Boxicity (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Boxicity" in English language version.

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13doi.org

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9semanticscholar.org

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8arxiv.org

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3ams.org

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1archive.org

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1combinatorics.org

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acm.org

portal.acm.org

See, e.g., Agarwal, van Kreveld & Suri (1998) and Berman et al. (2001) for approximations to the maximum independent set for intersection graphs of rectangles, and Chlebík & Chlebíková (2005) for results on hardness of approximation of these problems in higher dimensions. Agarwal, Pankaj K.; van Kreveld, Marc; Suri, Subhash (1998), "Label placement by maximum independent set in rectangles", Computational Geometry Theory and Applications, 11 (3–4): 209–218, doi:10.1016/S0925-7721(98)00028-5, hdl:1874/18908, S2CID 2381363. Berman, Piotr; DasGupta, B.; Muthukrishnan, S.; Ramaswami, S. (2001), "Efficient approximation algorithms for tiling and packing problems with rectangles", J. Algorithms, 41 (2): 443–470, doi:10.1006/jagm.2001.1188. Chlebík, Miroslav; Chlebíková, Janka (2005), "Approximation hardness of optimization problems in intersection graphs of d-dimensional boxes", Proceedings of the Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms, Society for Industrial and Applied Mathematics, pp. 267–276, ISBN 978-0-89871-585-9.

ams.org

mathscinet.ams.org

E.g., see Chandran, Francis & Sivadasan (2010) and Chandran & Sivadasan (2007). Chandran, L. Sunil; Francis, Mathew C.; Sivadasan, Naveen (2010), "Geometric representation of graphs in low dimension using axis parallel boxes", Algorithmica, 56 (2): 129–140, arXiv:cs.DM/0605013, doi:10.1007/s00453-008-9163-5, MR 2576537, S2CID 17838951. Chandran, L. Sunil; Sivadasan, Naveen (2007), "Boxicity and treewidth", Journal of Combinatorial Theory, Series B, 97 (5): 733–744, arXiv:math.CO/0505544, doi:10.1016/j.jctb.2006.12.004, S2CID 9854207.
Chandran, Francis & Sivadasan (2010) observe that this follows from the fact that these graphs have a polynomial number of maximal cliques, i.e., the class of graphs with bounded boxicity is said to have few cliques. An explicit box representation is not needed to list all maximal cliques efficiently. Chandran, L. Sunil; Francis, Mathew C.; Sivadasan, Naveen (2010), "Geometric representation of graphs in low dimension using axis parallel boxes", Algorithmica, 56 (2): 129–140, arXiv:cs.DM/0605013, doi:10.1007/s00453-008-9163-5, MR 2576537, S2CID 17838951.
Chandran, Francis & Sivadasan (2010) Chandran, L. Sunil; Francis, Mathew C.; Sivadasan, Naveen (2010), "Geometric representation of graphs in low dimension using axis parallel boxes", Algorithmica, 56 (2): 129–140, arXiv:cs.DM/0605013, doi:10.1007/s00453-008-9163-5, MR 2576537, S2CID 17838951.

archive.org

Scheinerman (1984). Scheinerman, E. R. (1984), Intersection Classes and Multiple Intersection Parameters, Ph. D thesis, Princeton University.

