Online Access:	Get full text
Tags:	Add Tag No Tags, Be the first to tag this record!

Abstract	We study a natural generalization of the maximum weight many-to-one matching problem. We are given an undirected bipartite graph G = ( A ∪ ˙ P , E ) with weights on the edges in E , and with lower and upper quotas on the vertices in P . We seek a maximum weight many-to-one matching satisfying two sets of constraints: vertices in A are incident to at most one matching edge, while vertices in P are either unmatched or they are incident to a number of matching edges between their lower and upper quota. This problem, which we call maximum weight many-to-one matching with lower and upper quotas (WMLQ), has applications to the assignment of students to projects within university courses, where there are constraints on the minimum and maximum numbers of students that must be assigned to each project. In this paper, we provide a comprehensive analysis of the complexity of WMLQ from the viewpoints of classical polynomial time algorithms, fixed-parameter tractability, as well as approximability. We draw the line between NP -hard and polynomially tractable instances in terms of degree and quota constraints and provide efficient algorithms to solve the tractable ones. We further show that the problem can be solved in polynomial time for instances with bounded treewidth; however, the corresponding runtime is exponential in the treewidth with the maximum upper quota u max as basis, and we prove that this dependence is necessary unless FPT = W [ 1 ] . The approximability of WMLQ is also discussed: we present an approximation algorithm for the general case with performance guarantee u max + 1 , which is asymptotically best possible unless P = NP . Finally, we elaborate on how most of our positive results carry over to matchings in arbitrary graphs with lower quotas.
AbstractList	We study a natural generalization of the maximum weight many-to-one matching problem. We are given an undirected bipartite graph G = ( A ∪ ˙ P , E ) with weights on the edges in E , and with lower and upper quotas on the vertices in P . We seek a maximum weight many-to-one matching satisfying two sets of constraints: vertices in A are incident to at most one matching edge, while vertices in P are either unmatched or they are incident to a number of matching edges between their lower and upper quota. This problem, which we call maximum weight many-to-one matching with lower and upper quotas (WMLQ), has applications to the assignment of students to projects within university courses, where there are constraints on the minimum and maximum numbers of students that must be assigned to each project. In this paper, we provide a comprehensive analysis of the complexity of WMLQ from the viewpoints of classical polynomial time algorithms, fixed-parameter tractability, as well as approximability. We draw the line between NP -hard and polynomially tractable instances in terms of degree and quota constraints and provide efficient algorithms to solve the tractable ones. We further show that the problem can be solved in polynomial time for instances with bounded treewidth; however, the corresponding runtime is exponential in the treewidth with the maximum upper quota u max as basis, and we prove that this dependence is necessary unless FPT = W [ 1 ] . The approximability of WMLQ is also discussed: we present an approximation algorithm for the general case with performance guarantee u max + 1 , which is asymptotically best possible unless P = NP . Finally, we elaborate on how most of our positive results carry over to matchings in arbitrary graphs with lower quotas. We study a natural generalization of the maximum weight many-to-one matching problem. We are given an undirected bipartite graph G=(A∪˙P,E) with weights on the edges in E, and with lower and upper quotas on the vertices in P. We seek a maximum weight many-to-one matching satisfying two sets of constraints: vertices in A are incident to at most one matching edge, while vertices in P are either unmatched or they are incident to a number of matching edges between their lower and upper quota. This problem, which we call maximum weight many-to-one matching with lower and upper quotas (WMLQ), has applications to the assignment of students to projects within university courses, where there are constraints on the minimum and maximum numbers of students that must be assigned to each project. In this paper, we provide a comprehensive analysis of the complexity of WMLQ from the viewpoints of classical polynomial time algorithms, fixed-parameter tractability, as well as approximability. We draw the line between NP-hard and polynomially tractable instances in terms of degree and quota constraints and provide efficient algorithms to solve the tractable ones. We further show that the problem can be solved in polynomial time for instances with bounded treewidth; however, the corresponding runtime is exponential in the treewidth with the maximum upper quota umax as basis, and we prove that this dependence is necessary unless FPT=W[1]. The approximability of WMLQ is also discussed: we present an approximation algorithm for the general case with performance guarantee umax+1, which is asymptotically best possible unless P=NP. Finally, we elaborate on how most of our positive results carry over to matchings in arbitrary graphs with lower quotas.
