Parameterized Counting of Partially Injective Homomorphisms

We study the parameterized complexity of the problem of counting graph homomorphisms with given partial injectivity constraints, i.e., inequalities between pairs of vertices, which subsumes counting of graph homomorphisms, subgraph counting and, more generally, counting of answers to equi-join queri...

Celý popis

Uloženo v:

Podrobná bibliografie
Vydáno v:	Algorithmica Ročník 83; číslo 6; s. 1829 - 1860
Hlavní autor:	Roth, Marc
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	New York Springer US 01.06.2021 Springer Nature B.V
Témata:	Algorithm Analysis and Problem Complexity Algorithms Apexes Classification Complexity Computer Science Computer Systems Organization and Communication Networks Data Structures and Information Theory Graph theory Graphs Homomorphisms Inequalities Mathematics of Computing Parameterization Parameters Theorems Theory of Computation Matroid lattices Graph homomorphisms Parameterized complexity theory Counting problems Möbius function
ISSN:	0178-4617, 1432-0541
On-line přístup:	Získat plný text
Tagy:	Přidat tag Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!

Abstract	We study the parameterized complexity of the problem of counting graph homomorphisms with given partial injectivity constraints, i.e., inequalities between pairs of vertices, which subsumes counting of graph homomorphisms, subgraph counting and, more generally, counting of answers to equi-join queries with inequalities. Our main result presents an exhaustive complexity classification for the problem in fixed-parameter tractable and # W [ 1 ] -complete cases. The proof relies on the framework of linear combinations of homomorphisms as independently discovered by Chen and Mengel (PODS 16) and by Curticapean, Dell and Marx in the recent breakthrough result regarding the exact complexity of the subgraph counting problem (STOC 17). Moreover, we invoke Rota’s NBC-Theorem to obtain an explicit criterion for fixed-parameter tractability based on treewidth. The abstract classification theorem is then applied to the problem of counting locally injective graph homomorphisms from small pattern graphs to large target graphs. As a consequence, we are able to fully classify its parameterized complexity depending on the class of allowed pattern graphs.
AbstractList	We study the parameterized complexity of the problem of counting graph homomorphisms with given partial injectivity constraints, i.e., inequalities between pairs of vertices, which subsumes counting of graph homomorphisms, subgraph counting and, more generally, counting of answers to equi-join queries with inequalities. Our main result presents an exhaustive complexity classification for the problem in fixed-parameter tractable and $$\#\mathsf {W[1]}$$ # W [ 1 ] -complete cases. The proof relies on the framework of linear combinations of homomorphisms as independently discovered by Chen and Mengel (PODS 16) and by Curticapean, Dell and Marx in the recent breakthrough result regarding the exact complexity of the subgraph counting problem (STOC 17). Moreover, we invoke Rota’s NBC-Theorem to obtain an explicit criterion for fixed-parameter tractability based on treewidth. The abstract classification theorem is then applied to the problem of counting locally injective graph homomorphisms from small pattern graphs to large target graphs. As a consequence, we are able to fully classify its parameterized complexity depending on the class of allowed pattern graphs. We study the parameterized complexity of the problem of counting graph homomorphisms with given partial injectivity constraints, i.e., inequalities between pairs of vertices, which subsumes counting of graph homomorphisms, subgraph counting and, more generally, counting of answers to equi-join queries with inequalities. Our main result presents an exhaustive complexity classification for the problem in fixed-parameter tractable and # W [ 1 ] -complete cases. The proof relies on the framework of linear combinations of homomorphisms as independently discovered by Chen and Mengel (PODS 16) and by Curticapean, Dell and Marx in the recent breakthrough result regarding the exact complexity of the subgraph counting problem (STOC 17). Moreover, we invoke Rota’s NBC-Theorem to obtain an explicit criterion for fixed-parameter tractability based on treewidth. The abstract classification theorem is then applied to the problem of counting locally injective graph homomorphisms from small pattern graphs to large target graphs. As a consequence, we are able to fully classify its parameterized complexity depending on the class of allowed pattern graphs. We study the parameterized complexity of the problem of counting graph homomorphisms with given partial injectivity constraints, i.e., inequalities between pairs of vertices, which subsumes counting of graph homomorphisms, subgraph counting and, more generally, counting of answers to equi-join queries with inequalities. Our main result presents an exhaustive complexity classification for the problem in fixed-parameter tractable and #W[1]-complete cases. The proof relies on the framework of linear combinations of homomorphisms as independently discovered by Chen and Mengel (PODS 16) and by Curticapean, Dell and Marx in the recent breakthrough result regarding the exact complexity of the subgraph counting problem (STOC 17). Moreover, we invoke Rota’s NBC-Theorem to obtain an explicit criterion for fixed-parameter tractability based on treewidth. The abstract classification theorem is then applied to the problem of counting locally injective graph homomorphisms from small pattern graphs to large target graphs. As a consequence, we are able to fully classify its parameterized complexity depending on the class of allowed pattern graphs.