arxiv.org

E.g., see Chandran, Francis & Sivadasan (2010) and Chandran & Sivadasan (2007). Chandran, L. Sunil; Francis, Mathew C.; Sivadasan, Naveen (2010), "Geometric representation of graphs in low dimension using axis parallel boxes", Algorithmica, 56 (2): 129–140, arXiv:cs.DM/0605013, doi:10.1007/s00453-008-9163-5, MR 2576537, S2CID 17838951. Chandran, L. Sunil; Sivadasan, Naveen (2007), "Boxicity and treewidth", Journal of Combinatorial Theory, Series B, 97 (5): 733–744, arXiv:math.CO/0505544, doi:10.1016/j.jctb.2006.12.004, S2CID 9854207.
Chandran, Francis & Sivadasan (2010) observe that this follows from the fact that these graphs have a polynomial number of maximal cliques, i.e., the class of graphs with bounded boxicity is said to have few cliques. An explicit box representation is not needed to list all maximal cliques efficiently. Chandran, L. Sunil; Francis, Mathew C.; Sivadasan, Naveen (2010), "Geometric representation of graphs in low dimension using axis parallel boxes", Algorithmica, 56 (2): 129–140, arXiv:cs.DM/0605013, doi:10.1007/s00453-008-9163-5, MR 2576537, S2CID 17838951.
Chandran & Sivadasan (2007, Theorem 14) Chandran, L. Sunil; Sivadasan, Naveen (2007), "Boxicity and treewidth", Journal of Combinatorial Theory, Series B, 97 (5): 733–744, arXiv:math.CO/0505544, doi:10.1016/j.jctb.2006.12.004, S2CID 9854207.
Chandran, Francis & Sivadasan (2010) Chandran, L. Sunil; Francis, Mathew C.; Sivadasan, Naveen (2010), "Geometric representation of graphs in low dimension using axis parallel boxes", Algorithmica, 56 (2): 129–140, arXiv:cs.DM/0605013, doi:10.1007/s00453-008-9163-5, MR 2576537, S2CID 17838951.
Esperet (2016) Esperet, Louis (2016), "Boxicity and topological invariants", European Journal of Combinatorics, 51: 495–499, arXiv:1503.05765, doi:10.1016/j.ejc.2015.07.020, S2CID 5548385.
Adiga, Chandran & Mathew (2014) Adiga, Abhijin; Chandran, L. Sunil; Mathew, Rogers (2014), "Cubicity, Degeneracy, and Crossing Number", European Journal of Combinatorics, 35: 2–12, arXiv:1105.5225, doi:10.1016/j.ejc.2013.06.021, S2CID 2069078.
Esperet & Wiechert (2018) Esperet, Louis; Wiechert, Veit (2018), "Boxicity, poset dimension, and excluded minors", Electronic Journal of Combinatorics, 25 (4): #P4.51, arXiv:1804.00850, doi:10.37236/7787, S2CID 119148637.
Esperet (2016) Esperet, Louis (2016), "Boxicity and topological invariants", European Journal of Combinatorics, 51: 495–499, arXiv:1503.05765, doi:10.1016/j.ejc.2015.07.020, S2CID 5548385.

combinatorics.org

Esperet & Wiechert (2018) Esperet, Louis; Wiechert, Veit (2018), "Boxicity, poset dimension, and excluded minors", Electronic Journal of Combinatorics, 25 (4): #P4.51, arXiv:1804.00850, doi:10.37236/7787, S2CID 119148637.

