Cover contact graphs

N. Atienza; N. Castro, de; C. Cortes; M.A. Garrido; C. Grima; G. Hernandez; A. Márquez; A. Moreno; M. Nöllenburg; J.R. Portillo; P. Reyes; J. Valenzuela; M.T. Villar; A. Wolff

doi:10.1007/978-3-540-77537-9_18

Cover contact graphs

N. Atienza, N. Castro, de, C. Cortes, M.A. Garrido, C. Grima, G. Hernandez, A. Márquez, A. Moreno, M. Nöllenburg, J.R. Portillo, P. Reyes, J. Valenzuela, M.T. Villar, A. Wolff

Algorithms

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

1 Citation (Scopus)

Abstract

We study problems that arise in the context of covering certain geometric objects (so-called seeds, e.g., points or disks) by a set of other geometric objects (a so-called cover, e.g., a set of disks or homothetic triangles). We insist that the interiors of the seeds and the cover elements are pairwise disjoint, but they can touch. We call the contact graph of a cover a cover contact graph (CCG). We are interested in two types of tasks: (a) deciding whether a given seed set has a connected CCG, and (b) deciding whether a given graph has a realization as a CCG on a given seed set. Concerning task (a) we give efficient algorithms for the case that seeds are points and covers are disks or triangles. We show that the problem becomes NP-hard if seeds and covers are disks. Concerning task (b) we show that it is even NP-hard for point seeds and disk covers (given a fixed correspondence between vertices and seeds).

Original language	English
Title of host publication	Graph Drawing (15th International Symposium, GD'07, Sydney, Australia, September 23-26, 2007, Revised Papers)
Editors	S.K. Hong, T. Nishizeki, W. Quan
Place of Publication	Berlin
Publisher	Springer
Pages	171-182
ISBN (Print)	978-3-540-77536-2
DOIs	https://doi.org/10.1007/978-3-540-77537-9_18
Publication status	Published - 2008

Publication series

Name	Lecture Notes in Computer Science
Volume	4875
ISSN (Print)	0302-9743

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10.1007/978-3-540-77537-9_18

Cite this

Atienza, N., Castro, de, N., Cortes, C., Garrido, M. A., Grima, C., Hernandez, G., Márquez, A., Moreno, A., Nöllenburg, M., Portillo, J. R., Reyes, P., Valenzuela, J., Villar, M. T., & Wolff, A. (2008). Cover contact graphs. In S. K. Hong, T. Nishizeki, & W. Quan (Eds.), Graph Drawing (15th International Symposium, GD'07, Sydney, Australia, September 23-26, 2007, Revised Papers) (pp. 171-182). (Lecture Notes in Computer Science; Vol. 4875). Springer. https://doi.org/10.1007/978-3-540-77537-9_18

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title = "Cover contact graphs",

abstract = "We study problems that arise in the context of covering certain geometric objects (so-called seeds, e.g., points or disks) by a set of other geometric objects (a so-called cover, e.g., a set of disks or homothetic triangles). We insist that the interiors of the seeds and the cover elements are pairwise disjoint, but they can touch. We call the contact graph of a cover a cover contact graph (CCG). We are interested in two types of tasks: (a) deciding whether a given seed set has a connected CCG, and (b) deciding whether a given graph has a realization as a CCG on a given seed set. Concerning task (a) we give efficient algorithms for the case that seeds are points and covers are disks or triangles. We show that the problem becomes NP-hard if seeds and covers are disks. Concerning task (b) we show that it is even NP-hard for point seeds and disk covers (given a fixed correspondence between vertices and seeds).",

author = "N. Atienza and {Castro, de}, N. and C. Cortes and M.A. Garrido and C. Grima and G. Hernandez and A. M{\'a}rquez and A. Moreno and M. N{\"o}llenburg and J.R. Portillo and P. Reyes and J. Valenzuela and M.T. Villar and A. Wolff",

year = "2008",

doi = "10.1007/978-3-540-77537-9_18",

language = "English",

isbn = "978-3-540-77536-2",

series = "Lecture Notes in Computer Science",

publisher = "Springer",

pages = "171--182",

editor = "S.K. Hong and T. Nishizeki and W. Quan",

booktitle = "Graph Drawing (15th International Symposium, GD'07, Sydney, Australia, September 23-26, 2007, Revised Papers)",

