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

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.

UR - http://www.scopus.com/inward/record.url?scp=84891864548&partnerID=8YFLogxK

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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 -