Simultaneous FPQ-ordering and hybrid planarity testing

We introduce and study a constrained planarity testing problem, called 1-Fixed Constrained Planarity, and prove that this problem can be solved in quadratic time for biconnected graphs. Our solution is based on a novel definition of fixedness that makes it possible to simplify and extend known techn...

Full description

Saved in:
Bibliographic Details
Published inTheoretical computer science Vol. 874; pp. 59 - 79
Main Authors Liotta, Giuseppe, Rutter, Ignaz, Tappini, Alessandra
Format Journal Article
LanguageEnglish
Published Elsevier B.V 12.06.2021
Subjects
Graph drawing
Hybrid planarity testing
Simultaneous FPQ-ordering
Graph drawing
Simultaneous FPQ-ordering
Hybrid planarity testing
Online AccessGet full text

Cover

Abstract We introduce and study a constrained planarity testing problem, called 1-Fixed Constrained Planarity, and prove that this problem can be solved in quadratic time for biconnected graphs. Our solution is based on a novel definition of fixedness that makes it possible to simplify and extend known techniques about Simultaneous PQ-Ordering. We exploit this result to study different versions of the hybrid planarity testing problem. Namely, we show polynomial-time solutions for a variant of NodeTrix Planarity with fixed sides, for PolyLink Planarity, and for Clique Planarity with fixed sides.
AbstractList We introduce and study a constrained planarity testing problem, called 1-Fixed Constrained Planarity, and prove that this problem can be solved in quadratic time for biconnected graphs. Our solution is based on a novel definition of fixedness that makes it possible to simplify and extend known techniques about Simultaneous PQ-Ordering. We exploit this result to study different versions of the hybrid planarity testing problem. Namely, we show polynomial-time solutions for a variant of NodeTrix Planarity with fixed sides, for PolyLink Planarity, and for Clique Planarity with fixed sides.
Author Rutter, Ignaz
Liotta, Giuseppe
Tappini, Alessandra
Author_xml – sequence: 1
  givenname: Giuseppe
  surname: Liotta
  fullname: Liotta, Giuseppe
  email: giuseppe.liotta@unipg.it
  organization: Dipartimento di Ingegneria, Università degli Studi di Perugia, Perugia, Italy
– sequence: 2
  givenname: Ignaz
  surname: Rutter
  fullname: Rutter, Ignaz
  email: rutter@fim.uni-passau.de
  organization: Department of Computer Science and Mathematics, University of Passau, Germany
– sequence: 3
  givenname: Alessandra
  surname: Tappini
  fullname: Tappini, Alessandra
  email: alessandra.tappini@unipg.it
  organization: Dipartimento di Ingegneria, Università degli Studi di Perugia, Perugia, Italy
BookMark eNp9j91KAzEQRoNUsK0-gHf7Arvmd7PBKynWCgUV9TqkyaymtNmSpMK-vSn12rmZgeF8fGeGJmEIgNAtwQ3BpL3bNtmmhmJKGiwaTOgFmpJOqppSxSdoihnmNVNSXKFZSltcRsh2itp3vz_usgkwHFO1fH2rh-gg-vBVmeCq73ETvasOOxNM9HmsMqRcntfosje7BDd_e44-l48fi1W9fnl6Xjysa0uVzLWyG8Flx5iUXBnjXCssF4w4ymXPbQvU4a4j1PXl6C101gkOTLUd0N4yyeaInHNtHFKK0OtD9HsTR02wPonrrS7i-iSusdBFvDD3ZwZKsR8PUSfrIVhwPoLN2g3-H_oXJj1ipQ
CitedBy_id crossref_primary_10_1109_TVCG_2022_3233389
crossref_primary_10_1111_cgf_15076
crossref_primary_10_1016_j_jcss_2023_02_007
crossref_primary_10_1145_3607474
crossref_primary_10_1016_j_tcs_2021_09_044
Cites_doi 10.1145/2738054
10.1007/s00453-019-00585-6
10.7155/jgaa.00437
10.1137/S0097539794280736
10.1109/TVCG.2007.70582
10.1109/TVCG.2010.265
10.7155/jgaa.00461
10.2307/2371086
10.1016/S0022-0000(76)80045-1
10.1145/2629341
10.3390/a13080194
10.7155/jgaa.00044
10.7155/jgaa.00160
10.1016/j.tcs.2019.11.024
ContentType Journal Article
Copyright 2021 Elsevier B.V.