Author	Manlove, David F. Arulselvan, Ashwin Matuschke, Jannik Groß, Martin Cseh, Ágnes
Author_xml	– sequence: 1 givenname: Ashwin surname: Arulselvan fullname: Arulselvan, Ashwin organization: Department of Management Science, University of Strathclyde – sequence: 2 givenname: Ágnes orcidid: 0000-0003-4991-2599 surname: Cseh fullname: Cseh, Ágnes email: cseh.agnes@krtk.mta.hu organization: Institute of Economics, Hungarian Academy of Sciences – sequence: 3 givenname: Martin surname: Groß fullname: Groß, Martin organization: Institute for Mathematics, TU Berlin – sequence: 4 givenname: David F. surname: Manlove fullname: Manlove, David F. organization: School of Computing Science, University of Glasgow – sequence: 5 givenname: Jannik surname: Matuschke fullname: Matuschke, Jannik organization: TUM School of Management, Technische Universität München
BookMark	eNp9kF1LwzAUhoNMcJv-AO8KXkfPSdsk9W4Mv2Aigl6HNE23jq6ZScbcv7ejXoigVwcO7_OewzMho851lpBLhGsEEDcBIMtTCsgpsJxRfkLGmKWMQp7hiIwBhaQZR3FGJiGsAZCJgo8Jf9bRrJpuGZJ9E1fJwu2tT153Lupwm8zapfP9ehMS3VXJ3G22rf1s4uGcnNa6Dfbie07J-_3d2_yRLl4enuazBTVpXkRqwDI0qCHntrZlKmVV1lXGjDFFhVpU0mDJWI3cMKhkbZAzUWVWS20M52U6JVdD79a7j50NUa3dznf9SYWF7PuEBNGnxJAy3oXgba1ME3VsXBe9blqFoI6S1CBJ9ZLUUZLiPYm_yK1vNtof_mXYwIQ-2y2t__HTn9AXef97Xw
CitedBy_id	crossref_primary_10_1145_3546605 crossref_primary_10_1007_s00182_021_00789_7 crossref_primary_10_1007_s00453_019_00636_y crossref_primary_10_1137_20M1385779
Cites_doi	10.4086/toc.2007.v003a006 10.1016/j.econlet.2013.03.007 10.1007/BF01889914 10.1016/j.tcs.2010.05.005 10.1016/j.jda.2012.02.001 10.1007/s10601-009-9079-y 10.1257/aer.102.3.366 10.1016/j.jda.2006.03.006 10.1006/jagm.2000.1155 10.1016/j.jda.2008.07.003 10.1016/S0304-3975(98)00158-3 10.1007/BF02276100 10.1137/S0097539793251219 10.1145/2841226 10.1002/net.20266 10.1016/0095-8956(88)90068-8 10.1016/j.ifacol.2016.07.757 10.1142/8591 10.1109/TMC.2009.50 10.1016/j.disc.2005.11.059 10.1016/j.orl.2013.07.006 10.1093/acprof:oso/9780198566076.001.0001 10.1057/jors.1990.3 10.1007/s00453-014-9951-z 10.1006/jctb.1993.1035 10.1145/800061.808776 10.1007/978-3-319-19315-1_19 10.1145/952532.952698
ContentType	Journal Article
Copyright	The Author(s) 2016 Copyright Springer Science & Business Media 2018
Copyright_xml	– notice: The Author(s) 2016 – notice: Copyright Springer Science & Business Media 2018
DBID	C6C AAYXX CITATION JQ2
DOI	10.1007/s00453-016-0252-6
DatabaseName	Springer Nature OA Free Journals CrossRef ProQuest Computer Science Collection
DatabaseTitle	CrossRef ProQuest Computer Science Collection
DatabaseTitleList	ProQuest Computer Science Collection
DeliveryMethod	fulltext_linktorsrc
Discipline	Computer Science
EISSN	1432-0541
EndPage	208
ExternalDocumentID	10_1007_s00453_016_0252_6
GrantInformation_xml	– fundername: EU Marie Curie Actions – fundername: Magyar Tudományos Akadémia grantid: LP2016-3 funderid: http://dx.doi.org/10.13039/501100003825 – fundername: Deutscher Akademischer Austauschdienst grantid: BMBF funderid: http://dx.doi.org/10.13039/501100001655 – fundername: Deutsche Forschungsgemeinschaft grantid: A07 of CRC TRR 154 funderid: http://dx.doi.org/10.13039/501100001659 – fundername: COST Action grantid: IC1205 – fundername: Engineering and Physical Sciences Research Council grantid: EP/K010042/1 funderid: http://dx.doi.org/10.13039/501100000266