doi.org

E.g., see Chandran, Francis & Sivadasan (2010) and Chandran & Sivadasan (2007). Chandran, L. Sunil; Francis, Mathew C.; Sivadasan, Naveen (2010), "Geometric representation of graphs in low dimension using axis parallel boxes", Algorithmica, 56 (2): 129–140, arXiv:cs.DM/0605013, doi:10.1007/s00453-008-9163-5, MR 2576537, S2CID 17838951. Chandran, L. Sunil; Sivadasan, Naveen (2007), "Boxicity and treewidth", Journal of Combinatorial Theory, Series B, 97 (5): 733–744, arXiv:math.CO/0505544, doi:10.1016/j.jctb.2006.12.004, S2CID 9854207.
Thomassen (1986). Thomassen, Carsten (1986), "Interval representations of planar graphs", Journal of Combinatorial Theory, Series B, 40: 9–20, doi:10.1016/0095-8956(86)90061-4.
Bellantoni et al. (1993). Bellantoni, Stephen J.; Ben-Arroyo Hartman, Irith; Przytycka, Teresa; Whitesides, Sue (1993), "Grid intersection graphs and boxicity", Discrete Mathematics, 114 (1–3): 41–49, doi:10.1016/0012-365X(93)90354-V.
Chandran, Francis & Sivadasan (2010) observe that this follows from the fact that these graphs have a polynomial number of maximal cliques, i.e., the class of graphs with bounded boxicity is said to have few cliques. An explicit box representation is not needed to list all maximal cliques efficiently. Chandran, L. Sunil; Francis, Mathew C.; Sivadasan, Naveen (2010), "Geometric representation of graphs in low dimension using axis parallel boxes", Algorithmica, 56 (2): 129–140, arXiv:cs.DM/0605013, doi:10.1007/s00453-008-9163-5, MR 2576537, S2CID 17838951.
See, e.g., Agarwal, van Kreveld & Suri (1998) and Berman et al. (2001) for approximations to the maximum independent set for intersection graphs of rectangles, and Chlebík & Chlebíková (2005) for results on hardness of approximation of these problems in higher dimensions. Agarwal, Pankaj K.; van Kreveld, Marc; Suri, Subhash (1998), "Label placement by maximum independent set in rectangles", Computational Geometry Theory and Applications, 11 (3–4): 209–218, doi:10.1016/S0925-7721(98)00028-5, hdl:1874/18908, S2CID 2381363. Berman, Piotr; DasGupta, B.; Muthukrishnan, S.; Ramaswami, S. (2001), "Efficient approximation algorithms for tiling and packing problems with rectangles", J. Algorithms, 41 (2): 443–470, doi:10.1006/jagm.2001.1188. Chlebík, Miroslav; Chlebíková, Janka (2005), "Approximation hardness of optimization problems in intersection graphs of d-dimensional boxes", Proceedings of the Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms, Society for Industrial and Applied Mathematics, pp. 267–276, ISBN 978-0-89871-585-9.
Cozzens (1981) shows that computing the boxicity is NP-complete; Yannakakis (1982) shows that even checking whether the boxicity is at most 3 is NP-hard; finally Kratochvil (1994) showed that recognising boxicity 2 is NP-hard. Cozzens, M. B. (1981), Higher and Multidimensional Analogues of Interval Graphs, Ph.D. thesis, Rutgers University. Yannakakis, Mihalis (1982), "The complexity of the partial order dimension problem", SIAM Journal on Algebraic and Discrete Methods, 3 (3): 351–358, doi:10.1137/0603036. Kratochvil, Jan (1994), "A special planar satisfiability problem and a consequence of its NP–completeness", Discrete Applied Mathematics, 52 (3): 233–252, doi:10.1016/0166-218X(94)90143-0.
Adiga, Chitnis & Saurabh (2010). Adiga, Abhijin; Chitnis, Rajesh; Saurabh, Saket (2010), "Parameterized algorithms for boxicity", Algorithms and Computation: 21st International Symposium, ISAAC 2010, Jeju Island, Korea, December 15-17, 2010, Proceedings, Part I (PDF), Lecture Notes in Computer Science, vol. 6506, pp. 366–377, doi:10.1007/978-3-642-17517-6_33, ISBN 978-3-642-17516-9, archived from the original (PDF) on 2017-08-30, retrieved 2018-01-22
Chandran & Sivadasan (2007, Theorem 14) Chandran, L. Sunil; Sivadasan, Naveen (2007), "Boxicity and treewidth", Journal of Combinatorial Theory, Series B, 97 (5): 733–744, arXiv:math.CO/0505544, doi:10.1016/j.jctb.2006.12.004, S2CID 9854207.
Chandran, Francis & Sivadasan (2010) Chandran, L. Sunil; Francis, Mathew C.; Sivadasan, Naveen (2010), "Geometric representation of graphs in low dimension using axis parallel boxes", Algorithmica, 56 (2): 129–140, arXiv:cs.DM/0605013, doi:10.1007/s00453-008-9163-5, MR 2576537, S2CID 17838951.
Esperet (2016) Esperet, Louis (2016), "Boxicity and topological invariants", European Journal of Combinatorics, 51: 495–499, arXiv:1503.05765, doi:10.1016/j.ejc.2015.07.020, S2CID 5548385.
Adiga, Chandran & Mathew (2014) Adiga, Abhijin; Chandran, L. Sunil; Mathew, Rogers (2014), "Cubicity, Degeneracy, and Crossing Number", European Journal of Combinatorics, 35: 2–12, arXiv:1105.5225, doi:10.1016/j.ejc.2013.06.021, S2CID 2069078.
Esperet & Wiechert (2018) Esperet, Louis; Wiechert, Veit (2018), "Boxicity, poset dimension, and excluded minors", Electronic Journal of Combinatorics, 25 (4): #P4.51, arXiv:1804.00850, doi:10.37236/7787, S2CID 119148637.
Esperet (2016) Esperet, Louis (2016), "Boxicity and topological invariants", European Journal of Combinatorics, 51: 495–499, arXiv:1503.05765, doi:10.1016/j.ejc.2015.07.020, S2CID 5548385.

