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

Tatsuya Akutsu, Hisao Tamaki, Takeshi Tokuyama

研究成果: Paper査読

13 被引用数 (Scopus)

抄録

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 which is congruent to some subset of Q. We introduce a combinatorial-geometric quantity λ(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 non-trivial upper bound on λ(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 the four-dimensional space.

本文言語English
ページ314-323
ページ数10
DOI
出版ステータスPublished - 1997 1 1
イベントProceedings of the 1997 13th Annual Symposium on Computational Geometry - Nice, Fr
継続期間: 1997 6 41997 6 6

Other

OtherProceedings of the 1997 13th Annual Symposium on Computational Geometry
CityNice, Fr
Period97/6/497/6/6

ASJC Scopus subject areas

  • 理論的コンピュータサイエンス
  • 幾何学とトポロジー
  • 計算数学

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