GroupedDBID	-4Z -59 -5G -BR -EM -Y2 -~C -~X .86 .DC .VR 06D 0R~ 0VY 199 1N0 1SB 203 23M 28- 2J2 2JN 2JY 2KG 2KM 2LR 2P1 2VQ 2~H 30V 4.4 406 408 409 40D 40E 5GY 5QI 5VS 67Z 6NX 78A 8TC 8UJ 95- 95. 95~ 96X AAAVM AABHQ AACDK AAHNG AAIAL AAJBT AAJKR AANZL AAOBN AARHV AARTL AASML AATNV AATVU AAUYE AAWCG AAYIU AAYQN AAYTO AAYZH ABAKF ABBBX ABBXA ABDPE ABDZT ABECU ABFSI ABFTV ABHLI ABHQN ABJNI ABJOX ABKCH ABKTR ABLJU ABMNI ABMQK ABNWP ABQBU ABQSL ABSXP ABTAH ABTEG ABTHY ABTKH ABTMW ABULA ABWNU ABXPI ACAOD ACBXY ACDTI ACGFS ACHSB ACHXU ACKNC ACMDZ ACMLO ACOKC ACOMO ACPIV ACZOJ ADHHG ADHIR ADIMF ADINQ ADKNI ADKPE ADRFC ADTPH ADURQ ADYFF ADZKW AEBTG AEFIE AEFQL AEGAL AEGNC AEJHL AEJRE AEKMD AEMSY AENEX AEOHA AEPYU AESKC AETLH AEVLU AEXYK AFBBN AFEXP AFGCZ AFLOW AFQWF AFWTZ AFZKB AGAYW AGDGC AGGDS AGJBK AGMZJ AGQEE AGQMX AGRTI AGWIL AGWZB AGYKE AHAVH AHBYD AHKAY AHSBF AHYZX AI. AIAKS AIGIU AIIXL AILAN AITGF AJBLW AJRNO AJZVZ ALMA_UNASSIGNED_HOLDINGS ALWAN AMKLP AMXSW AMYLF AMYQR AOCGG ARMRJ ASPBG AVWKF AXYYD AYJHY AZFZN B-. BA0 BBWZM BDATZ BGNMA BSONS C6C CAG COF CS3 CSCUP DDRTE DL5 DNIVK DPUIP E.L EBLON EBS EIOEI EJD ESBYG FEDTE FERAY FFXSO FIGPU FINBP FNLPD FRRFC FSGXE FWDCC GGCAI GGRSB GJIRD GNWQR GQ6 GQ7 GQ8 GXS H13 HF~ HG5 HG6 HMJXF HQYDN HRMNR HVGLF HZ~ H~9 I09 IHE IJ- IKXTQ ITM IWAJR IXC IZIGR IZQ I~X I~Z J-C J0Z JBSCW JCJTX JZLTJ KDC KOV KOW LAS LLZTM M4Y MA- N2Q N9A NB0 NDZJH NPVJJ NQJWS NU0 O9- O93 O9G O9I O9J OAM P19 P9O PF- PT4 PT5 QOK QOS R4E R89 R9I RHV RIG RNI RNS ROL RPX RSV RZK S16 S1Z S26 S27 S28 S3B SAP SCJ SCLPG SCO SDH SDM SHX SISQX SJYHP SNE SNPRN SNX SOHCF SOJ SPISZ SRMVM SSLCW STPWE SZN T13 T16 TN5 TSG TSK TSV TUC U2A UG4 UOJIU UQL UTJUX UZXMN VC2 VFIZW VH1 VXZ W23 W48 WK8 YLTOR Z45 Z7X Z83 Z88 Z8R Z8W Z92 ZMTXR ZY4 ~EX AAPKM AAYXX ABBRH ABDBE ABFSG ABRTQ ACSTC ADHKG AEZWR AFDZB AFHIU AFOHR AGQPQ AHPBZ AHWEU AIXLP ATHPR AYFIA CITATION JQ2
ID	FETCH-LOGICAL-c359t-c0e21c1a056efeb388dbfd42ccc9d1a7d8c1b22f16c20d8fc1627d4ea8acc66b3
IEDL.DBID	RSV
ISICitedReferencesCount	9
ISICitedReferencesURI	http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000419148000009&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN	0178-4617
IngestDate	Thu Oct 02 16:27:58 EDT 2025 Sat Nov 29 02:20:27 EST 2025 Tue Nov 18 22:41:03 EST 2025 Fri Feb 21 02:43:08 EST 2025
IsDoiOpenAccess	true
IsOpenAccess	true
IsPeerReviewed	true
IsScholarly	true
Issue	1
Keywords	Maximum matching Bounded treewidth Many-to-one matching Inapproximability Project allocation
Language	English
LinkModel	DirectLink
MergedId	FETCHMERGED-LOGICAL-c359t-c0e21c1a056efeb388dbfd42ccc9d1a7d8c1b22f16c20d8fc1627d4ea8acc66b3
Notes	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
ORCID	0000-0003-4991-2599
OpenAccessLink	https://link.springer.com/10.1007/s00453-016-0252-6
PQID	1983887807
PQPubID	2043795
PageCount	24
