Distribution of distances and triangles in a point set and algorithms for computing the largest common point sets

被引:31
|
作者
Akutsu, T [1 ]
Tamaki, H
Tokuyama, T
机构
[1] Univ Tokyo, Inst Med Sci, Ctr Human Genome, Tokyo 108, Japan
[2] Meiji Univ, Sch Sci & Technol, Dept Comp Sci, Tama Ku, Kanagawa 214, Japan
[3] IBM Corp, Tokyo Res Lab, Kanagawa 242, Japan
关键词
D O I
10.1007/PL00009388
中图分类号
TP301 [理论、方法];
学科分类号
081202 ;
摘要
This paper considers the following problem, which we call the largest common point set problem (LCP): given two point sets P and Q in the Euclidean plane, find a subset of P with the maximum cardinality that is congruent to some subset of Q. We introduce a combinatorial-geometric quantity lambda(P, Q), which we call the inner product of the distance-multiplicity vectors of P and Q, show its relevance to the complexity of various algorithms for LCP, and give a nontrivial upper bound on lambda(P, Q). We generalize this notion to higher dimensions, give some upper bounds on the quantity, and apply them to algorithms for LCP in higher dimensions. Along the way, we prove a new upper bound on the number of congruent triangles in a point set in four-dimensional space.
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页码:307 / 331
页数:25
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