Counting Triangulations of Planar Point Sets
نویسندگان
چکیده
منابع مشابه
Counting Triangulations of Planar Point Sets
We study the maximal number of triangulations that a planar set of n points can have, and show that it is at most 30n. This new bound is achieved by a careful optimization of the charging scheme of Sharir and Welzl (2006), which has led to the previous best upper bound of 43n for the problem. Moreover, this new bound is useful for bounding the number of other types of planar (i.e., crossing-fre...
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Given a finite planar point set, we consider all possible spanning cycles whose straight line realizations are crossing-free – such cycles are also called simple polygonizations – and we are interested in the number of such simple polygonizations a set of N points can have. While the minumum number over all point configurations is easy to obtain – this is 1 for points in convex position –, the ...
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We give a brief account of results concerning the number of triangulations on finite point sets in the plane, both for arbitrary sets and for specific sets such as the n× n integer lattice. Given a finite point set P in the plane, a geometric graph is a straight line embedded graph with vertex set P where no segment realizing an edge contains points from P other than its endpoints. We are inter...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2011
ISSN: 1077-8926
DOI: 10.37236/557