Paula Zabala

Facets of the graph coloring polytope

2002, Annals of Operations Research 116, 79-90, 2002
Citas: 67
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Autor(es)

Pablo Coll and Javier Marenco and Isabel Méndez Díaz and Paula Zabala

Abstract

In this paper we present a study of the polytope associated to a classic linear integer programming formulation of the graph coloring problem. We determine some families of facets. This is the initial step for the development of a branch-and-cut algorithm to solve large instances of the graph coloring problem.

Plot de citas

Citas de Scrapping

# Año #Citas Título Autores Journal Editor
1 2010 335 A supernodal formulation of vertex colouring with applications in course timetabling EK Burke, J Mareček, AJ Parkes, H Rudová  Annals of Operations …, 2010 Springer
2 2006 279 A branch-and-cut algorithm for graph coloring I Méndez-Díaz, P Zabala  Discrete Applied Mathematics, 2006 Elsevier
3 2013 105 Minimizing warehouse space with a dedicated storage policy A Fumi, L Scarabotti…  International Journal of …, 2013 journals.sagepub.com
4 2008 151 Packing and partitioning orbitopes V Kaibel, M Pfetsch  Mathematical Programming, 2008 Springer
5 2008 142 On the asymmetric representatives formulation for the vertex coloring problem M Campêlo, VA Campos, RC Corrêa  Discrete Applied Mathematics, 2008 Elsevier
6 2012 127 Exact solution of graph coloring problems via constraint programming and column generation S Gualandi, F Malucelli  INFORMS Journal on Computing, 2012 pubsonline.informs.org
7 2013 96 Dual connectivity in LTE HetNets with split control-and user-plane A Zakrzewska, D López-Pérez…  2013 IEEE …, 2013 ieeexplore.ieee.org
8 2012 94 A branch-and-cut procedure for the Udine course timetabling problem EK Burke, J Mareček, AJ Parkes, H Rudová  Annals of Operations …, 2012 Springer
9 2009 73 Set covering and packing formulations of graph coloring: Algorithms and first polyhedral results P Hansen, M Labbé, D Schindl  Discrete Optimization, 2009 Elsevier
10 2014 41 Multiproduct slot allocation heuristic to minimize storage space C Battista, A Fumi, L Laura…  International Journal of …, 2014 emerald.com
11 2008 39 A one-to-one correspondence between colorings and stable sets D Cornaz, V Jost  Operations Research Letters, 2008 Elsevier
12 2020 13 Content placement in cache networks using graph coloring M Javedankherad, Z Zeinalpour-Yazdi…  IEEE Systems …, 2020 ieeexplore.ieee.org
13 2016 19 Advances in combinatorial optimization: linear programming formulations of the traveling salesman and other hard combinatorial optimization problems M Diaby, MH Karwan 2016 books.google.com
14 2011 23 Describing orbitopes by linear inequalities and projection based tools A Loos 2011 core.ac.uk
15 2010 30 Linear programming formulation of the vertex colouring problem M Diaby  … Journal of Mathematics in Operational Research, 2010 inderscienceonline.com
16 2019 12 An integer programming approach to b-coloring I Koch, J Marenco  Discrete Optimization, 2019 Elsevier
17 2013 16 On the optimal design of a spectrum-switched optical network with multiple modulation formats and rates I Popescu, I Cerutti, N Sambo…  Journal of Optical …, 2013 opg.optica.org
18 2011 15 R Hansmann 2011 Cuvillier Verlag
19 2023 5 Derivations of large classes of facet defining inequalities of the weak order polytope using ranking structures AR Escobedo, R Yasmin  Journal of Combinatorial Optimization, 2023 Springer
20 2020 7 Symmetry-breaking inequalities for ILP with structured sub-symmetry P Bendotti, P Fouilhoux, C Rottner  Mathematical Programming, 2020 Springer
21 2023 1 Polyhedral Approach to Total Matching and Total Coloring Problems L Ferrarini 2023 boa.unimib.it
22 2012 14 Graph coloring facets from all-different systems D Bergman, JN Hooker  … Conference on Integration of Artificial Intelligence …, 2012 Springer
23 2018 5 Heuristic algorithms for graph coloring problems W Sun 2018 theses.hal.science
24 2010 12 Facet-inducing web and antiweb inequalities for the graph coloring polytope G Palubeckis  Discrete Applied Mathematics, 2010 Elsevier
25 2021 3 Implementing cutting planes for the chromatic violation problem D Delle Donne, MS Escalante…  Proceedings of the …, 2021 openproceedings.org
26 2014 9 Graph coloring inequalities from all-different systems D Bergman, JN Hooker  Constraints, 2014 Springer
27 2005 16 Set covering and packing formulations of graph coloring: algorithms and first polyhedral results P Hansen, M Labbé, D Schindl 2005 Citeseer
28 2013 9 New techniques for discrete optimization D Bergman 2013 search.proquest.com
29 2016 8 Polyhedral studies of vertex coloring problems: The standard formulation D Delle Donne, J Marenco  Discrete Optimization, 2016 Elsevier