Copyright_xml – notice: 2021 Elsevier B.V.
DBID AAYXX
CITATION
DOI 10.1016/j.tcs.2021.05.012
DatabaseName CrossRef
DatabaseTitle CrossRef
DatabaseTitleList
DeliveryMethod fulltext_linktorsrc
Discipline Mathematics
Computer Science
EISSN 1879-2294
EndPage 79
ExternalDocumentID 10_1016_j_tcs_2021_05_012
S0304397521002693
GrantInformation_xml – fundername: MIUR
  grantid: 20174LF3T8
  funderid: https://doi.org/10.13039/501100003407
– fundername: Università degli Studi di Perugia
  grantid: RICBA18WD-RICBA19FM: “Modelli, algoritmi e sistemi per la visualizzazione di grafi e reti”
  funderid: https://doi.org/10.13039/501100010607
– fundername: DFG
  grantid: 1903/3-1
  funderid: https://doi.org/10.13039/501100001659
GroupedDBID --K
--M
-~X
.DC
.~1
0R~
123
1B1
1RT
1~.
1~5
4.4
457
4G.
5VS
7-5
71M
8P~
9JN
AABNK
AACTN
AAEDW
AAFTH
AAIAV
AAIKJ
AAKOC
AALRI
AAOAW
AAQFI
AAXUO
AAYFN
ABAOU
ABBOA
ABJNI
ABMAC
ABYKQ
ACAZW
ACDAQ
ACGFS
ACRLP
ACZNC
ADBBV
ADEZE
AEBSH
AEKER
AENEX
AFKWA
AFTJW
AGUBO
AGYEJ
AHHHB
AHZHX
AIALX
AIEXJ
AIKHN
AITUG
AJOXV
ALMA_UNASSIGNED_HOLDINGS
AMFUW
AMRAJ
AOUOD
ARUGR
AXJTR
BKOJK
BLXMC
CS3
DU5
EBS
EFJIC
EFLBG
EO8
EO9
EP2
EP3
F5P
FDB
FEDTE
FIRID
FNPLU
FYGXN
G-Q
GBLVA
GBOLZ
HVGLF
IHE
IXB
J1W
KOM
LG9
M26
M41
MHUIS
MO0
N9A
O-L
O9-
OAUVE
OK1
OZT
P-8
P-9
P2P
PC.
Q38
ROL
RPZ
SCC
SDF
SDG
SES
SPC
SPCBC
SSV
SSW
T5K
TN5
WH7
YNT
ZMT
~G-
0SF
29Q
6I.
AAEDT
AAQXK
AAXKI
AAYXX
ABEFU
ABFNM
ABTAH
ABVKL
ABXDB
ACNNM
ADMUD
ADVLN
AEXQZ
AFJKZ
AGHFR
AKRWK
ASPBG
AVWKF
AZFZN
CITATION
EJD
FGOYB
G-2
G8K
HZ~
NCXOZ
R2-
RIG
SEW
SSZ
TAE
WUQ
XJT
ZY4
ID FETCH-LOGICAL-c297t-9cb5478337749aadd65c4531d247f4c6e2d08812df2d0fce8cd54e3968e2fc373
IEDL.DBID AIKHN
ISSN 0304-3975
IngestDate Thu Sep 26 19:02:21 EDT 2024
Fri Feb 23 02:45:51 EST 2024
IsPeerReviewed true
IsScholarly true
Keywords Graph drawing
Simultaneous FPQ-ordering
Hybrid planarity testing
Language English
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c297t-9cb5478337749aadd65c4531d247f4c6e2d08812df2d0fce8cd54e3968e2fc373
PageCount 21
ParticipantIDs crossref_primary_10_1016_j_tcs_2021_05_012
elsevier_sciencedirect_doi_10_1016_j_tcs_2021_05_012
PublicationCentury 2000
PublicationDate 2021-06-12
PublicationDateYYYYMMDD 2021-06-12
PublicationDate_xml – month: 06
  year: 2021
  text: 2021-06-12
  day: 12
PublicationDecade 2020
PublicationTitle Theoretical computer science
PublicationYear 2021
Publisher Elsevier B.V
Publisher_xml – name: Elsevier B.V
References Angelini, Da Lozzo, Di Battista, Frati, Patrignani, Rutter (br0020) 2017; 21
Besa Vial, Da Lozzo, Goodrich (br0070) 2019
Da Lozzo, Di Battista, Frati, Patrignani (br0100) 2018; 22
