Deciding Whether a Grid is a Topological Subgraph of a Planar Graph is NP-Complete

The Topological Subgraph Containment (TSC) Problem is to decide, for two given graphs G and H, whether H is a topological subgraph of G. It is known that the TSC Problem is NP-complete when H is part of the input, that it can be solved in polynomial time when H is fixed, and that it is fixed-paramet...
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Autor*in:	Ortiz Jimenez, Andrea Patricia - 1986- [verfasserIn] Schmidt, Tina Janne [verfasserIn]
Körperschaften:	Technische Universität Hamburg Technische Universität Hamburg-Harburg, Institut für Mathematik
Kongresse:	Latin and American Algorithms, Graphs and Optimization Symposium (LAGOS) ; 10 ; Belo Horizonte ; 2019.06.02-07 LAGOS 2019 ; 10 ; Belo Horizonte ; 2019.06.02-07

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2019

Schlagwörter:	grids NP-complete planar graph subdivision subgraph homeomorphism topological subgraph

Anmerkung:	Sonstige Körperschaft: Technische Universität Hamburg Sonstige Körperschaft: Institut für Mathematik
Umfang:	Diagramme

Übergeordnetes Werk:	Enthalten in: Electronic notes in theoretical computer science - Amsterdam [u.a.] : Elsevier Science, 1995, 346(2019), Special issue, Seite 545-556
Übergeordnetes Werk:	volume:346 ; year:2019 ; supplement:Special issue ; pages:545-556

Links:	Link aufrufen Link aufrufen Link aufrufen Link aufrufen

DOI / URN:	urn:nbn:de:gbv:830-882.060692 10.15480/882.2552 10.1016%2Fj.entcs.2019.08.048

Katalog-ID:	1689621729

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topic_title	510: Mathematik Deciding Whether a Grid is a Topological Subgraph of a Planar Graph is NP-Complete Andrea Jiménez (Instituto de Ingeniería Matemática, Facultad de Ingeniería, Universidad de Valparaíso, Valparaíso, Chile), Tina Janne Schmidt (Institut für Mathematik, TU Hamburg, Hamburg, Germany) grids DSpace NP-complete DSpace planar graph DSpace subdivision DSpace subgraph homeomorphism DSpace topological subgraph DSpace
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title_full	Deciding Whether a Grid is a Topological Subgraph of a Planar Graph is NP-Complete Andrea Jiménez (Instituto de Ingeniería Matemática, Facultad de Ingeniería, Universidad de Valparaíso, Valparaíso, Chile), Tina Janne Schmidt (Institut für Mathematik, TU Hamburg, Hamburg, Germany)
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title_sort	deciding whether a grid is a topological subgraph of a planar graph is np-complete
title_auth	Deciding Whether a Grid is a Topological Subgraph of a Planar Graph is NP-Complete
abstract	The Topological Subgraph Containment (TSC) Problem is to decide, for two given graphs G and H, whether H is a topological subgraph of G. It is known that the TSC Problem is NP-complete when H is part of the input, that it can be solved in polynomial time when H is fixed, and that it is fixed-parameter tractable by the order of H. Motivated by the great significance of grids in graph theory and algorithms due to the Grid-Minor Theorem by Robertson and Seymour, we investigate the computational complexity of the Grid TSC Problem in planar graphs. More precisely, we study the following decision problem: given a positive integer k and a planar graph G, is the k × k grid a topological subgraph of G? We prove that this problem is NP-complete, even when restricted to planar graphs of maximum degree six, via a novel reduction from the Planar Monotone 3-SAT Problem. Sonstige Körperschaft: Technische Universität Hamburg Sonstige Körperschaft: Institut für Mathematik