handle.net

hdl.handle.net

See, e.g., Agarwal, van Kreveld & Suri (1998) and Berman et al. (2001) for approximations to the maximum independent set for intersection graphs of rectangles, and Chlebík & Chlebíková (2005) for results on hardness of approximation of these problems in higher dimensions. Agarwal, Pankaj K.; van Kreveld, Marc; Suri, Subhash (1998), "Label placement by maximum independent set in rectangles", Computational Geometry Theory and Applications, 11 (3–4): 209–218, doi:10.1016/S0925-7721(98)00028-5, hdl:1874/18908, S2CID 2381363. Berman, Piotr; DasGupta, B.; Muthukrishnan, S.; Ramaswami, S. (2001), "Efficient approximation algorithms for tiling and packing problems with rectangles", J. Algorithms, 41 (2): 443–470, doi:10.1006/jagm.2001.1188. Chlebík, Miroslav; Chlebíková, Janka (2005), "Approximation hardness of optimization problems in intersection graphs of d-dimensional boxes", Proceedings of the Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms, Society for Industrial and Applied Mathematics, pp. 267–276, ISBN 978-0-89871-585-9.

semanticscholar.org

api.semanticscholar.org

E.g., see Chandran, Francis & Sivadasan (2010) and Chandran & Sivadasan (2007). Chandran, L. Sunil; Francis, Mathew C.; Sivadasan, Naveen (2010), "Geometric representation of graphs in low dimension using axis parallel boxes", Algorithmica, 56 (2): 129–140, arXiv:cs.DM/0605013, doi:10.1007/s00453-008-9163-5, MR 2576537, S2CID 17838951. Chandran, L. Sunil; Sivadasan, Naveen (2007), "Boxicity and treewidth", Journal of Combinatorial Theory, Series B, 97 (5): 733–744, arXiv:math.CO/0505544, doi:10.1016/j.jctb.2006.12.004, S2CID 9854207.
Chandran, Francis & Sivadasan (2010) observe that this follows from the fact that these graphs have a polynomial number of maximal cliques, i.e., the class of graphs with bounded boxicity is said to have few cliques. An explicit box representation is not needed to list all maximal cliques efficiently. Chandran, L. Sunil; Francis, Mathew C.; Sivadasan, Naveen (2010), "Geometric representation of graphs in low dimension using axis parallel boxes", Algorithmica, 56 (2): 129–140, arXiv:cs.DM/0605013, doi:10.1007/s00453-008-9163-5, MR 2576537, S2CID 17838951.
See, e.g., Agarwal, van Kreveld & Suri (1998) and Berman et al. (2001) for approximations to the maximum independent set for intersection graphs of rectangles, and Chlebík & Chlebíková (2005) for results on hardness of approximation of these problems in higher dimensions. Agarwal, Pankaj K.; van Kreveld, Marc; Suri, Subhash (1998), "Label placement by maximum independent set in rectangles", Computational Geometry Theory and Applications, 11 (3–4): 209–218, doi:10.1016/S0925-7721(98)00028-5, hdl:1874/18908, S2CID 2381363. Berman, Piotr; DasGupta, B.; Muthukrishnan, S.; Ramaswami, S. (2001), "Efficient