Author	Roth, Marc
Author_xml	– sequence: 1 givenname: Marc orcidid: 0000-0003-3159-9418 surname: Roth fullname: Roth, Marc email: marc.roth@merton.ox.ac.uk organization: Cluster of Excellence (MMCI), Saarland Informatics Campus (SIC), Merton College, University of Oxford
BookMark	eNp9kE1LAzEQhoNUsK3-AU8LnqOTj81u8SRFbaGgBz2HbJrUlG5Sk1RYf72rKwgeyhzmMO8zMzwTNPLBG4QuCVwTgOomAfCSYaAEA9RQ4u4EjQlnFEPJyQiNgVQ15oJUZ2iS0haA0Gomxuj2WUXVmmyi-zTrYh4OPju_KYIt-kl2arfriqXfGp3dhykWoe0r7t9catM5OrVql8zFb5-i14f7l_kCr54el_O7FdZMsIy1trwmgolaUA5NSbRa08oIy_maa1OryjLGueJcNNoCMA5WzEw5s41tGlKyKboa9u5jeD-YlOU2HKLvT0paMkpYJXjdp-iQ0jGkFI2V--haFTtJQH5LkoMk2UuSP5Jk10P1P0i7rLILPkfldsdRNqCpv-M3Jv59dYT6AikXfl8
CitedBy_id	crossref_primary_10_1145_3689634
Cites_doi	10.1016/j.jcss.2009.08.003 10.1137/16M1073984 10.1016/j.apal.2005.06.010 10.1016/0020-0190(79)90004-8 10.1016/j.ic.2005.05.001 10.1145/321864.321877 10.1016/0020-0190(71)90019-6 10.1145/3212622 10.1063/1.1703953 10.1006/jcss.2000.1727 10.1112/S1461157000000243 10.1007/s00037-015-0118-3 10.1137/0218077 10.1137/S0097539703427203 10.1016/j.cosrev.2008.06.001 10.1016/j.jcss.2006.04.007 10.1137/070682575 10.1016/j.tcs.2004.08.008 10.1016/S0304-3975(02)00017-8 10.1080/14786436108243366 10.1016/0012-365X(71)90014-8 10.4086/toc.2010.v006a005 10.1016/0020-0190(94)00085-9 10.1137/S0097539797321602 10.1016/j.tcs.2007.05.023 10.1137/0208032 10.1016/0031-8914(61)90063-5 10.1016/j.jcss.2010.06.005 10.1007/s00453-012-9626-6 10.1016/0304-3975(79)90044-6 10.1145/2656335 10.1137/0130017 10.1137/S0097539794266766 10.1007/978-3-319-51829-9 10.1017/CBO9780511804106 10.1145/800133.804350 10.1137/1.9781611975031.118 10.1109/FOCS.2017.38 10.4230/LIPIcs.ESA.2017.63 10.1007/978-3-642-39206-1_30 10.1109/FOCS.2015.81 10.1007/978-3-319-58747-9_10 10.1007/3-540-29953-X 10.4230/LIPIcs.ICALP.2019.113 10.1137/1.9781611975482.137 10.1145/3055399.3055502 10.4230/LIPIcs.IPEC.2018.24 10.1016/j.jctb.2008.06.004 10.1007/BF00531932 10.1109/FOCS.2017.37 10.1093/acprof:oso/9780198566946.001.0001 10.1017/CBO9781139058520.002 10.1090/coll/060 10.1145/2902251.2902279 10.1109/FOCS.2014.22 10.1007/978-3-319-21275-3 10.4230/LIPIcs.ICALP.2018.12
ContentType	Journal Article
Copyright	The Author(s) 2021 The Author(s) 2021. 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.
Copyright_xml	– notice: The Author(s) 2021 – notice: The Author(s) 2021. 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.