abstractGer	The Topological Subgraph Containment (TSC) Problem is to decide, for two given graphs G and H, whether H is a topological subgraph of G. It is known that the TSC Problem is NP-complete when H is part of the input, that it can be solved in polynomial time when H is fixed, and that it is fixed-parameter tractable by the order of H. Motivated by the great significance of grids in graph theory and algorithms due to the Grid-Minor Theorem by Robertson and Seymour, we investigate the computational complexity of the Grid TSC Problem in planar graphs. More precisely, we study the following decision problem: given a positive integer k and a planar graph G, is the k × k grid a topological subgraph of G? We prove that this problem is NP-complete, even when restricted to planar graphs of maximum degree six, via a novel reduction from the Planar Monotone 3-SAT Problem. Sonstige Körperschaft: Technische Universität Hamburg Sonstige Körperschaft: Institut für Mathematik
abstract_unstemmed	The Topological Subgraph Containment (TSC) Problem is to decide, for two given graphs G and H, whether H is a topological subgraph of G. It is known that the TSC Problem is NP-complete when H is part of the input, that it can be solved in polynomial time when H is fixed, and that it is fixed-parameter tractable by the order of H. Motivated by the great significance of grids in graph theory and algorithms due to the Grid-Minor Theorem by Robertson and Seymour, we investigate the computational complexity of the Grid TSC Problem in planar graphs. More precisely, we study the following decision problem: given a positive integer k and a planar graph G, is the k × k grid a topological subgraph of G? We prove that this problem is NP-complete, even when restricted to planar graphs of maximum degree six, via a novel reduction from the Planar Monotone 3-SAT Problem. Sonstige Körperschaft: Technische Universität Hamburg Sonstige Körperschaft: Institut für Mathematik
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author2	Schmidt, Tina Janne Technische Universität Hamburg Technische Universität Hamburg-Harburg Institut für Mathematik Latin and American Algorithms, Graphs and Optimization Symposium (LAGOS) LAGOS 2019
author2Str	Schmidt, Tina Janne Technische Universität Hamburg Technische Universität Hamburg-Harburg Institut für Mathematik Latin and American Algorithms, Graphs and Optimization Symposium (LAGOS) LAGOS 2019
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allfields	urn:nbn:de:gbv:830-882.060692 urn 10.15480/882.2552 doi 10.1016%2Fj.entcs.2019.08.048 doi 11420/4252 hdl (DE-627)1689621729 (DE-599)KXP1689621729 DE-627 ger DE-627 rda eng 510: Mathematik Ortiz Jimenez, Andrea Patricia 1986- verfasserin (DE-588)1201167434 (DE-627)168463590X aut Deciding Whether a Grid is a Topological Subgraph of a Planar Graph is NP-Complete Andrea Jiménez (Instituto de Ingeniería Matemática, Facultad de Ingeniería, Universidad de Valparaíso, Valparaíso, Chile), Tina Janne Schmidt (Institut für Mathematik, TU Hamburg, Hamburg, Germany) 2019 Diagramme Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Sonstige Körperschaft: Technische Universität Hamburg Sonstige Körperschaft: Institut für Mathematik The Topological Subgraph Containment (TSC) Problem is to decide, for two given graphs G and H, whether H is a topological subgraph of G. It is known that the TSC Problem is NP-complete when H is part of the input, that it can be solved in polynomial time when H is fixed, and that it is fixed-parameter tractable by the order of H. Motivated by the great significance of grids in graph theory and algorithms