On Embedding an Outer-Planar Graph in a Point Set
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منابع مشابه
On the Hardness of Point-Set Embeddability⋆
A point-set embedding of a plane graph G with n vertices on a set S of n points is a straight-line drawing of G, where the vertices of G are mapped to distinct points of S. The problem of deciding whether a plane graph admits a point-set embedding on a given set of points is NPcomplete for 2-connected planar graphs, but polynomial-time solvable for outerplanar graphs and plane 3-trees. In this ...
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Given an n-vertex outer-planar graph G and a set P of n points in the plane, we present an O(n log 3 n) time and O(n) space algorithm to compute a straight-line embedding of G in P, improving upon the algorithm in GMPP91, CU96] that requires O(n 2) time. Our algorithm is near-optimal as there is an (n log n) lower bound for the problem BMS95]. We present a simpler O(nd) time and O(n) space algo...
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A point-set embedding of a planar graph G with n vertices on a set P of n points in R, d ≥ 1, is a straight-line drawing of G, where the vertices of G are mapped to distinct points of P . The problem of computing a point-set embedding of G on P is NP-complete in R, even when G is 2-outerplanar and the points are in general position. On the other hand, if the points of P are in general position ...
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Abstract A set of planar graphs share a simultaneous embedding if they can be drawn on the same vertex set V of n vertices in the plane without crossings between edges of the same graph. Fixed edges are common edges between graphs that share the same Jordan curve in the simultaneous drawing. We give a necessary condition for when pairs of graphs can have a simultaneous embedding with fixed edge...
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