Gutwenger, Klein, Mutzel (br0160) 2008; 12
Di Giacomo, Lenhart, Liotta, Randolph, Tappini (br0130) 2019
Dornheim (br0150) 2002; 6
Bläsius, Rutter (br0080) 2016; 12
Di Battista (br0120) 1996; 25
Batagelj, Brandenburg, Didimo, Liotta, Palladino, Patrignani (br0060) 2011; 17
Liotta, Rutter, Tappini (br0180) 2019
Di Giacomo, Liotta, Patrignani, Rutter, Tappini (br0140) 2019; 81
Patrignani (br0190) 2013
Henry, Fekete, McGuffin (br0170) 2007; 13
Angelini, Eades, Hong, Klein, Kobourov, Liotta, Navarra, Tappini (br0050) 2020; 13
br0010
Angelini, Da Lozzo, Di Battista, Frati, Patrignani, Rutter (br0030) 2020; 804
Angelini, Di Battista, Frati, Jelínek, Kratochvíl, Patrignani, Rutter (br0040) 2015; 11
Booth, Lueker (br0090) 1976; 13
Di Battista, Eades, Tamassia, Tollis (br0110) 1999
Whitney (br0200) 1932; 54
Angelini (10.1016/j.tcs.2021.05.012_br0040) 2015; 11
Angelini (10.1016/j.tcs.2021.05.012_br0050) 2020; 13
Batagelj (10.1016/j.tcs.2021.05.012_br0060) 2011; 17
Di Giacomo (10.1016/j.tcs.2021.05.012_br0140) 2019; 81
Whitney (10.1016/j.tcs.2021.05.012_br0200) 1932; 54
Booth (10.1016/j.tcs.2021.05.012_br0090) 1976; 13
Di Battista (10.1016/j.tcs.2021.05.012_br0120) 1996; 25
Angelini (10.1016/j.tcs.2021.05.012_br0030) 2020; 804
Da Lozzo (10.1016/j.tcs.2021.05.012_br0100) 2018; 22
Besa Vial (10.1016/j.tcs.2021.05.012_br0070) 2019
Angelini (10.1016/j.tcs.2021.05.012_br0020) 2017; 21
Bläsius (10.1016/j.tcs.2021.05.012_br0080) 2016; 12
Di Giacomo (10.1016/j.tcs.2021.05.012_br0130) 2019
Henry (10.1016/j.tcs.2021.05.012_br0170) 2007; 13
Di Battista (10.1016/j.tcs.2021.05.012_br0110) 1999
Gutwenger (10.1016/j.tcs.2021.05.012_br0160) 2008; 12
Liotta (10.1016/j.tcs.2021.05.012_br0180)
Dornheim (10.1016/j.tcs.2021.05.012_br0150) 2002; 6
Patrignani (10.1016/j.tcs.2021.05.012_br0190) 2013
References_xml – start-page: 1
  year: 2013
  end-page: 42
  ident: br0190
  article-title: Planarity testing and embedding
  publication-title: Handbook on Graph Drawing and Visualization
  contributor:
    fullname: Patrignani
– volume: 13
  start-page: 335
  year: 1976
  end-page: 379
  ident: br0090
  article-title: Testing for the consecutive ones property, interval graphs, and graph planarity using PQ-tree algorithms
  publication-title: J. Comput. Syst. Sci.
  contributor:
    fullname: Lueker
– year: 1999
  ident: br0110
  article-title: Graph Drawing
  contributor:
    fullname: Tollis
– volume: 17
  start-page: 1587
  year: 2011
  end-page: 1598
  ident: br0060
  article-title: Visual analysis of large graphs using (X,Y)-Clustering and hybrid visualizations
  publication-title: IEEE Trans. Vis. Comput. Graph.