due to the Grid-Minor Theorem by Robertson and Seymour, we investigate the computational complexity of the Grid TSC Problem in planar graphs. More precisely, we study the following decision problem: given a positive integer k and a planar graph G, is the k × k grid a topological subgraph of G? We prove that this problem is NP-complete, even when restricted to planar graphs of maximum degree six, via a novel reduction from the Planar Monotone 3-SAT Problem. grids DSpace NP-complete DSpace planar graph DSpace subdivision DSpace subgraph homeomorphism DSpace topological subgraph DSpace Schmidt, Tina Janne verfasserin (DE-588)1202369383 (DE-627)1686398743 aut Technische Universität Hamburg (DE-588)1112763473 (DE-627)866918418 (DE-576)476770564 oth Technische Universität Hamburg-Harburg Institut für Mathematik (DE-588)16345899-6 (DE-627)689801602 (DE-576)363268626 oth Latin and American Algorithms, Graphs and Optimization Symposium (LAGOS) 10 Belo Horizonte 2019.06.02-07 LAGOS 2019 10 Belo Horizonte 2019.06.02-07 Enthalten in Electronic notes in theoretical computer science Amsterdam [u.a.] : Elsevier Science, 1995 346(2019), Special issue, Seite 545-556 Online-Ressource (DE-627)324960042 (DE-600)2033227-0 (DE-576)259272124 1571-0661 nnns volume:346 year:2019 supplement:Special issue pages:545-556 http://nbn-resolving.de/urn:nbn:de:gbv:830-882.060692 Resolving-System kostenfrei https://doi.org/10.15480/882.2552 Resolving-System kostenfrei http://hdl.handle.net/11420/4252 Resolving-System kostenfrei https://doi.org/10.1016%2Fj.entcs.2019.08.048 Resolving-System GBV_USEFLAG_U GBV_ILN_23 ISIL_DE-830 SYSFLAG_1 GBV_KXP GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2004 GBV_ILN_2014 GBV_ILN_2336 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 GBV_ILN_2403 GBV_ILN_2403 ISIL_DE-LFER DSpace AR 346 2019 Special issue 545-556 045F 510: Mathematik 23 01 0830 3589476168 tubdok Elektronischer Volltext f z 07-02-20 2403 01 DE-LFER 3596932416 00 --%%-- --%%-- n --%%-- l01 20-02-20 23 01 0830 https://doi.org/10.15480/882.2552 LF 2403 01 DE-LFER https://doi.org/10.1016%2Fj.entcs.2019.08.048 2403 01 DE-LFER http://nbn-resolving.de/urn:nbn:de:gbv:830-882.060692 23 01 0830 tubdok 23 01 0830 tuhh
spelling	urn:nbn:de:gbv:830-882.060692 urn 10.15480/882.2552 doi 10.1016%2Fj.entcs.2019.08.048 doi 11420/4252 hdl (DE-627)1689621729 (DE-599)KXP1689621729 DE-627 ger DE-627 rda eng 510: Mathematik Ortiz Jimenez, Andrea Patricia 1986- verfasserin (DE-588)1201167434 (DE-627)168463590X aut Deciding Whether a Grid is a Topological Subgraph of a Planar Graph is NP-Complete Andrea Jiménez (Instituto de Ingeniería Matemática, Facultad de Ingeniería, Universidad de Valparaíso, Valparaíso, Chile), Tina Janne Schmidt (Institut für Mathematik, TU Hamburg, Hamburg, Germany) 2019 Diagramme Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Sonstige Körperschaft: Technische Universität Hamburg Sonstige Körperschaft: Institut für Mathematik The Topological Subgraph Containment (TSC) Problem is to decide, for two given graphs G and H, whether H is a topological subgraph of G. It is known that the TSC Problem is NP-complete when H is part of the input, that it can be solved in polynomial time when H is fixed, and that it is fixed-parameter tractable by the order of H. Motivated by the great significance of grids in graph theory and algorithms due to the Grid-Minor Theorem by Robertson and Seymour, we investigate the computational complexity of the Grid TSC Problem in planar graphs. More precisely, we study the following decision problem: given a positive integer k and a planar graph