DBID	C6C AAYXX CITATION JQ2
DOI	10.1007/s00453-021-00805-y
DatabaseName	Springer Nature OA Free Journals CrossRef ProQuest Computer Science Collection
DatabaseTitle	CrossRef ProQuest Computer Science Collection
DatabaseTitleList	CrossRef ProQuest Computer Science Collection
DeliveryMethod	fulltext_linktorsrc
Discipline	Computer Science
EISSN	1432-0541
EndPage	1860
ExternalDocumentID	10_1007_s00453_021_00805_y
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-c363t-ccf48163686240b51cad27e6f44d4ce8a7f3344a446bcf00340f69e59fbfbb153
IEDL.DBID	RSV
ISICitedReferencesCount	2
ISICitedReferencesURI	http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000627705900002&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	Sun Nov 09 08:10:57 EST 2025 Sat Nov 29 02:20:30 EST 2025 Tue Nov 18 22:32:05 EST 2025 Fri Feb 21 02:48:53 EST 2025
IsDoiOpenAccess	true
IsOpenAccess	true
IsPeerReviewed	true
IsScholarly	true
Issue	6
Keywords	Matroid lattices Graph homomorphisms Parameterized complexity theory Counting problems Möbius function
Language	English
LinkModel	DirectLink
MergedId	FETCHMERGED-LOGICAL-c363t-ccf48163686240b51cad27e6f44d4ce8a7f3344a446bcf00340f69e59fbfbb153
Notes	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
ORCID	0000-0003-3159-9418
OpenAccessLink	https://link.springer.com/10.1007/s00453-021-00805-y
PQID	2532137648
PQPubID	2043795
PageCount	32
ParticipantIDs	proquest_journals_2532137648 crossref_primary_10_1007_s00453_021_00805_y crossref_citationtrail_10_1007_s00453_021_00805_y springer_journals_10_1007_s00453_021_00805_y
PublicationCentury	2000
PublicationDate	2021-06-01
PublicationDateYYYYMMDD	2021-06-01
PublicationDate_xml	– month: 06 year: 2021 text: 2021-06-01 day: 01
PublicationDecade	2020
PublicationPlace	New York
PublicationPlace_xml	– name: New York
PublicationTitle	Algorithmica
PublicationTitleAbbrev	Algorithmica
PublicationYear	2021
Publisher	Springer US Springer Nature B.V
Publisher_xml	– name: Springer US – name: Springer Nature B.V
References	Dyer, Goldberg, Jerrum (CR23) 2010; 76 Lin (CR40) 2018; 65 Huang, Lu (CR33) 2016; 25 van Aardenne-Ehrenfest, de Bruijn (CR1) 1951; 28 Impagliazzo, Paturi (CR34) 2001; 62 CR31 CR30 Cai, Huang, Lu (CR7) 2012; 64 CR2 CR4 Ladner (CR39) 1975; 22 CR3 Hopcroft, Tarjan (CR32) 1971; 1 Valiant (CR58) 2008; 37 CR6 Vadhan (CR55) 2001; 31 CR5 Jerrum (CR35) 1994; 51 CR49 Marx (CR42) 2010; 6 CR48 Olteanu, Závodný (CR47) 2015; 40 Valiant (CR56) 1979; 8 Goldberg, Jerrum (CR28) 2000; 3 McCartin (CR45) 2006; 138 CR41 Fiala, Kratochvíl (CR25) 2008; 2 Nešetřil (CR46) 1971; 1 Valiant (CR57) 1979; 8 Feder, Vardi (CR24) 1998; 28 Temperley, Fisher (CR54) 1961; 6 Flum, Grohe (CR26) 2004; 33 CR18 CR17 CR16 CR15 Kasteleyn (CR37) 1961; 27 CR59 CR14 CR11 Cai, Lu (CR8) 2011; 77 CR10 CR53 Maurer (CR44) 1976; 30 CR52 CR51 Díaz, Serna, Thilikos (CR22) 2002; 281 CR50 Dalmau, Jonsson (CR19) 2004; 329 Chen, Huang, Kanj, Xia (CR13) 2006; 72 Jerrum, Sinclair (CR36) 1989; 18 CR29 CR27 Chen, Chor, Fellows, Huang, Juedes, Kanj, Xia (CR12) 2005; 201 Kasteleyn (CR38) 1963; 4 CR21 CR20 CR61 Xia, Zhang, Zhao (CR60) 2007; 384 Mathon (CR43) 1979; 8 Cai, Lu, Xia (CR9) 2017; 46 805_CR29 LA Goldberg (805_CR28) 2000; 3 805_CR21 LG Valiant (805_CR57) 1979; 8 J Cai (805_CR9) 2017; 46 805_CR27 805_CR61 J Díaz (805_CR22) 2002; 281 RE Ladner (805_CR39) 1975; 22 805_CR20 T van Aardenne-Ehrenfest (805_CR1) 1951; 28 J Chen (805_CR12) 2005; 201 PW Kasteleyn (805_CR38) 1963; 4 805_CR18 PW Kasteleyn (805_CR37) 1961; 27 805_CR10 805_CR11 805_CR14 ME Dyer (805_CR23) 2010; 76 805_CR15 805_CR59 805_CR16 J Cai (805_CR8) 2011; 77 805_CR17 J Chen (805_CR13) 2006; 72 LG Valiant (805_CR56) 1979; 8 J Flum (805_CR26) 2004; 33 M Jerrum (805_CR35) 1994; 51 805_CR50 805_CR51 805_CR52 805_CR53 S Huang (805_CR33) 2016; 25 R Mathon (805_CR43) 1979; 8 SB Maurer (805_CR44) 1976; 30 C McCartin (805_CR45) 2006; 138 805_CR48 805_CR49 LG Valiant (805_CR58) 2008; 37 805_CR41 D Olteanu (805_CR47) 2015; 40 D Marx (805_CR42) 2010; 6 J Nešetřil (805_CR46) 1971; 1 B Lin (805_CR40) 2018; 65 M Jerrum (805_CR36) 1989; 18 HNV Temperley (805_CR54) 1961; 6 V Dalmau (805_CR19) 2004; 329 SP Vadhan (805_CR55) 2001; 31 J Fiala (805_CR25) 2008; 2 T Feder (805_CR24) 1998; 28 M Xia (805_CR60) 2007; 384 805_CR30 J Cai (805_CR7) 2012; 64 805_CR31 805_CR5 805_CR6 R Impagliazzo (805_CR34) 2001; 62 JE Hopcroft (805_CR32) 1971; 1 805_CR2 805_CR3 805_CR4
References_xml	– volume: 76 start-page: 267 issue: 3–4 year: 2010 end-page: 277 ident: CR23 article-title: An approximation trichotomy for Boolean #CSP publication-title: J. Comput. Syst. Sci. doi: 10.1016/j.jcss.2009.08.003 – volume: 46 start-page: 853 issue: 3 year: 2017 end-page: 889 ident: CR9 article-title: Holographic Algorithms with Matchgates Capture Precisely Tractable Planar #CSP publication-title: SIAM J. Comput. doi: 10.1137/16M1073984 – volume: 138 start-page: 147 issue: 1–3 year: 2006 end-page: 182 ident: CR45 article-title: Parameterized counting problems publication-title: Ann. Pure Appl. Logic doi: 10.1016/j.apal.2005.06.010 – ident: CR49 – ident: CR4 – volume: 8 start-page: 131 issue: 3 year: 1979 end-page: 132 ident: CR43 article-title: A Note on the Graph Isomorphism Counting Problem publication-title: Inf. Process. Lett. doi: 10.1016/0020-0190(79)90004-8 – ident: CR16 – volume: 201 start-page: 216 issue: 2 year: 2005 end-page: 231 ident: CR12 article-title: Tight lower bounds for certain parameterized NP-hard problems publication-title: Inf. Comput. doi: 10.1016/j.ic.2005.05.001 – ident: CR51 – volume: 22 start-page: 155 issue: 1 year: 1975 end-page: 171 ident: CR39 article-title: On the structure of polynomial time reducibility publication-title: J. ACM doi: 10.1145/321864.321877 – volume: 1 start-page: 32 issue: 1 year: 1971 end-page: 34 ident: CR32 article-title: A V Algorithm for Determining Isomorphism of Planar Graphs publication-title: Inf. Process. Lett. doi: 10.1016/0020-0190(71)90019-6 – ident: CR29 – ident: CR61 – volume: 65 start-page: 34:1 issue: 5 year: 2018 end-page: 34:23 ident: CR40 article-title: The Parameterized Complexity of the k-Biclique Problem publication-title: J. ACM doi: 10.1145/3212622 – volume: 4 start-page: 287 issue: 2 year: 1963 end-page: 293 ident: CR38 article-title: Dimer Statistics and Phase Transitions publication-title: Journal of Mathematical Physics doi: 10.1063/1.1703953 – volume: 62 start-page: 367 issue: 2 year: 2001 end-page: 375 ident: CR34 article-title: On the Complexity of k-SAT publication-title: J. Comput. Syst. Sci. doi: 10.1006/jcss.2000.1727 – ident: CR21 – volume: 3 start-page: 117 year: 2000 end-page: 124 ident: CR28 article-title: Counting Unlabelled Subtrees of a Tree is #P-complete publication-title: LMS Journal of Computation and Mathematics doi: 10.1112/S1461157000000243 – volume: 25 start-page: 255 issue: 1 year: 2016 end-page: 304 ident: CR33 article-title: A Dichotomy for Real Weighted Holant Problems publication-title: Computational Complexity doi: 10.1007/s00037-015-0118-3 – volume: 18 start-page: 1149 issue: 6 year: 1989 end-page: 1178 ident: CR36 article-title: Approximating the Permanent publication-title: SIAM J. Comput. doi: 10.1137/0218077 – volume: 33 start-page: 892 issue: 4 year: 