approximation algorithms for tiling and packing problems with rectangles", J. Algorithms, 41 (2): 443–470, doi:10.1006/jagm.2001.1188. Chlebík, Miroslav; Chlebíková, Janka (2005), "Approximation hardness of optimization problems in intersection graphs of d-dimensional boxes", Proceedings of the Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms, Society for Industrial and Applied Mathematics, pp. 267–276, ISBN 978-0-89871-585-9.
Chandran & Sivadasan (2007, Theorem 14) Chandran, L. Sunil; Sivadasan, Naveen (2007), "Boxicity and treewidth", Journal of Combinatorial Theory, Series B, 97 (5): 733–744, arXiv:math.CO/0505544, doi:10.1016/j.jctb.2006.12.004, S2CID 9854207.
Chandran, Francis & Sivadasan (2010) Chandran, L. Sunil; Francis, Mathew C.; Sivadasan, Naveen (2010), "Geometric representation of graphs in low dimension using axis parallel boxes", Algorithmica, 56 (2): 129–140, arXiv:cs.DM/0605013, doi:10.1007/s00453-008-9163-5, MR 2576537, S2CID 17838951.
Esperet (2016) Esperet, Louis (2016), "Boxicity and topological invariants", European Journal of Combinatorics, 51: 495–499, arXiv:1503.05765, doi:10.1016/j.ejc.2015.07.020, S2CID 5548385.
Adiga, Chandran & Mathew (2014) Adiga, Abhijin; Chandran, L. Sunil; Mathew, Rogers (2014), "Cubicity, Degeneracy, and Crossing Number", European Journal of Combinatorics, 35: 2–12, arXiv:1105.5225, doi:10.1016/j.ejc.2013.06.021, S2CID 2069078.
Esperet & Wiechert (2018) Esperet, Louis; Wiechert, Veit (2018), "Boxicity, poset dimension, and excluded minors", Electronic Journal of Combinatorics, 25 (4): #P4.51, arXiv:1804.00850, doi:10.37236/7787, S2CID 119148637.
Esperet (2016) Esperet, Louis (2016), "Boxicity and topological invariants", European Journal of Combinatorics, 51: 495–499, arXiv:1503.05765, doi:10.1016/j.ejc.2015.07.020, S2CID 5548385.

web.archive.org

Adiga, Chitnis & Saurabh (2010). Adiga, Abhijin; Chitnis, Rajesh; Saurabh, Saket (2010), "Parameterized algorithms for boxicity", Algorithms and Computation: 21st International Symposium, ISAAC 2010, Jeju Island, Korea, December 15-17, 2010, Proceedings, Part I (PDF), Lecture Notes in Computer Science, vol. 6506, pp. 366–377, doi:10.1007/978-3-642-17517-6_33, ISBN 978-3-642-17516-9, archived from the original (PDF) on 2017-08-30, retrieved 2018-01-22

weizmann.ac.il

wisdom.weizmann.ac.il

Adiga, Chitnis & Saurabh (2010). Adiga, Abhijin; Chitnis, Rajesh; Saurabh, Saket (2010), "Parameterized algorithms for boxicity", Algorithms and Computation: 21st International Symposium, ISAAC 2010, Jeju Island, Korea, December 15-17, 2010, Proceedings, Part I (PDF), Lecture Notes in Computer Science, vol. 6506, pp. 366–377, doi:10.1007/978-3-642-17517-6_33, ISBN 978-3-642-17516-9, archived from the original (PDF) on 2017-08-30, retrieved 2018-01-22