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.
|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 4 → 1997 6 6
|Other||Proceedings of the 1997 13th Annual Symposium on Computational Geometry|
|Period||97/6/4 → 97/6/6|
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