A-027 Convex Drawings of Internally Triconnected Plane Graphs on O(n^2) Grids

概要

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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 within a coefficient. 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.
FIT(電子情報通信学会・情報処理学会)推進委員会の論文
2009-08-20