ParticipantIDs	proquest_journals_1983887807 crossref_citationtrail_10_1007_s00453_016_0252_6 crossref_primary_10_1007_s00453_016_0252_6 springer_journals_10_1007_s00453_016_0252_6
PublicationCentury	2000
PublicationDate	20180100 2018-1-00 20180101
PublicationDateYYYYMMDD	2018-01-01
PublicationDate_xml	– month: 1 year: 2018 text: 20180100
PublicationDecade	2010
PublicationPlace	New York
PublicationPlace_xml	– name: New York
PublicationTitle	Algorithmica
PublicationTitleAbbrev	Algorithmica
PublicationYear	2018
Publisher	Springer US Springer Nature B.V
Publisher_xml	– name: Springer US – name: Springer Nature B.V
References	Bejerano, Han (CR3) 2009; 8 Kamiyama (CR18) 2013; 41 Sebő (CR33) 1993; 58 Manlove, O’Malley (CR25) 2008; 6 Niedermeier (CR27) 2006 Chandra, Halldórsson (CR7) 2001; 39 Lovász (CR23) 1973; 4 Zuckerman (CR35) 2007; 3 Bodlaender (CR5) 1994; 11 CR13 Kloks (CR20) 1994 Plummer (CR29) 2007; 307 CR12 CR34 CR11 CR10 Hamada, Iwama, Miyazaki (CR14) 2014; 74 CR31 CR30 Manlove (CR24) 2013 Samer, Szeider (CR32) 2011; 16 Fragiadakis, Iwasaki, Troyan, Ueda, Yokoo (CR9) 2016; 4 Monte, Tumennasan (CR26) 2013; 120 Lovász (CR22) 1972; 23 Abraham, Irving, Manlove (CR1) 2007; 5 CR21 Hanna, Albert, Chen, Stone (CR15) 2016; 49 Kamada, Kojima (CR17) 2012; 102 Ólafsson (CR28) 1990; 41 Cornuéjols (CR8) 1988; 45 Klasing, Kosowski, Navarra (CR19) 2009; 53 Iwama, Miyazaki, Yanagisawa (CR16) 2012; 13 Bodlaender (CR6) 1996; 25 Alimonti, Kann (CR2) 2000; 237 Biró, Fleiner, Irving, Manlove (CR4) 2010; 411 P Biró (252_CR4) 2010; 411 K Iwama (252_CR16) 2012; 13 G Cornuéjols (252_CR8) 1988; 45 N Kamiyama (252_CR18) 2013; 41 Y Kamada (252_CR17) 2012; 102 252_CR21 L Lovász (252_CR22) 1972; 23 252_CR13 252_CR12 252_CR34 M Samer (252_CR32) 2011; 16 DF Manlove (252_CR25) 2008; 6 S Ólafsson (252_CR28) 1990; 41 MD Plummer (252_CR29) 2007; 307 D Fragiadakis (252_CR9) 2016; 4 HL Bodlaender (252_CR5) 1994; 11 JP Hanna (252_CR15) 2016; 49 D Monte (252_CR26) 2013; 120 R Niedermeier (252_CR27) 2006 K Hamada (252_CR14) 2014; 74 R Klasing (252_CR19) 2009; 53 L Lovász (252_CR23) 1973; 4 D Zuckerman (252_CR35) 2007; 3 P Alimonti (252_CR2) 2000; 237 252_CR31 252_CR30 252_CR11 252_CR10 HL Bodlaender (252_CR6) 1996; 25 B Chandra (252_CR7) 2001; 39 T Kloks (252_CR20) 1994 Y Bejerano (252_CR3) 2009; 8 DF Manlove (252_CR24) 2013 DJ Abraham (252_CR1) 2007; 5 A Sebő (252_CR33) 1993; 58
References_xml	– volume: 3 start-page: 103 issue: 6 year: 2007 end-page: 128 ident: CR35 article-title: Linear degree extractors and the inapproximability of max clique and chromatic number publication-title: Theory Comput. doi: 10.4086/toc.2007.v003a006 – volume: 120 start-page: 14 year: 2013 end-page: 17 ident: CR26 article-title: Matching with quorums publication-title: Econ. Lett. doi: 10.1016/j.econlet.2013.03.007 – ident: CR12 – volume: 23 start-page: 179 issue: 1–2 year: 1972 end-page: 195 ident: CR22 article-title: On the structure of factorizable graphs publication-title: Acta Math. Acad. Sci. Hung. doi: 10.1007/BF01889914 – ident: CR30 – volume: 411 start-page: 3136 year: 