  contributor:
    fullname: Patrignani
– volume: 12
  start-page: 16:1
  year: 2016
  end-page: 16:46
  ident: br0080
  article-title: Simultaneous PQ-ordering with applications to constrained embedding problems
  publication-title: ACM Trans. Algorithms
  contributor:
    fullname: Rutter
– start-page: 148
  year: 2019
  end-page: 159
  ident: br0130
  article-title: (k, p)-Planarity: a relaxation of hybrid planarity
  publication-title: WALCOM: Algorithms and Computation - 13th International Conference
  contributor:
    fullname: Tappini
– volume: 13
  start-page: 194
  year: 2020
  ident: br0050
  article-title: Graph planarity by replacing cliques with paths
  publication-title: Algorithms
  contributor:
    fullname: Tappini
– volume: 22
  start-page: 139
  year: 2018
  end-page: 176
  ident: br0100
  article-title: Computing NodeTrix representations of clustered graphs
  publication-title: J. Graph Algorithms Appl.
  contributor:
    fullname: Patrignani
– volume: 13
  start-page: 1302
  year: 2007
  end-page: 1309
  ident: br0170
  article-title: NodeTrix: a hybrid visualization of social networks
  publication-title: IEEE Trans. Vis. Comput. Graph.
  contributor:
    fullname: McGuffin
– ident: br0010
– volume: 21
  start-page: 731
  year: 2017
  end-page: 755
  ident: br0020
  article-title: Intersection-link representations of graphs
  publication-title: J. Graph Algorithms Appl.
  contributor:
    fullname: Rutter
– volume: 25
  start-page: 956
  year: 1996
  end-page: 997
  ident: br0120
  article-title: On-line planarity testing
  publication-title: SIAM J. Comput.
  contributor:
    fullname: Di Battista
– volume: 11
  start-page: 32:1
  year: 2015
  end-page: 32:42
  ident: br0040
  article-title: Testing planarity of partially embedded graphs
  publication-title: ACM Trans. Algorithms
  contributor:
    fullname: Rutter
– volume: 12
  start-page: 73
  year: 2008
  end-page: 95
  ident: br0160
  article-title: Planarity testing and optimal edge insertion with embedding constraints
  publication-title: J. Graph Algorithms Appl.
  contributor:
    fullname: Mutzel
– volume: 54
  start-page: 150
  year: 1932
  end-page: 168
  ident: br0200
  article-title: Congruent graphs and the connectivity of graphs
  publication-title: Am. J. Math.
  contributor:
    fullname: Whitney
– start-page: 19:1
  year: 2019
  end-page: 19:16
  ident: br0070
  article-title: Computing k-modal embeddings of planar digraphs
  publication-title: 27th Annual European Symposium on Algorithms, ESA
  contributor:
    fullname: Goodrich
– volume: 81
  start-page: 3464
  year: 2019
  end-page: 3493
  ident: br0140
  article-title: NodeTrix planarity testing with small clusters
  publication-title: Algorithmica
  contributor:
    fullname: Tappini
– year: 2019
  ident: br0180
  article-title: Graph planarity testing with hierarchical embedding constraints
  contributor:
    fullname: Tappini
– volume: 804
  start-page: 161
  year: 2020
  end-page: 170
  ident: br0030
  article-title: Beyond level planarity: cyclic, torus, and simultaneous level planarity
  publication-title: Theor. Comput. Sci.
  contributor:
    fullname: Rutter
– volume: 6
  start-page: 27
  year: 2002
  end-page: 66
  ident: br0150
  article-title: Planar graphs with topological constraints
  publication-title: J. Graph Algorithms Appl.
  contributor:
    fullname: Dornheim
– volume: 12
  start-page: 16:1
  issue: 2
  year: 2016
  ident: 10.1016/j.tcs.2021.05.012_br0080
  article-title: Simultaneous PQ-ordering with applications to constrained embedding problems
  publication-title: ACM Trans. Algorithms
  doi: 10.1145/2738054
  contributor:
    fullname: Bläsius
– volume: 81
  start-page: 3464
  issue: 9
  year: 2019
  ident: 10.1016/j.tcs.2021.05.012_br0140
  article-title: NodeTrix planarity testing with small clusters
  publication-title: Algorithmica
  doi: 10.1007/s00453-019-00585-6
  contributor:
    fullname: Di Giacomo
– start-page: 19:1
  year: 2019
  ident: 10.1016/j.tcs.2021.05.012_br0070
  article-title: Computing k-modal embeddings of planar digraphs
  contributor:
    fullname: Besa Vial
– volume: 21
  start-page: 731
  issue: 4
  year: 2017
  ident: 10.1016/j.tcs.2021.05.012_br0020
  article-title: Intersection-link representations of graphs
  publication-title: J. Graph Algorithms Appl.