30 2015 6 Branch-and-cut algorithms for graph problems B Yüceoglu 2015 cris.maastrichtuniversity.nl
31 2020 4 An exact algorithm for the edge coloring by total labeling problem F Borghini, I Méndez-Díaz, P Zabala  Annals of Operations Research, 2020 Springer
32 2015 5 Polyhedral studies of vertex coloring problems: The asymmetric representatives formulation V Campos, RC Corrêa, DD Donne, J Marenco…  arXiv preprint arXiv …, 2015 arxiv.org
33 2022 1 Handling sub-symmetries in integer linear programming using activation handlers S Wessel, T Verhoeff, CAJ Hurkens  Master's thesis, Eindhoven …, 2022 assets.w3.tue.nl
34 2007 9 An integer programming approach to equitable coloring problems L Bahiense, S Jurkiewicz, A Lozano…  Proceedings of the …, 2007 ws2.din.uem.br
35 2007 5 Polyhedral studies for minimum‐span graph labelling with integer distance constraints V Mak  International Transactions in Operational Research, 2007 Wiley Online Library
36 2017 3 The maximum‐impact coloring polytope M Braga, D Delle Donne, R Linfati…  International …, 2017 Wiley Online Library
37 2004 7 Some combinatorial optimization problems in graphs with applications in telecommunications and tomography D Schindl 2004 infoscience.epfl.ch
38 2023 0 J Staszek 2023 Dissertation, Erlangen, Friedrich …
39 2018 2 Cache placement phase based on graph coloring M Javedankherad, Z Zeinalpour-Yazdi…  2018 9th International …, 2018 ieeexplore.ieee.org
40 2016 6 Estudios poliedrales de problemas de coloreo de grafos DA Delle Donne 2016 bibliotecadigital.exactas.uba.ar
41 2019 2 Sub-symmetry-breaking inequalities for ILP with structured symmetry P Bendotti, P Fouilhoux, C Rottner  … Conference, IPCO 2019, Ann Arbor, MI …, 2019 Springer
42 2022 0 Minimum Conflict Balanced Graph Coloring Problem NE Hanoğlu 2022 search.proquest.com
43 2015 2 Evaluation of transparent optical multiplexing techniques in transport networks I Popescu 2015 hal.science
44 2014 2 Mixed Integer Linear Programming Models for Combinatorial Optimization Problems F Della Croce  Concepts of Combinatorial Optimization, 2014 Wiley Online Library
45 2007 6 Optimised grid-partitioning for block structured grids in parallel computing D Junglas 2007 tuprints.ulb.tu-darmstadt.de
46 2017 1 Bilevel Clique Interdiction and Related Problems T Becker 2017 repository.rice.edu
47 2006 2 On forests, stable sets and polyhedra associated with clique partitions D Cornaz  Manuscript available on Optimization Online, 2006 optimization-online.org
48 2016 1 A polyhedral investigation of star colorings C Hojny, ME Pfetsch  Discrete Applied Mathematics, 2016 Elsevier
49 2013 1 4G and Beyond-Exploiting Heterogeneity in Mobile Networks A Zakrzewska 2013 orbit.dtu.dk
50 2013 1 Branch and price for a reliability oriented darp model A Quilliot, S Deleplanque, B Benoit 2013 hal.science
51 2007 1 A supernodal formulation of vertex colouring with applications in course timetabling EK Burke, J Marecek, AJ Parkes…  Ann. Oper. Res, to appear …, 2007 academia.edu
52 2012 2 Finite-domain cuts for graph coloring D Bergman, JN Hooker 2012 Citeseer
53 2017 0 Exact algorithms for the Vertex Coloring Problem and its generalisations IC Ternier 2017 theses.hal.science
54 0 Master Degree Thesis Report I Popescu, I Cerutti, N Sambo researchgate.net
55 2015 0 Decomposition of Integer Programs with Matchability Structure F Dahms 2015 fdahms.com
56 2007 2 Modelagem matemática e aplicações do problema de coloração em grafos D Lozano 2007 repositorio.unesp.br
57 0 11vo Simposio Argentino de Investigacion Operativa, SIO 2013 D Delle Donnea, J Marencob academia.edu
58 2009 0 Quotient and power methods for the graph colouring problem I Juhos 2009 doktori.bibl.u-szeged.hu
59 0 Graph Coloring via Constraint Programming-based Column Generation SGF Malucelli researchgate.net
60 0 Univerzitní rozvrhování pomocí celoˇcíselného programování J Marecek is.muni.cz
61 2012 1 Estudio poliedral y algoritmo branch-and-cut para el problema de coloreo equitativo en grafos DE Severin 2012 bibliotecadigital.exactas.uba.ar
62 2012 1 組合せ最適化問題に対する効率的な厳密解法のための問題の記述法に関する研究 乾伸雄  (No Title), 2012 ir.soken.ac.jp
63 2008 1 Limites inferiores para o problema de coloração de vértices via geração de cortes e colunas CD Rodrigues 2008 repositorio.ufc.br
64 2015 0 MG Vilas Boas 2015
65 2013 0 Polyhedral studies on vertex coloring problems D Delle Donne, J Marenco  XI Simposio Argentino de …, 2013 sedici.unlp.edu.ar
66 0 組み合わせ最適化問題に対する効率的な厳密解法のための問題の記述法に関する研究 乾伸雄, イヌイノブオ ir.soken.ac.jp
67 2013 0 Mixed Integer Linear Programming Models for Combinatorial Optimization Problems FD Croce  Concepts of Combinatorial Optimization, 2013 Wiley Online Library
68 0 MRW CALVO, MI LJUBIC