2010 end-page: 3153 ident: CR4 article-title: The College Admissions problem with lower and common quotas publication-title: Theor. Comput. Sci. doi: 10.1016/j.tcs.2010.05.005 – ident: CR10 – volume: 13 start-page: 59 year: 2012 end-page: 66 ident: CR16 article-title: Improved approximation bounds for the student–project allocation problem with preferences over projects publication-title: J. Discrete Algorithms doi: 10.1016/j.jda.2012.02.001 – volume: 16 start-page: 1 year: 2011 end-page: 24 ident: CR32 article-title: Tractable cases of the extended global cardinality constraint publication-title: Constraints doi: 10.1007/s10601-009-9079-y – volume: 102 start-page: 366 issue: 3 year: 2012 end-page: 370 ident: CR17 article-title: Stability and strategy-proofness for matching with constraints: a problem in the Japanese medical match and its solution publication-title: Am. Econ. Rev. doi: 10.1257/aer.102.3.366 – volume: 5 start-page: 79 issue: 1 year: 2007 end-page: 91 ident: CR1 article-title: Two algorithms for the student–project allocation problem publication-title: J. Discrete Algorithms doi: 10.1016/j.jda.2006.03.006 – volume: 39 start-page: 223 issue: 2 year: 2001 end-page: 240 ident: CR7 article-title: Greedy local improvement and weighted set packing approximation publication-title: J. Algorithms doi: 10.1006/jagm.2000.1155 – volume: 6 start-page: 553 year: 2008 end-page: 560 ident: CR25 article-title: Student project allocation with preferences over projects publication-title: J. Discrete Algorithms doi: 10.1016/j.jda.2008.07.003 – volume: 237 start-page: 123 issue: 1–2 year: 2000 end-page: 134 ident: CR2 article-title: Some APX-completeness results for cubic graphs publication-title: Theor. Comput. Sci. doi: 10.1016/S0304-3975(98)00158-3 – volume: 4 start-page: 121 issue: 2–3 year: 1973 end-page: 123 ident: CR23 article-title: Antifactors of graphs publication-title: Period. Math. Hung. doi: 10.1007/BF02276100 – ident: CR21 – volume: 11 start-page: 1 issue: 1–2 year: 1994 ident: CR5 article-title: A tourist guide through treewidth publication-title: Acta Cybern. – volume: 25 start-page: 1305 issue: 6 year: 1996 end-page: 1317 ident: CR6 article-title: A linear-time algorithm for finding tree-decompositions of small treewidth publication-title: SIAM J. Comput. doi: 10.1137/S0097539793251219 – volume: 4 start-page: 6:1 issue: 1 year: 2016 end-page: 40 ident: CR9 article-title: Strategyproof matching with minimum quotas publication-title: ACM Trans. Econ. Comput. doi: 10.1145/2841226 – ident: CR31 – ident: CR13 – volume: 53 start-page: 266 issue: 3 year: 2009 end-page: 275 ident: CR19 article-title: Cost minimization in wireless networks with a bounded and unbounded number of interfaces publication-title: Networks doi: 10.1002/net.20266 – ident: CR11 – volume: 45 start-page: 185 issue: 2 year: 1988 end-page: 198 ident: CR8 article-title: General factors of graphs publication-title: J. Comb. Theory Ser. B doi: 10.1016/0095-8956(88)90068-8 – volume: 49 start-page: 254 issue: 15 year: 2016 end-page: 259 ident: CR15 