TY - GEN

T1 - Convex drawings of internally triconnected plane graphs on O(n 2) grids

AU - Zhou, Xiao

AU - Nishizeki, Takao

N1 - Funding Information:
This work is supported in part by a Grant-in-Aid for Scientific Research (C) 19500001 from Japan Society for the Promotion of Science (JSPS).

PY - 2009

Y1 - 2009

N2 - In a convex grid drawing of a plane graph, every edge is drawn as a straight-line segment without any edge-intersection, every vertex is located at a grid point, and every facial cycle is drawn as a convex polygon. A plane graph G has a convex drawing if and only if G is internally triconnected. It has been known that an internally triconnected plane graph G of n vertices has a convex grid drawing on a grid of O(n 3) area if the triconnected component decomposition tree of G has at most four leaves. In this paper, we improve the area bound O(n 3) to O(n 2), which is optimal up to a constant factor. More precisely, we show that G has a convex grid drawing on a 2n×4n grid. We also present an algorithm to find such a drawing in linear time.

AB - In a convex grid drawing of a plane graph, every edge is drawn as a straight-line segment without any edge-intersection, every vertex is located at a grid point, and every facial cycle is drawn as a convex polygon. A plane graph G has a convex drawing if and only if G is internally triconnected. It has been known that an internally triconnected plane graph G of n vertices has a convex grid drawing on a grid of O(n 3) area if the triconnected component decomposition tree of G has at most four leaves. In this paper, we improve the area bound O(n 3) to O(n 2), which is optimal up to a constant factor. More precisely, we show that G has a convex grid drawing on a 2n×4n grid. We also present an algorithm to find such a drawing in linear time.

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U2 - 10.1007/978-3-642-10631-6_77

DO - 10.1007/978-3-642-10631-6_77

M3 - Conference contribution

AN - SCOPUS:75649145000

SN - 3642106307

SN - 9783642106309

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

SP - 760

EP - 770

BT - Algorithms and Computation - 20th International Symposium, ISAAC 2009, Proceedings

T2 - 20th International Symposium on Algorithms and Computation, ISAAC 2009

Y2 - 16 December 2009 through 18 December 2009

ER -