G, is the k × k grid a topological subgraph of G? We prove that this problem is NP-complete, even when restricted to planar graphs of maximum degree six, via a novel reduction from the Planar Monotone 3-SAT Problem. grids DSpace NP-complete DSpace planar graph DSpace subdivision DSpace subgraph homeomorphism DSpace topological subgraph DSpace Schmidt, Tina Janne verfasserin (DE-588)1202369383 (DE-627)1686398743 aut Technische Universität Hamburg (DE-588)1112763473 (DE-627)866918418 (DE-576)476770564 oth Technische Universität Hamburg-Harburg Institut für Mathematik (DE-588)16345899-6 (DE-627)689801602 (DE-576)363268626 oth Latin and American Algorithms, Graphs and Optimization Symposium (LAGOS) 10 Belo Horizonte 2019.06.02-07 LAGOS 2019 10 Belo Horizonte 2019.06.02-07 Enthalten in Electronic notes in theoretical computer science Amsterdam [u.a.] : Elsevier Science, 1995 346(2019), Special issue, Seite 545-556 Online-Ressource (DE-627)324960042 (DE-600)2033227-0 (DE-576)259272124 1571-0661 nnns volume:346 year:2019 supplement:Special issue pages:545-556 http://nbn-resolving.de/urn:nbn:de:gbv:830-882.060692 Resolving-System kostenfrei https://doi.org/10.15480/882.2552 Resolving-System kostenfrei http://hdl.handle.net/11420/4252 Resolving-System kostenfrei https://doi.org/10.1016%2Fj.entcs.2019.08.048 Resolving-System GBV_USEFLAG_U GBV_ILN_23 ISIL_DE-830 SYSFLAG_1 GBV_KXP GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2004 GBV_ILN_2014 GBV_ILN_2336 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 GBV_ILN_2403 GBV_ILN_2403 ISIL_DE-LFER DSpace AR 346 2019 Special issue 545-556 045F 510: Mathematik 23 01 0830 3589476168 tubdok Elektronischer Volltext f z 07-02-20 2403 01 DE-LFER 3596932416 00 --%%-- --%%-- n --%%-- l01 20-02-20 23 01 0830 https://doi.org/10.15480/882.2552 LF 2403 01 DE-LFER https://doi.org/10.1016%2Fj.entcs.2019.08.048 2403 01 DE-LFER http://nbn-resolving.de/urn:nbn:de:gbv:830-882.060692 23 01 0830 tubdok 23 01 0830 tuhh
allfields_unstemmed	urn:nbn:de:gbv:830-882.060692 urn 10.15480/882.2552 doi 10.1016%2Fj.entcs.2019.08.048 doi 11420/4252 hdl (DE-627)1689621729 (DE-599)KXP1689621729 DE-627 ger DE-627 rda eng 510: Mathematik Ortiz Jimenez, Andrea Patricia 1986- verfasserin (DE-588)1201167434 (DE-627)168463590X aut Deciding Whether a Grid is a Topological Subgraph of a Planar Graph is NP-Complete Andrea Jiménez (Instituto de Ingeniería Matemática, Facultad de Ingeniería, Universidad de Valparaíso, Valparaíso, Chile), Tina Janne Schmidt (Institut für Mathematik, TU Hamburg, Hamburg, Germany) 2019 Diagramme Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Sonstige Körperschaft: Technische Universität Hamburg Sonstige Körperschaft: Institut für Mathematik The Topological Subgraph Containment (TSC) Problem is to decide, for two given graphs G and H, whether H is a topological subgraph of G. It is known that the TSC Problem is NP-complete when H is part of the input, that it can be solved in polynomial time when H is fixed, and that it is fixed-parameter tractable by the order of H. Motivated by the great significance of grids in graph theory and algorithms due to the Grid-Minor Theorem by Robertson and Seymour, we investigate the computational complexity of the Grid TSC Problem in planar graphs. More precisely, we study the following decision problem: given a positive integer k and a planar graph G, is the k × k grid a topological subgraph of G? We prove that this problem is NP-complete, even when restricted to planar graphs of maximum degree six, via a novel reduction from the Planar Monotone 3-SAT Problem. grids DSpace NP-complete