article-title: Minimum cost matching for autonomous carsharing publication-title: IFAC PapersOnLine doi: 10.1016/j.ifacol.2016.07.757 – ident: CR34 – year: 1994 ident: CR20 publication-title: Treewidth, Computations and Approximations, volume 842 of Lecture Notes in Computer Science – year: 2013 ident: CR24 publication-title: Algorithmics of Matching Under Preferences doi: 10.1142/8591 – volume: 8 start-page: 735 issue: 6 year: 2009 end-page: 749 ident: CR3 article-title: Cell breathing techniques for load balancing in wireless lans publication-title: IEEE Trans. Mob. Comput. doi: 10.1109/TMC.2009.50 – volume: 307 start-page: 791 issue: 7–8 year: 2007 end-page: 821 ident: CR29 article-title: Graph factors and factorization: 1985–2003: a survey publication-title: Discrete Math. doi: 10.1016/j.disc.2005.11.059 – volume: 41 start-page: 559 year: 2013 end-page: 561 ident: CR18 article-title: A note on the serial dictatorship with project closures publication-title: Oper. Res. Lett. doi: 10.1016/j.orl.2013.07.006 – year: 2006 ident: CR27 publication-title: Invitation to Fixed-Parameter Algorithms doi: 10.1093/acprof:oso/9780198566076.001.0001 – volume: 41 start-page: 17 issue: 1 year: 1990 end-page: 24 ident: CR28 article-title: Weighted matching in chess tournaments publication-title: J. Oper. Res. Soc. doi: 10.1057/jors.1990.3 – volume: 74 start-page: 440 issue: 1 year: 2014 end-page: 465 ident: CR14 article-title: The hospitals/residents problem with lower quotas publication-title: Algorithmica doi: 10.1007/s00453-014-9951-z – volume: 58 start-page: 174 issue: 2 year: 1993 end-page: 184 ident: CR33 article-title: General antifactors of graphs publication-title: J. Comb. Theory Ser. B doi: 10.1006/jctb.1993.1035 – ident: 252_CR11 – ident: 252_CR34 – volume: 411 start-page: 3136 year: 2010 ident: 252_CR4 publication-title: Theor. Comput. Sci. doi: 10.1016/j.tcs.2010.05.005 – ident: 252_CR10 doi: 10.1145/800061.808776 – volume: 3 start-page: 103 issue: 6 year: 2007 ident: 252_CR35 publication-title: Theory Comput. doi: 10.4086/toc.2007.v003a006 – volume: 8 start-page: 735 issue: 6 year: 2009 ident: 252_CR3 publication-title: IEEE Trans. Mob. Comput. doi: 10.1109/TMC.2009.50 – volume: 11 start-page: 1 issue: 1–2 year: 1994 ident: 252_CR5 publication-title: Acta Cybern. – volume: 49 start-page: 254 issue: 15 year: 2016 ident: 252_CR15 publication-title: IFAC PapersOnLine doi: 10.1016/j.ifacol.2016.07.757 – volume: 16 start-page: 1 year: 2011 ident: 252_CR32 publication-title: Constraints doi: 10.1007/s10601-009-9079-y – ident: 252_CR21 doi: 10.1007/978-3-319-19315-1_19 – volume: 237 start-page: 123 issue: 1–2 year: 2000 ident: 252_CR2 publication-title: Theor. Comput. Sci. doi: 10.1016/S0304-3975(98)00158-3 – volume: 41 start-page: 559 year: 2013 ident: 252_CR18 publication-title: Oper. Res. Lett. doi: 10.1016/j.orl.2013.07.006 – volume: 25 start-page: 1305 issue: 6 year: 1996 ident: 252_CR6 publication-title: SIAM J. Comput. doi: 10.1137/S0097539793251219 – volume: 13 start-page: 59 year: 2012 ident: 252_CR16 publication-title: J. Discrete Algorithms doi: 10.1016/j.jda.2012.02.001 – volume: 120 start-page: 14 year: 2013 ident: 252_CR26 publication-title: Econ. Lett. doi: 10.1016/j.econlet.2013.03.007 – ident: 252_CR13 – volume: 4 start-page: 121 issue: 2–3 year: 1973 ident: 252_CR23 publication-title: Period. Math. Hung. doi: 10.1007/BF02276100 – volume: 102 start-page: 366 issue: 3 year: 2012 ident: 252_CR17 publication-title: Am. Econ. Rev. doi: 10.1257/aer.102.3.366 – ident: 252_CR30 doi: 10.1145/952532.952698 – volume: 45 start-page: 185 issue: 2 year: 1988 ident: 252_CR8 publication-title: J. Comb. Theory Ser. B doi: 10.1016/0095-8956(88)90068-8 – volume: 58 start-page: 174 issue: 2 year: 1993 ident: 252_CR33 publication-title: J. Comb. Theory Ser. B doi: 10.1006/jctb.1993.1035 – volume: 5 start-page: 79 issue: 1 year: 2007 ident: 252_CR1 publication-title: J. Discrete Algorithms doi: 10.1016/j.jda.2006.03.006 – ident: 252_CR12 – volume: 307 start-page: 791 issue: 7–8 year: 2007 ident: 252_CR29 publication-title: Discrete Math. doi: 10.1016/j.disc.2005.11.059 – volume: 74 start-page: 440 issue: 1 year: 2014 ident: 252_CR14 publication-title: Algorithmica doi: 10.1007/s00453-014-9951-z – volume-title: Algorithmics of Matching Under Preferences year: 2013 ident: 252_CR24 doi: 10.1142/8591 – volume: 41 start-page: 17 issue: 1 year: 1990 ident: 252_CR28 publication-title: J. Oper. Res. Soc. doi: 10.1057/jors.1990.3 – volume: 6 start-page: 553 year: 2008 ident: 252_CR25 publication-title: J. Discrete Algorithms doi: 10.1016/j.jda.2008.07.003 – volume-title: Treewidth, Computations and Approximations, volume 842 of Lecture Notes in Computer Science year: 1994 ident: 252_CR20 – volume: 4 start-page: 6:1 issue: 1 year: 2016 ident: 252_CR9 publication-title: ACM Trans. Econ. Comput. doi: 10.1145/2841226 – volume: 23 start-page: 179 issue: 1–2 year: 1972 ident: 252_CR22 publication-title: Acta Math. Acad. Sci. Hung. doi: 10.1007/BF01889914 – volume-title: Invitation to Fixed-Parameter Algorithms year: 2006 ident: 252_CR27 doi: 10.1093/acprof:oso/9780198566076.001.0001 – volume: 39 start-page: 223 issue: 2 year: 2001 ident: 252_CR7 publication-title: J. Algorithms doi: 10.1006/jagm.2000.1155 – volume: 53 start-page: 266 issue: 3 year: 2009 ident: 252_CR19 publication-title: Networks doi: 10.1002/net.20266 – ident: 252_CR31
SSID	ssj0012796
Score	2.2767947
Snippet	We study a natural generalization of the maximum weight many-to-one matching problem. We are given an undirected bipartite graph G = ( A ∪ ˙ P , E ) with... We study a natural generalization of the maximum weight many-to-one matching problem. We are given an undirected bipartite graph G=(A∪˙P,E) with weights on the...
SourceID	proquest crossref springer
SourceType	Aggregation Database Enrichment Source Index Database Publisher
StartPage	185
SubjectTerms	Algorithm Analysis and Problem Complexity Algorithms Colleges & universities Complexity Computer Science Computer Systems Organization and Communication Networks Data Structures and Information Theory Graph theory Graphs Matching Mathematics of Computing Polynomials Quotas Students Theory of Computation