2004 end-page: 922 ident: CR26 article-title: The Parameterized Complexity of Counting Problems publication-title: SIAM J. Comput. doi: 10.1137/S0097539703427203 – volume: 2 start-page: 97 issue: 2 year: 2008 end-page: 111 ident: CR25 article-title: Locally constrained graph homomorphisms - structure, complexity, and applications publication-title: Computer Science Review doi: 10.1016/j.cosrev.2008.06.001 – volume: 72 start-page: 1346 issue: 8 year: 2006 end-page: 1367 ident: CR13 article-title: Strong computational lower bounds via parameterized complexity publication-title: J. Comput. Syst. Sci. doi: 10.1016/j.jcss.2006.04.007 – ident: CR15 – volume: 37 start-page: 1565 issue: 5 year: 2008 end-page: 1594 ident: CR58 article-title: Holographic Algorithms publication-title: SIAM J. Comput. doi: 10.1137/070682575 – volume: 329 start-page: 315 issue: 1–3 year: 2004 end-page: 323 ident: CR19 article-title: The complexity of counting homomorphisms seen from the other side publication-title: Theor. Comput. Sci. doi: 10.1016/j.tcs.2004.08.008 – ident: CR50 – volume: 281 start-page: 291 issue: 1–2 year: 2002 end-page: 309 ident: CR22 article-title: Counting H-colorings of partial k-trees publication-title: Theor. Comput. Sci. doi: 10.1016/S0304-3975(02)00017-8 – volume: 6 start-page: 1061 issue: 68 year: 1961 end-page: 1063 ident: CR54 article-title: Dimer problem in statistical mechanics-an exact result publication-title: The Philosophical Magazine: A Journal of Theoretical Experimental and Applied Physics doi: 10.1080/14786436108243366 – volume: 1 start-page: 257 issue: 3 year: 1971 end-page: 268 ident: CR46 article-title: Homomorphisms of derivative graphs publication-title: Discrete Mathematics doi: 10.1016/0012-365X(71)90014-8 – ident: CR11 – volume: 28 start-page: 203 year: 1951 end-page: 217 ident: CR1 article-title: Circuits and trees in oriented linear graphs publication-title: Simon Stevin: Wis- en Natuurkundig Tijdschrift – volume: 6 start-page: 85 issue: 1 year: 2010 end-page: 112 ident: CR42 article-title: Can You Beat Treewidth? publication-title: Theory of Computing doi: 10.4086/toc.2010.v006a005 – ident: CR5 – volume: 51 start-page: 111 issue: 3 year: 1994 end-page: 116 ident: CR35 article-title: Counting Trees in a Graph is #P-Complete publication-title: Inf. Process. Lett. doi: 10.1016/0020-0190(94)00085-9 – volume: 31 start-page: 398 issue: 2 year: 2001 end-page: 427 ident: CR55 article-title: The Complexity of Counting in Sparse, Regular, and Planar Graphs publication-title: SIAM J. Comput. doi: 10.1137/S0097539797321602 – ident: CR18 – volume: 384 start-page: 111 issue: 1 year: 2007 end-page: 125 ident: CR60 article-title: Computational complexity of counting problems on 3-regular planar graphs publication-title: Theor. Comput. Sci. doi: 10.1016/j.tcs.2007.05.023 – ident: CR14 – volume: 8 start-page: 410 issue: 3 year: 1979 end-page: 421 ident: CR57 article-title: The Complexity of Enumeration and Reliability Problems publication-title: SIAM J. Comput. doi: 10.1137/0208032 – ident: CR2 – ident: CR53 – ident: CR30 – volume: 27 start-page: 1209 issue: 12 year: 1961 end-page: 1225 ident: CR37 article-title: The statistics of dimers on a lattice: I. The number of dimer arrangements on a quadratic lattice publication-title: Physica doi: 10.1016/0031-8914(61)90063-5 – ident: CR10 – volume: 77 start-page: 41 issue: 1 year: 2011 end-page: 61 ident: CR8 article-title: Holographic algorithms: From art to science publication-title: J. Comput. Syst. Sci. doi: 10.1016/j.jcss.2010.06.005 – ident: CR6 – volume: 64 start-page: 511 issue: 3 year: 