DSpace planar graph DSpace subdivision DSpace subgraph homeomorphism DSpace topological subgraph DSpace Schmidt, Tina Janne verfasserin (DE-588)1202369383 (DE-627)1686398743 aut Technische Universität Hamburg (DE-588)1112763473 (DE-627)866918418 (DE-576)476770564 oth Technische Universität Hamburg-Harburg Institut für Mathematik (DE-588)16345899-6 (DE-627)689801602 (DE-576)363268626 oth Latin and American Algorithms, Graphs and Optimization Symposium (LAGOS) 10 Belo Horizonte 2019.06.02-07 LAGOS 2019 10 Belo Horizonte 2019.06.02-07 Enthalten in Electronic notes in theoretical computer science Amsterdam [u.a.] : Elsevier Science, 1995 346(2019), Special issue, Seite 545-556 Online-Ressource (DE-627)324960042 (DE-600)2033227-0 (DE-576)259272124 1571-0661 nnns volume:346 year:2019 supplement:Special issue pages:545-556 http://nbn-resolving.de/urn:nbn:de:gbv:830-882.060692 Resolving-System kostenfrei https://doi.org/10.15480/882.2552 Resolving-System kostenfrei http://hdl.handle.net/11420/4252 Resolving-System kostenfrei https://doi.org/10.1016%2Fj.entcs.2019.08.048 Resolving-System GBV_USEFLAG_U GBV_ILN_23 ISIL_DE-830 SYSFLAG_1 GBV_KXP GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2004 GBV_ILN_2014 GBV_ILN_2336 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 GBV_ILN_2403 GBV_ILN_2403 ISIL_DE-LFER DSpace AR 346 2019 Special issue 545-556 045F 510: Mathematik 23 01 0830 3589476168 tubdok Elektronischer Volltext f z 07-02-20 2403 01 DE-LFER 3596932416 00 --%%-- --%%-- n --%%-- l01 20-02-20 23 01 0830 https://doi.org/10.15480/882.2552 LF 2403 01 DE-LFER https://doi.org/10.1016%2Fj.entcs.2019.08.048 2403 01 DE-LFER http://nbn-resolving.de/urn:nbn:de:gbv:830-882.060692 23 01 0830 tubdok 23 01 0830 tuhh
allfieldsGer	urn:nbn:de:gbv:830-882.060692 urn 10.15480/882.2552 doi 10.1016%2Fj.entcs.2019.08.048 doi 11420/4252 hdl (DE-627)1689621729 (DE-599)KXP1689621729 DE-627 ger DE-627 rda eng 510: Mathematik Ortiz Jimenez, Andrea Patricia 1986- verfasserin (DE-588)1201167434 (DE-627)168463590X aut Deciding Whether a Grid is a Topological Subgraph of a Planar Graph is NP-Complete Andrea Jiménez (Instituto de Ingeniería Matemática, Facultad de Ingeniería, Universidad de Valparaíso, Valparaíso, Chile), Tina Janne Schmidt (Institut für Mathematik, TU Hamburg, Hamburg, Germany) 2019 Diagramme Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Sonstige Körperschaft: Technische Universität Hamburg Sonstige Körperschaft: Institut für Mathematik The Topological Subgraph Containment (TSC) Problem is to decide, for two given graphs G and H, whether H is a topological subgraph of G. It is known that the TSC Problem is NP-complete when H is part of the input, that it can be solved in polynomial time when H is fixed, and that it is fixed-parameter tractable by the order of H. Motivated by the great significance of grids in graph theory and algorithms due to the Grid-Minor Theorem by Robertson and Seymour, we investigate the computational complexity of the Grid TSC Problem in planar graphs. More precisely, we study the following decision problem: given a positive integer k and a planar graph G, is the k × k grid a topological subgraph of G? We prove that this problem is NP-complete, even when restricted to planar graphs of maximum degree six, via a novel reduction from the Planar Monotone 3-SAT Problem. grids DSpace NP-complete DSpace planar graph DSpace subdivision DSpace subgraph homeomorphism DSpace topological subgraph DSpace Schmidt, Tina Janne verfasserin (DE-588)1202369383 (DE-627)1686398743 aut Technische Universität Hamburg (DE-588)1112763473 (DE-627)866918418 (DE-576)476770564 oth Technische Universität Hamburg-Harburg Institut für Mathematik (DE-588)16345899-6 (DE-627)689801602 (DE-576)363268626 oth Latin and American Algorithms, Graphs and Optimization Symposium (LAGOS) 10 Belo Horizonte 2019.06.02-07 LAGOS 2019 10 Belo Horizonte 2019.06.02-07 Enthalten in Electronic notes in theoretical computer science Amsterdam [u.a.] : Elsevier Science, 1995 346(2019), Special issue, Seite 545-556 Online-Ressource (DE-627)324960042 (DE-600)2033227-0 (DE-576)259272124 1571-0661 nnns volume:346 year:2019 supplement:Special issue pages:545-556 http://nbn-resolving.de/urn:nbn:de:gbv:830-882.060692 Resolving-System kostenfrei https://doi.org/10.15480/882.2552 Resolving-System kostenfrei http://hdl.handle.net/11420/4252 Resolving-System kostenfrei https://doi.org/10.1016%2Fj.entcs.2019.08.048 Resolving-System GBV_USEFLAG_U GBV_ILN_23 ISIL_DE-830 SYSFLAG_1 GBV_KXP GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2004 GBV_ILN_2014 GBV_ILN_2336 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 GBV_ILN_2403 GBV_ILN_2403 ISIL_DE-LFER DSpace AR 346 2019 Special issue 545-556 045F 510: Mathematik 23 01 0830 3589476168 tubdok Elektronischer Volltext f z 07-02-20 2403 01 DE-LFER 3596932416 00 --%%-- --%%-- n --%%-- l01 20-02-20 23 01 0830 https://doi.org/10.15480/882.2552 LF 2403 01 DE-LFER https://doi.org/10.1016%2Fj.entcs.2019.08.048 2403 01 DE-LFER http://nbn-resolving.de/urn:nbn:de:gbv:830-882.060692 23 01 0830 tubdok 23 01 0830 tuhh
allfieldsSound	urn:nbn:de:gbv:830-882.060692 urn 10.15480/882.2552 doi 10.1016%2Fj.entcs.2019.08.048 doi 11420/4252 hdl (DE-627)1689621729 (DE-599)KXP1689621729 DE-627 ger DE-627 rda eng 510: Mathematik Ortiz Jimenez, Andrea Patricia 1986- verfasserin (DE-588)1201167434 (DE-627)168463590X aut Deciding Whether a Grid is a Topological Subgraph of a Planar Graph is NP-Complete Andrea Jiménez (Instituto de Ingeniería Matemática, Facultad de Ingeniería, Universidad de Valparaíso, Valparaíso, Chile), Tina Janne Schmidt (Institut für Mathematik, TU Hamburg, Hamburg, Germany) 2019 Diagramme Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Sonstige Körperschaft: Technische Universität Hamburg Sonstige Körperschaft: Institut für Mathematik The Topological Subgraph Containment (TSC) Problem is to decide, for two given graphs G and H, whether H is a topological subgraph of G. It is known that the TSC Problem is NP-complete when H is part of the input, that it can be solved in polynomial time when H is fixed, and that it is fixed-parameter tractable by the order of H. Motivated by the great significance of grids in graph theory and algorithms due to the Grid-Minor Theorem by Robertson and Seymour, we investigate the computational complexity of the Grid TSC Problem in planar graphs. More precisely, we study the following decision problem: given a positive integer k and a planar graph G, is the k × k grid a topological subgraph of G? We prove that this problem is NP-complete, even when restricted to planar graphs of maximum degree six, via a novel reduction from the Planar Monotone 3-SAT Problem. grids DSpace NP-complete DSpace planar graph DSpace subdivision DSpace subgraph homeomorphism DSpace topological subgraph DSpace Schmidt, Tina Janne verfasserin (DE-588)1202369383 (DE-627)1686398743 aut Technische Universität Hamburg (DE-588)1112763473 (DE-627)866918418 (DE-576)476770564 oth Technische Universität Hamburg-Harburg Institut für Mathematik (DE-588)16345899-6 (DE-627)689801602 (DE-576)363268626 oth Latin and American Algorithms, Graphs and Optimization Symposium (LAGOS) 10 Belo Horizonte 2019.06.02-07 