Title	Matchings with Lower Quotas: Algorithms and Complexity
URI	https://link.springer.com/article/10.1007/s00453-016-0252-6 https://www.proquest.com/docview/1983887807
Volume	80
WOSCitedRecordID	wos000419148000009&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 Contemporary 1997-Present customDbUrl: eissn: 1432-0541 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0012796 issn: 0178-4617 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/eLvHCXMwnV1LS8QwEB509eDF9Ymrq-TgSQk0aZuHt0VcPOjiG28lTVIR1l3ZdgX_vUm3rQ9U0GvzIJ1kMl8yk_kA9nkoNBMqw0RJgSPJnEoJnuLQGktUmPGYm5Jsgg8G4v5eXlTvuPM62r12SZY7dfPYzaMPH_vjg2Zjitk8LDhrJzxfw9X1XeM6oLwk5fK08zhy9rl2ZX7XxWdj9I4wvzhFS1vTb_9rlCuwXEFL1JuthVWYs6M1aNe0DajS4nVg5277Lek6kb-FRWeeKA1dTseFyo9Qb_gwnrjPTzlSI4N8c58zs3jdgNv-yc3xKa7oE7AOY1lgHVhKNFEO4tjMnZmFMGlmIqq1loYoboQmKaUZYZoGRmSaMMpNZJVQWjOWhpvQGo1HdgtQ5tO0SxpkUZhGSkWSKBHbVNnAWJlq1YGglmOiq9zinuJimDRZkUu5JD6ezMslYR04aJo8zxJr_Fa5W09OUulYnhAp3D9xEfAOHNaT8aH4p862_1R7B5YcRhKzW5cutIrJ1O7Con4pHvPJXrn03gDrqNKj
linkProvider	Springer Nature
linkToHtml	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1bS8MwFD7oFPTFecXp1Dz4pBSatMvFtyEOxW14mbK3kiapCHOTtRP89yZdOy-ooK_NhfQkJ-ck5-T7AA5ZwBXlMvGwFNwLBbUqxVnsBUYbLIOENZjOySZYt8v7fXFVvONOy2z3MiSZ79Szx27O-3C5Py5ptkE8Og8LoTVYDjD_5vZ-FjogLCflcrTzXmjtcxnK_K6Lz8bo3cP8EhTNbU2r-q9RrsJK4Vqi5nQtrMGcGa5DtaRtQIUWbwDt2O03p-tE7hYWtR1RGrqejDKZnqDm4GE0tp-fUiSHGrnmDjMze92Eu9ZZ7_TcK-gTPBU0ROYp3xCssLQujknsmZlzHSc6JEopobFkmiscE5JgqoiveaIwJUyHRnKpFKVxsAWV4WhotgElDqZdED8JgziUMhRY8oaJpfG1EbGSNfBLOUaqwBZ3FBeDaIaKnMslcvlkTi4RrcHRrMnzFFjjt8r1cnKiQsfSCAtu_4lxn9XguJyMD8U_dbbzp9oHsHTe67Sj9kX3cheWrb_Epzcwdahk44nZg0X1kj2m4_18Gb4B1NnVhw
linkToPdf	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1bS8MwFD7oFPHFecXp1Dz4pBSbtMvFt6EOxTkmXvCtpLmIMDtZq-C_t-naeUEF8bW5kJ7k5JzknHwfwC4LuKJcWg9Lwb1Q0FylOIu9wGiDZWBZi-mCbIL1evzuTvRLntO0ynavQpLjNw0OpSnJDp60PZg8fHOeiMsDcgm0LeLRaZgJXR69O65f3U7CCIQVBF2Ogt4Lc1tdhTW_6-KzYXr3Nr8ESAu706n_e8SLsFC6nKg9XiNLMGWSZahXdA6o1O4VoBf5tlzQeCJ3O4u6jkANXT4PM5keovbgfjjKPz-mSCYaueYOSzN7XYWbzsn10alX0ip4KmiJzFO-IVhhmbs-xuZnac51bHVIlFJCY8k0VzgmxGKqiK-5VZgSpkMjuVSK0jhYg1oyTMw6IOvg2wXxbRjEoZShwJK3TCyNr42IlWyAX8k0UiXmuKO-GEQTtORCLpHLM3NyiWgD9iZNnsaAG79VblYTFZW6l0ZY8PyfGPdZA_ariflQ_FNnG3-qvQNz_eNO1D3rnW_CfO5G8fHFTBNq2ejZbMGseske0tF2sSLfABse3ms
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=Matchings+with+Lower+Quotas%3A+Algorithms+and+Complexity&rft.jtitle=Algorithmica&rft.au=Arulselvan%2C+Ashwin&rft.au=Cseh%2C+%C3%81gnes&rft.au=Gro%C3%9F%2C+Martin&rft.au=Manlove%2C+David+F.&rft.date=2018-01-01&rft.pub=Springer+US&rft.issn=0178-4617&rft.eissn=1432-0541&rft.volume=80&rft.issue=1&rft.spage=185&rft.epage=208&rft_id=info:doi/10.1007%2Fs00453-016-0252-6&rft.externalDocID=10_1007_s00453_016_0252_6
thumbnail_l	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0178-4617&client=summon
thumbnail_m	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0178-4617&client=summon
thumbnail_s	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0178-4617&client=summon