  doi: 10.7155/jgaa.00437
  contributor:
    fullname: Angelini
– volume: 25
  start-page: 956
  issue: 5
  year: 1996
  ident: 10.1016/j.tcs.2021.05.012_br0120
  article-title: On-line planarity testing
  publication-title: SIAM J. Comput.
  doi: 10.1137/S0097539794280736
  contributor:
    fullname: Di Battista
– volume: 13
  start-page: 1302
  issue: 6
  year: 2007
  ident: 10.1016/j.tcs.2021.05.012_br0170
  article-title: NodeTrix: a hybrid visualization of social networks
  publication-title: IEEE Trans. Vis. Comput. Graph.
  doi: 10.1109/TVCG.2007.70582
  contributor:
    fullname: Henry
– volume: 17
  start-page: 1587
  issue: 11
  year: 2011
  ident: 10.1016/j.tcs.2021.05.012_br0060
  article-title: Visual analysis of large graphs using (X,Y)-Clustering and hybrid visualizations
  publication-title: IEEE Trans. Vis. Comput. Graph.
  doi: 10.1109/TVCG.2010.265
  contributor:
    fullname: Batagelj
– start-page: 148
  year: 2019
  ident: 10.1016/j.tcs.2021.05.012_br0130
  article-title: (k, p)-Planarity: a relaxation of hybrid planarity
  contributor:
    fullname: Di Giacomo
– start-page: 1
  year: 2013
  ident: 10.1016/j.tcs.2021.05.012_br0190
  article-title: Planarity testing and embedding
  contributor:
    fullname: Patrignani
– volume: 22
  start-page: 139
  issue: 2
  year: 2018
  ident: 10.1016/j.tcs.2021.05.012_br0100
  article-title: Computing NodeTrix representations of clustered graphs
  publication-title: J. Graph Algorithms Appl.
  doi: 10.7155/jgaa.00461
  contributor:
    fullname: Da Lozzo
– volume: 54
  start-page: 150
  issue: 1
  year: 1932
  ident: 10.1016/j.tcs.2021.05.012_br0200
  article-title: Congruent graphs and the connectivity of graphs
  publication-title: Am. J. Math.
  doi: 10.2307/2371086
  contributor:
    fullname: Whitney
– volume: 13
  start-page: 335
  issue: 3
  year: 1976
  ident: 10.1016/j.tcs.2021.05.012_br0090
  article-title: Testing for the consecutive ones property, interval graphs, and graph planarity using PQ-tree algorithms
  publication-title: J. Comput. Syst. Sci.
  doi: 10.1016/S0022-0000(76)80045-1
  contributor:
    fullname: Booth
– ident: 10.1016/j.tcs.2021.05.012_br0180
  contributor:
    fullname: Liotta
– year: 1999
  ident: 10.1016/j.tcs.2021.05.012_br0110
  contributor:
    fullname: Di Battista
– volume: 11
  start-page: 32:1
  issue: 4
  year: 2015
  ident: 10.1016/j.tcs.2021.05.012_br0040
  article-title: Testing planarity of partially embedded graphs
  publication-title: ACM Trans. Algorithms
  doi: 10.1145/2629341
  contributor:
    fullname: Angelini
– volume: 13
  start-page: 194
  issue: 8
  year: 2020
  ident: 10.1016/j.tcs.2021.05.012_br0050
  article-title: Graph planarity by replacing cliques with paths
  publication-title: Algorithms
  doi: 10.3390/a13080194
  contributor:
    fullname: Angelini
– volume: 6
  start-page: 27
  issue: 1
  year: 2002
  ident: 10.1016/j.tcs.2021.05.012_br0150
  article-title: Planar graphs with topological constraints
  publication-title: J. Graph Algorithms Appl.
  doi: 10.7155/jgaa.00044
  contributor:
    fullname: Dornheim
– volume: 12
  start-page: 73
  issue: 1
  year: 2008
  ident: 10.1016/j.tcs.2021.05.012_br0160
  article-title: Planarity testing and optimal edge insertion with embedding constraints
  publication-title: J. Graph Algorithms Appl.
  doi: 10.7155/jgaa.00160
  contributor:
    fullname: Gutwenger
– volume: 804
  start-page: 161
  year: 2020
  ident: 10.1016/j.tcs.2021.05.012_br0030
  article-title: Beyond level planarity: cyclic, torus, and simultaneous level planarity
  publication-title: Theor. Comput. Sci.
  doi: 10.1016/j.tcs.2019.11.024
  contributor:
    fullname: Angelini
SSID ssj0000576
Score 2.3992846
Snippet We introduce and study a constrained planarity testing problem, called 1-Fixed Constrained Planarity, and prove that this problem can be solved in quadratic...