2012 end-page: 533 ident: CR7 article-title: From Holant to #CSP and Back: Dichotomy for Holant Problems publication-title: Algorithmica doi: 10.1007/s00453-012-9626-6 – ident: CR27 – volume: 8 start-page: 189 year: 1979 end-page: 201 ident: CR56 article-title: The Complexity of Computing the Permanent publication-title: Theor. Comput. Sci. doi: 10.1016/0304-3975(79)90044-6 – volume: 40 start-page: 2:1 issue: 1 year: 2015 end-page: 2:44 ident: CR47 article-title: Size Bounds for Factorised Representations of Query Results publication-title: ACM Trans. Database Syst. doi: 10.1145/2656335 – ident: CR48 – ident: CR3 – ident: CR52 – ident: CR17 – ident: CR31 – volume: 30 start-page: 143 issue: 1 year: 1976 end-page: 148 ident: CR44 article-title: Matrix Generalizations of Some Theorems on Trees, Cycles and Cocycles in Graphs publication-title: SIAM Journal on Applied Mathematics doi: 10.1137/0130017 – ident: CR59 – ident: CR41 – volume: 28 start-page: 57 issue: 1 year: 1998 end-page: 104 ident: CR24 article-title: The Computational Structure of Monotone Monadic SNP and Constraint Satisfaction: A Study through Datalog and Group Theory publication-title: SIAM J. Comput. doi: 10.1137/S0097539794266766 – ident: CR20 – volume: 201 start-page: 216 issue: 2 year: 2005 ident: 805_CR12 publication-title: Inf. Comput. doi: 10.1016/j.ic.2005.05.001 – volume: 138 start-page: 147 issue: 1–3 year: 2006 ident: 805_CR45 publication-title: Ann. Pure Appl. Logic doi: 10.1016/j.apal.2005.06.010 – volume: 65 start-page: 34:1 issue: 5 year: 2018 ident: 805_CR40 publication-title: J. ACM doi: 10.1145/3212622 – ident: 805_CR3 doi: 10.1007/978-3-319-51829-9 – volume: 8 start-page: 410 issue: 3 year: 1979 ident: 805_CR57 publication-title: SIAM J. Comput. doi: 10.1137/0208032 – volume: 64 start-page: 511 issue: 3 year: 2012 ident: 805_CR7 publication-title: Algorithmica doi: 10.1007/s00453-012-9626-6 – volume: 28 start-page: 203 year: 1951 ident: 805_CR1 publication-title: Simon Stevin: Wis- en Natuurkundig Tijdschrift – ident: 805_CR29 doi: 10.1017/CBO9780511804106 – volume: 6 start-page: 85 issue: 1 year: 2010 ident: 805_CR42 publication-title: Theory of Computing doi: 10.4086/toc.2010.v006a005 – ident: 805_CR52 doi: 10.1145/800133.804350 – ident: 805_CR10 doi: 10.1137/1.9781611975031.118 – ident: 805_CR61 doi: 10.1109/FOCS.2017.38 – ident: 805_CR50 doi: 10.4230/LIPIcs.ESA.2017.63 – volume: 46 start-page: 853 issue: 3 year: 2017 ident: 805_CR9 publication-title: SIAM J. Comput. doi: 10.1137/16M1073984 – volume: 51 start-page: 111 issue: 3 year: 1994 ident: 805_CR35 publication-title: Inf. Process. Lett. doi: 10.1016/0020-0190(94)00085-9 – ident: 805_CR14 doi: 10.1007/978-3-642-39206-1_30 – ident: 805_CR6 doi: 10.1109/FOCS.2015.81 – ident: 805_CR4 doi: 10.1007/978-3-319-58747-9_10 – volume: 18 start-page: 1149 issue: 6 year: 1989 ident: 805_CR36 publication-title: SIAM J. Comput. doi: 10.1137/0218077 – volume: 8 start-page: 189 year: 1979 ident: 805_CR56 publication-title: Theor. Comput. Sci. doi: 10.1016/0304-3975(79)90044-6 – ident: 805_CR27 doi: 10.1007/3-540-29953-X – ident: 805_CR20 doi: 10.4230/LIPIcs.ICALP.2019.113 – volume: 281 start-page: 291 issue: 1–2 year: 2002 ident: 805_CR22 publication-title: Theor. Comput. Sci. doi: 10.1016/S0304-3975(02)00017-8 – ident: 805_CR31 doi: 10.1137/1.9781611975482.137 – ident: 805_CR21 – volume: 1 start-page: 32 issue: 1 year: 1971 ident: 805_CR32 publication-title: Inf. Process. Lett. doi: 10.1016/0020-0190(71)90019-6 – ident: 805_CR15 – volume: 6 start-page: 1061 issue: 68 year: 1961 ident: 805_CR54 publication-title: The