TY - GEN

T1 - Constrained simultaneous and near-simultaneous embeddings

AU - Frati, Fabrizio

AU - Kaufmann, Michael

AU - Kobourov, Stephen G.

PY - 2008

Y1 - 2008

N2 - A geometric simultaneous embedding of two graphs G 1∈= ∈(V 1,E 1) and G 2∈=∈(V 2,E 2) with a bijective mapping of their vertex sets γ: V 1 →V 2 is a pair of planar straight-line drawings Γ 1 of G 1 and Γ 2 of G 2, such that each vertex v 2∈=∈γ(v 1) is mapped in Γ 2 to the same point where v 1 is mapped in Γ 1, where v 1∈ ∈V 1 and v 2∈ ∈V 2. In this paper we examine several constrained versions and a relaxed version of the geometric simultaneous embedding problem. We show that if the input graphs are assumed to share no common edges this does not seem to yield large classes of graphs that can be simultaneously embedded. Further, if a prescribed combinatorial embedding for each input graph must be preserved, then we can answer some of the problems that are still open for geometric simultaneous embedding. Finally, we present some positive and negative results on the near-simultaneous embedding problem, in which vertices are not mapped exactly to the same but to "near" points in the different drawings.

AB - A geometric simultaneous embedding of two graphs G 1∈= ∈(V 1,E 1) and G 2∈=∈(V 2,E 2) with a bijective mapping of their vertex sets γ: V 1 →V 2 is a pair of planar straight-line drawings Γ 1 of G 1 and Γ 2 of G 2, such that each vertex v 2∈=∈γ(v 1) is mapped in Γ 2 to the same point where v 1 is mapped in Γ 1, where v 1∈ ∈V 1 and v 2∈ ∈V 2. In this paper we examine several constrained versions and a relaxed version of the geometric simultaneous embedding problem. We show that if the input graphs are assumed to share no common edges this does not seem to yield large classes of graphs that can be simultaneously embedded. Further, if a prescribed combinatorial embedding for each input graph must be preserved, then we can answer some of the problems that are still open for geometric simultaneous embedding. Finally, we present some positive and negative results on the near-simultaneous embedding problem, in which vertices are not mapped exactly to the same but to "near" points in the different drawings.

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U2 - 10.1007/978-3-540-77537-9_27

DO - 10.1007/978-3-540-77537-9_27

M3 - Conference contribution

AN - SCOPUS:49949084876

SN - 3540775366

SN - 9783540775362

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 268

EP - 279

BT - Graph Drawing - 15th International Symposium, GD 2007, Revised Papers

T2 - 15th International Symposium on Graph Drawing, GD 2007

Y2 - 24 September 2007 through 26 September 2007

ER -