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}

Atienza, N, Castro, de, N, Cortes, C, Garrido, MA, Grima, C, Hernandez, G, Márquez, A, Moreno, A, Nöllenburg, M, Portillo, JR, Reyes, P, Valenzuela, J, Villar, MT & Wolff, A 2008, Cover contact graphs. in SK Hong, T Nishizeki & W Quan (eds), Graph Drawing (15th International Symposium, GD'07, Sydney, Australia, September 23-26, 2007, Revised Papers). Lecture Notes in Computer Science, vol. 4875, Springer, Berlin, pp. 171-182. https://doi.org/10.1007/978-3-540-77537-9_18

Cover contact graphs. / Atienza, N.; Castro, de, N.; Cortes, C. et al.
Graph Drawing (15th International Symposium, GD'07, Sydney, Australia, September 23-26, 2007, Revised Papers). ed. / S.K. Hong; T. Nishizeki; W. Quan. Berlin: Springer, 2008. p. 171-182 (Lecture Notes in Computer Science; Vol. 4875).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

TY - GEN

T1 - Cover contact graphs

AU - Atienza, N.

AU - Castro, de, N.

AU - Cortes, C.

AU - Garrido, M.A.

AU - Grima, C.

AU - Hernandez, G.

AU - Márquez, A.

AU - Moreno, A.

AU - Nöllenburg, M.

AU - Portillo, J.R.

AU - Reyes, P.

AU - Valenzuela, J.

AU - Villar, M.T.

AU - Wolff, A.

PY - 2008

Y1 - 2008

N2 - We study problems that arise in the context of covering certain geometric objects (so-called seeds, e.g., points or disks) by a set of other geometric objects (a so-called cover, e.g., a set of disks or homothetic triangles). We insist that the interiors of the seeds and the cover elements are pairwise disjoint, but they can touch. We call the contact graph of a cover a cover contact graph (CCG). We are interested in two types of tasks: (a) deciding whether a given seed set has a connected CCG, and (b) deciding whether a given graph has a realization as a CCG on a given seed set. Concerning task (a) we give efficient algorithms for the case that seeds are points and covers are disks or triangles. We show that the problem becomes NP-hard if seeds and covers are disks. Concerning task (b) we show that it is even NP-hard for point seeds and disk covers (given a fixed correspondence between vertices and seeds).

AB - We study problems that arise in the context of covering certain geometric objects (so-called seeds, e.g., points or disks) by a set of other geometric objects (a so-called cover, e.g., a set of disks or homothetic triangles). We insist that the interiors of the seeds and the cover elements are pairwise disjoint, but they can touch. We call the contact graph of a cover a cover contact graph (CCG). We are interested in two types of tasks: (a) deciding whether a given seed set has a connected CCG, and (b) deciding whether a given graph has a realization as a CCG on a given seed set. Concerning task (a) we give efficient algorithms for the case that seeds are points and covers are disks or triangles. We show that the problem becomes NP-hard if seeds and covers are disks. Concerning task (b) we show that it is even NP-hard for point seeds and disk covers (given a fixed correspondence between vertices and seeds).

U2 - 10.1007/978-3-540-77537-9_18

DO - 10.1007/978-3-540-77537-9_18

M3 - Conference contribution

SN - 978-3-540-77536-2

T3 - Lecture Notes in Computer Science

SP - 171

EP - 182

BT - Graph Drawing (15th International Symposium, GD'07, Sydney, Australia, September 23-26, 2007, Revised Papers)

A2 - Hong, S.K.

A2 - Nishizeki, T.

A2 - Quan, W.

PB - Springer

CY - Berlin

ER -

Cover contact graphs

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