Philosophical Magazine: A Journal of Theoretical Experimental and Applied Physics doi: 10.1080/14786436108243366 – ident: 805_CR16 doi: 10.1145/3055399.3055502 – volume: 329 start-page: 315 issue: 1–3 year: 2004 ident: 805_CR19 publication-title: Theor. Comput. Sci. doi: 10.1016/j.tcs.2004.08.008 – ident: 805_CR51 doi: 10.4230/LIPIcs.IPEC.2018.24 – ident: 805_CR30 doi: 10.1016/j.jctb.2008.06.004 – volume: 8 start-page: 131 issue: 3 year: 1979 ident: 805_CR43 publication-title: Inf. Process. Lett. doi: 10.1016/0020-0190(79)90004-8 – ident: 805_CR49 doi: 10.1007/BF00531932 – volume: 62 start-page: 367 issue: 2 year: 2001 ident: 805_CR34 publication-title: J. Comput. Syst. Sci. doi: 10.1006/jcss.2000.1727 – ident: 805_CR5 doi: 10.1109/FOCS.2017.37 – volume: 72 start-page: 1346 issue: 8 year: 2006 ident: 805_CR13 publication-title: J. Comput. Syst. Sci. doi: 10.1016/j.jcss.2006.04.007 – volume: 25 start-page: 255 issue: 1 year: 2016 ident: 805_CR33 publication-title: Computational Complexity doi: 10.1007/s00037-015-0118-3 – volume: 3 start-page: 117 year: 2000 ident: 805_CR28 publication-title: LMS Journal of Computation and Mathematics doi: 10.1112/S1461157000000243 – ident: 805_CR48 doi: 10.1093/acprof:oso/9780198566946.001.0001 – volume: 30 start-page: 143 issue: 1 year: 1976 ident: 805_CR44 publication-title: SIAM Journal on Applied Mathematics doi: 10.1137/0130017 – ident: 805_CR53 doi: 10.1017/CBO9781139058520.002 – volume: 27 start-page: 1209 issue: 12 year: 1961 ident: 805_CR37 publication-title: Physica doi: 10.1016/0031-8914(61)90063-5 – volume: 37 start-page: 1565 issue: 5 year: 2008 ident: 805_CR58 publication-title: SIAM J. Comput. doi: 10.1137/070682575 – volume: 77 start-page: 41 issue: 1 year: 2011 ident: 805_CR8 publication-title: J. Comput. Syst. Sci. doi: 10.1016/j.jcss.2010.06.005 – volume: 31 start-page: 398 issue: 2 year: 2001 ident: 805_CR55 publication-title: SIAM J. Comput. doi: 10.1137/S0097539797321602 – volume: 4 start-page: 287 issue: 2 year: 1963 ident: 805_CR38 publication-title: Journal of Mathematical Physics doi: 10.1063/1.1703953 – ident: 805_CR41 doi: 10.1090/coll/060 – ident: 805_CR11 doi: 10.1145/2902251.2902279 – ident: 805_CR17 doi: 10.1109/FOCS.2014.22 – volume: 1 start-page: 257 issue: 3 year: 1971 ident: 805_CR46 publication-title: Discrete Mathematics doi: 10.1016/0012-365X(71)90014-8 – volume: 2 start-page: 97 issue: 2 year: 2008 ident: 805_CR25 publication-title: Computer Science Review doi: 10.1016/j.cosrev.2008.06.001 – volume: 22 start-page: 155 issue: 1 year: 1975 ident: 805_CR39 publication-title: J. ACM doi: 10.1145/321864.321877 – ident: 805_CR18 doi: 10.1007/978-3-319-21275-3 – volume: 33 start-page: 892 issue: 4 year: 2004 ident: 805_CR26 publication-title: SIAM J. Comput. doi: 10.1137/S0097539703427203 – volume: 384 start-page: 111 issue: 1 year: 2007 ident: 805_CR60 publication-title: Theor. Comput. Sci. doi: 10.1016/j.tcs.2007.05.023 – volume: 40 start-page: 2:1 issue: 1 year: 2015 ident: 805_CR47 publication-title: ACM Trans. Database Syst. doi: 10.1145/2656335 – volume: 28 start-page: 57 issue: 1 year: 1998 ident: 805_CR24 publication-title: SIAM J. Comput. doi: 10.1137/S0097539794266766 – volume: 76 start-page: 267 issue: 3–4 year: 2010 ident: 805_CR23 publication-title: J. Comput. Syst. Sci. doi: 10.1016/j.jcss.2009.08.003 – ident: 805_CR2 doi: 10.4230/LIPIcs.ICALP.2018.12 – ident: 805_CR59
SSID	ssj0012796
Score	2.308512
Snippet	We study the parameterized complexity of the problem of counting graph homomorphisms with given partial injectivity constraints, i.e., inequalities between...