LAGOS 2019 10 Belo Horizonte 2019.06.02-07 Enthalten in Electronic notes in theoretical computer science Amsterdam [u.a.] : Elsevier Science, 1995 346(2019), Special issue, Seite 545-556 Online-Ressource (DE-627)324960042 (DE-600)2033227-0 (DE-576)259272124 1571-0661 nnns volume:346 year:2019 supplement:Special issue pages:545-556 http://nbn-resolving.de/urn:nbn:de:gbv:830-882.060692 Resolving-System kostenfrei https://doi.org/10.15480/882.2552 Resolving-System kostenfrei http://hdl.handle.net/11420/4252 Resolving-System kostenfrei https://doi.org/10.1016%2Fj.entcs.2019.08.048 Resolving-System GBV_USEFLAG_U GBV_ILN_23 ISIL_DE-830 SYSFLAG_1 GBV_KXP GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2004 GBV_ILN_2014 GBV_ILN_2336 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 GBV_ILN_2403 GBV_ILN_2403 ISIL_DE-LFER DSpace AR 346 2019 Special issue 545-556 045F 510: Mathematik 23 01 0830 3589476168 tubdok Elektronischer Volltext f z 07-02-20 2403 01 DE-LFER 3596932416 00 --%%-- --%%-- n --%%-- l01 20-02-20 23 01 0830 https://doi.org/10.15480/882.2552 LF 2403 01 DE-LFER https://doi.org/10.1016%2Fj.entcs.2019.08.048 2403 01 DE-LFER http://nbn-resolving.de/urn:nbn:de:gbv:830-882.060692 23 01 0830 tubdok 23 01 0830 tuhh
language	English
source	Enthalten in Electronic notes in theoretical computer science 346(2019), Special issue, Seite 545-556 volume:346 year:2019 supplement:Special issue pages:545-556
sourceStr	Enthalten in Electronic notes in theoretical computer science 346(2019), Special issue, Seite 545-556 volume:346 year:2019 supplement:Special issue pages:545-556
format_phy_str_mv	Article
institution	findex.gbv.de
selectbib_iln_str_mv	23@ 2403@01
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authorswithroles_txt_mv	Ortiz Jimenez, Andrea Patricia @@aut@@ Schmidt, Tina Janne @@aut@@
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author	Ortiz Jimenez, Andrea Patricia 1986-
spellingShingle	Ortiz Jimenez, Andrea Patricia 1986- ddc 510: Mathematik DSpace grids DSpace NP-complete DSpace planar graph DSpace subdivision DSpace subgraph homeomorphism DSpace topological subgraph Deciding Whether a Grid is a Topological Subgraph of a Planar Graph is NP-Complete
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topic	ddc 510: Mathematik DSpace grids DSpace NP-complete DSpace planar graph DSpace subdivision DSpace subgraph homeomorphism DSpace topological subgraph
topic_unstemmed	ddc 510: Mathematik DSpace grids DSpace NP-complete DSpace planar graph DSpace subdivision DSpace subgraph homeomorphism DSpace topological subgraph
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title	Deciding Whether a Grid is a Topological Subgraph of a Planar Graph is NP-Complete
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title_short	Deciding Whether a Grid is a Topological Subgraph of a Planar Graph is NP-Complete
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GND_str_mv	Ortiz, Andrea Ortiz Jimenez, Andrea Patricia Schmidt, Tina Janne University of Technology (Hamburg) TU Hamburg Technical University (Hamburg) Université de Technologie de Hambourg Hamburg University of Technology Technische Universität Hamburg Technische Universität Hamburg-Harburg. Institut E-10 Institut für Mathematik (Hamburg-Harburg) Institut E-10 Technische Universität Hamburg-Harburg. Institute of Mathematics Technische Universität Hamburg-Harburg. Studiendekanat Elektrotechnik, Informatik und Mathematik. Institut für Mathematik Institute of Mathematics (Hamburg-Harburg) Technische Universität Hamburg-Harburg. Institut für Mathematik
