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• W1634767227 abstract "Given a set S of n points in the plane, a quadrangulation of S is a planar subdivision whose vertices are the points of S, whose outer face is the convex hull of S, and every face of the subdivision (except possibly the outer face) is a quadrilateral. We show that S admits a quadrangulation if and only if S does not have an odd number of extreme points. If S admits a quadrangulation, we present an algorithm that computes a quadrangulation of S in O(n log n) time even in the presence of collinear points. If S does not admit a quadrangulation, then our algorithm can quadrangulate S with the addition of one extra point, which is optimal. We also provide an Omega(n log n) time lower bound for the problem. Finally, our results imply that a k-angulation of a set of points can be achieved with the addition of at most k-3 extra points within the same time bound." @default.
• W1634767227 created "2016-06-24" @default.
• W1634767227 creator A5013674788 @default.
• W1634767227 creator A5057315478 @default.
• W1634767227 date "1995-01-01" @default.
• W1634767227 modified "2023-09-27" @default.
• W1634767227 title "No quadrangulation is extremely odd" @default.
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• W1634767227 doi "https://doi.org/10.1007/bfb0015443" @default.
• W1634767227 hasPublicationYear "1995" @default.
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