TY - GEN
T1 - Colored spanning graphs for set visualization
AU - Hurtado, Ferran
AU - Korman, Matias
AU - Van Kreveld, Marc
AU - Löffler, Maarten
AU - Sacristán, Vera
AU - Silveira, Rodrigo I.
AU - Speckmann, Bettina
N1 - Funding Information:
M.L. was supported by the Netherlands Organisation for Scientific Research (NWO) under grant 639.021.123. F. H., M. K., V. S. and R.I. S. were partially supported by ESF EUROCORES programme EuroGIGA, CRP ComPoSe: grant EUI-EURC-2011-4306, and by project MINECO MTM2012-30951. F. H., V. S. and R.I. S. were supported by project Gen. Cat. DGR 2009SGR1040. M. K. was supported by the Secretary for Universities and Research of the Ministry of Economy and Knowledge of the Government of Catalonia and the European Union. R. I. S. was funded by the FP7 Marie Curie Actions Individual Fellowship PIEF-GA-2009-251235 and by FCT through grant SFRH/BPD/88455/2012.
PY - 2013
Y1 - 2013
N2 - We study an algorithmic problem that is motivated by ink minimization for sparse set visualizations. Our input is a set of points in the plane which are either blue, red, or purple. Blue points belong exclusively to the blue set, red points belong exclusively to the red set, and purple points belong to both sets. A red-blue-purple spanning graph (RBP spanning graph) is a set of edges connecting the points such that the subgraph induced by the red and purple points is connected, and the subgraph induced by the blue and purple points is connected. We study the geometric properties of minimum RBP spanning graphs and the algorithmic problems associated with computing them. Specifically, we show that the general problem is NP-hard. Hence we give an (1/2ρ+1)- approximation, where ρ is the Steiner ratio. We also present efficient exact solutions if the points are located on a line or a circle. Finally we consider extensions to more than two sets.
AB - We study an algorithmic problem that is motivated by ink minimization for sparse set visualizations. Our input is a set of points in the plane which are either blue, red, or purple. Blue points belong exclusively to the blue set, red points belong exclusively to the red set, and purple points belong to both sets. A red-blue-purple spanning graph (RBP spanning graph) is a set of edges connecting the points such that the subgraph induced by the red and purple points is connected, and the subgraph induced by the blue and purple points is connected. We study the geometric properties of minimum RBP spanning graphs and the algorithmic problems associated with computing them. Specifically, we show that the general problem is NP-hard. Hence we give an (1/2ρ+1)- approximation, where ρ is the Steiner ratio. We also present efficient exact solutions if the points are located on a line or a circle. Finally we consider extensions to more than two sets.
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U2 - 10.1007/978-3-319-03841-4_25
DO - 10.1007/978-3-319-03841-4_25
M3 - Conference contribution
AN - SCOPUS:84891864548
SN - 9783319038407
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 280
EP - 291
BT - Graph Drawing - 21st International Symposium, GD 2013, Revised Selected Papers
PB - Springer Verlag
T2 - 21st International Symposium on Graph Drawing, GD 2013
Y2 - 23 September 2013 through 25 September 2013
ER -