SourceID crossref
elsevier
SourceType Aggregation Database
Publisher
StartPage 59
SubjectTerms Graph drawing
Hybrid planarity testing
Simultaneous FPQ-ordering
Title Simultaneous FPQ-ordering and hybrid planarity testing
URI https://dx.doi.org/10.1016/j.tcs.2021.05.012
Volume 874
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
link http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1LS8NAEB5qe9GDj6pYH2UPnoS1ze4maY6lWKpiUVTobUl2N1qRWDQevPjbncnDB-jFWxIYCJPdb77JzH4DcIg5AlK2wHEvcYL-VhmeBInkyMxNGlsqdhZdvtNgcqvOZv6sAaP6LAy1VVbYX2J6gdbVk17lzd5iPu9dU1EPoynGH0okIrkELQxHSjWhNTw9n0y_ANkPy5IlFQHQoC5uFm1euSHRbuGV-p3i9_D0LeSM12G14opsWL7OBjRc1oa1eg4Dq7ZlG1YuPrVXXzYhuJ5Tl2CcOUzq2fjyihfymhiiWJxZdv9GZ7TY4jHOYhpcx3LS2cjutuB2fHIzmvBqOgI3IgpzHpmEtLikRAIXxQhTgW8U7igrVJgqEzhhEUE8YVO8SI0bGOsrJ6Ng4ERqZCi3oZk9ZW4HWOj6jriQkQqzMeUlCDox5iY00tRaKTpwVDtFL0oRDF13hz1o9KAmD-q-r9GDHVC12_SPL6kRpP822_2f2R4s0x0vpgntQzN_fnUHSBPypAtLx-9et1oMH_J0uig
link.rule.ids 315,786,790,4521,24144,27957,27958,45620,45714
linkProvider Elsevier
linkToHtml http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1LS8NAEB5qe1APPqpife7Bk7DU7G6S5liKJbUPlLbQ25LsbrQisWg8-O-dzcMH6MVbSBgIk91vvsnMfgNwgTkCUjbPUCc2zP6tUjT2Yk6Rmask0rbYmXf5TrxwLm4W7qIGveosjG2rLLG_wPQcrcs77dKb7dVy2Z7aoh5GU4w_NpEI-Bo0hOs7og6N7mAYTr4A2fWLkqUtAqBBVdzM27wyZUW7mVPod7Lfw9O3kNPfga2SK5Ju8Tq7UDNpE7arOQyk3JZN2Bx_aq--7oE3XdouwSg1mNST_u0dzeU1MUSRKNXk4d2e0SKrpyiN7OA6klmdjfR-H-b961kvpOV0BKpY4Gc0ULHV4uIcCVwQIUx5rhK4ozQTfiKUZ5hGBHGYTvAiUaajtCsMD7yOYYniPj-AevqcmkMgvrkylgspLjAbE06MoBNhbmJHmmrNWQsuK6fIVSGCIavusEeJHpTWg_LKlejBFojKbfLHl5QI0n-bHf3P7BzWw9l4JEeDyfAYNuwTmk8WOoF69vJmTpEyZPFZuSQ-AHVWvBo
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=Simultaneous+FPQ-ordering+and+hybrid+planarity+testing&rft.jtitle=Theoretical+computer+science&rft.au=Liotta%2C+Giuseppe&rft.au=Rutter%2C+Ignaz&rft.au=Tappini%2C+Alessandra&rft.date=2021-06-12&rft.pub=Elsevier+B.V&rft.issn=0304-3975&rft.eissn=1879-2294&rft.volume=874&rft.spage=59&rft.epage=79&rft_id=info:doi/10.1016%2Fj.tcs.2021.05.012&rft.externalDocID=S0304397521002693
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0304-3975&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0304-3975&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0304-3975&client=summon