GND_txt_mv	Ortiz, Andrea Ortiz Jimenez, Andrea Patricia Schmidt, Tina Janne University of Technology (Hamburg) TU Hamburg Technical University (Hamburg) Université de Technologie de Hambourg Hamburg University of Technology Technische Universität Hamburg Technische Universität Hamburg-Harburg. Institut E-10 Institut für Mathematik (Hamburg-Harburg) Institut E-10 Technische Universität Hamburg-Harburg. Institute of Mathematics Technische Universität Hamburg-Harburg. Studiendekanat Elektrotechnik, Informatik und Mathematik. Institut für Mathematik Institute of Mathematics (Hamburg-Harburg) Technische Universität Hamburg-Harburg. Institut für Mathematik
GND_txtF_mv	Ortiz, Andrea Ortiz Jimenez, Andrea Patricia Schmidt, Tina Janne University of Technology (Hamburg) TU Hamburg Technical University (Hamburg) Université de Technologie de Hambourg Hamburg University of Technology Technische Universität Hamburg Technische Universität Hamburg-Harburg. Institut E-10 Institut für Mathematik (Hamburg-Harburg) Institut E-10 Technische Universität Hamburg-Harburg. Institute of Mathematics Technische Universität Hamburg-Harburg. Studiendekanat Elektrotechnik, Informatik und Mathematik. Institut für Mathematik Institute of Mathematics (Hamburg-Harburg) Technische Universität Hamburg-Harburg. Institut für Mathematik
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fullrecord_marcxml	<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a2200265 4500</leader><controlfield tag="001">1689621729</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20200211151932.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">200207s2019 xx \|\|\|\|\|o 00\| \|\|eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">urn:nbn:de:gbv:830-882.060692</subfield><subfield code="2">urn</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.15480/882.2552</subfield><subfield code="2">doi</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1016%2Fj.entcs.2019.08.048</subfield><subfield code="2">doi</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">11420/4252</subfield><subfield code="2">hdl</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)1689621729</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)KXP1689621729</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">510: Mathematik</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Ortiz Jimenez, Andrea Patricia</subfield><subfield code="d">1986-</subfield><subfield code="e">verfasserin</subfield><subfield code="0">(DE-588)1201167434</subfield><subfield code="0">(DE-627)168463590X</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Deciding Whether a Grid is a Topological Subgraph of a Planar Graph is NP-Complete</subfield><subfield code="c">Andrea Jiménez (Instituto de Ingeniería Matemática, Facultad de Ingeniería, Universidad de Valparaíso, Valparaíso, Chile), Tina Janne Schmidt (Institut für Mathematik, TU Hamburg, Hamburg, Germany)</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2019</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="b">Diagramme</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Sonstige Körperschaft: Technische Universität Hamburg</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Sonstige Körperschaft: Institut für Mathematik</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">The Topological Subgraph Containment (TSC) Problem is to decide, for two given graphs G and H, whether H is a topological subgraph of G. 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Deciding Whether a Grid is a Topological Subgraph of a Planar Graph is NP-Complete

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