SourceID	proquest crossref springer
SourceType	Aggregation Database Enrichment Source Index Database Publisher
StartPage	1829
SubjectTerms	Algorithm Analysis and Problem Complexity Algorithms Apexes Classification Complexity Computer Science Computer Systems Organization and Communication Networks Data Structures and Information Theory Graph theory Graphs Homomorphisms Inequalities Mathematics of Computing Parameterization Parameters Theorems Theory of Computation
Title	Parameterized Counting of Partially Injective Homomorphisms
URI	https://link.springer.com/article/10.1007/s00453-021-00805-y https://www.proquest.com/docview/2532137648
Volume	83
WOSCitedRecordID	wos000627705900002&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 Journals 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/eLvHCXMwnV3dS8MwED90-uCL8xOnU_LgmwbWNP0IPslwzJcx_GJvJU0TmGytrFOYf71JlnYoKih9bBrCXS536d39fgDnacYiHpni1phQTJVkmElFMJUsoGFmMLOEJZuIBoN4NGJD1xRWVtXuVUrSntR1s5uJPkzOUV9_dZgT4MU6bGh3FxtzvLt_qnMHJLKsXIZ3HlPtoF2rzPdzfHZHqxjzS1rUepte83_r3IFtF12i6-V22IU1me9Bs2JuQM6Q9-FqyE1RlsFpfpcZ6jrCCFQoNDR7iU8mC3SbPy9PQ9QvpvrRGhmX0_IAHns3D90-djQKWPihP8dCKBrrsMv2gnTSwBM8I5EMFaUZFTLmkfJ9Srm-GKZCGcCajgqZDJhKVZrqE_EQGnmRyyNAjIeCZJ5PAylN5KVtNlPSMxA2XAZUtcCrpJkIhzFuqC4mSY2ObKWTaOkkVjrJogUX9TcvS4SNX0e3KyUlztrKhAQ-0YsIadyCy0opq9c_z3b8t-EnsEWsXs1PmDY05rNXeQqb4m0-Lmdndhd-ABa61i8
linkProvider	Springer Nature
linkToHtml	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV3dS8MwED90Cvri_MTp1Dz4poEtTT-CTzIcG84xdMreQpsmMNk6Wacw_3qTrO1QVFD62DSEu0vu0rv7_QDOo5j5oW-KWwNCMVWSYSYVwVQyl3qxwcwSlmzC73aDwYD1sqawNK92z1OS9qQumt1M9GFyjvr6q8McF89XYY1qj2UK-e4fnorcAfEtK5fhncdUO-isVeb7OT67o2WM-SUtar1Ns_y_dW7DVhZdouuFOezAikx2oZwzN6BsI-_BVS80RVkGp_ldxqiREUagiUI9Y0vhaDRH7eR5cRqi1mSsH62RYTpO9-GxedNvtHBGo4CF4zkzLISigQ67bC9ILXLrIoyJLz1FaUyFDEJfOQ6lob4YRkIZwJqa8ph0mYpUFOkT8QBKySSRh4BY6AkS1x3qSmkiL71nYyXrBsImlC5VFajn0uQiwxg3VBcjXqAjW-lwLR1upcPnFbgovnlZIGz8OrqaK4lnuy3lxHWIXoRHgwpc5kpZvv55tqO_DT-DjVb_rsM77e7tMWwSq2PzQ6YKpdn0VZ7AunibDdPpqbXIDypF2RM
linkToPdf	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV3dS8MwED90ivji_MTp1D74pmU2TT-CTzIdG8oo-MHeSpomMNm6sVZh_vUm6cdUVBDpY9MQ7pLcXe_u9wM4jWLiUU8Vt_oIm1hwYhIukIk5cbAbK8wspskmvH7fHwxI8KGLX1e7lynJvKdBoTQlWWsai1bV-KY8EZV_lKGwdHkcc74MK1iRBql4_f6pyiMgTzN0KQ56E0tjXbTNfD_HZ9O08De_pEi15enU_7_mTdgovE7jKt8mW7DEk22ol4wORnHAd-AyoKpYS-E3v_HYaBdEEsZEGIHaY3Q0mhu95Dm_JY3uZCwfqalhOk534bFz89DumgW9gsls185MxgT2pTume0QuIsdiNEYedwXGMWbcp56wbYypDBgjJhSQzYVwCXeIiEQUyZtyD2rJJOH7YBDqMhRbNnY4Vx6ZPMux4JaCtqHcwaIBVinZkBXY44oCYxRWqMlaOqGUTqilE84bcFZ9M82RN34d3SwVFhanMA2RYyO5CBf7DTgvFbR4_fNsB38bfgJrwXUnvOv1bw9hHWkVq_80Tahlsxd-BKvsNRums2O9Od8B2HLh9w
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=Parameterized+Counting+of+Partially+Injective+Homomorphisms&rft.jtitle=Algorithmica&rft.au=Roth%2C+Marc&rft.date=2021-06-01&rft.pub=Springer+US&rft.issn=0178-4617&rft.eissn=1432-0541&rft.volume=83&rft.issue=6&rft.spage=1829&rft.epage=1860&rft_id=info:doi/10.1007%2Fs00453-021-00805-y&rft.externalDocID=10_1007_s00453_021_00805_y
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