On minimum and maximum spanning trees of linearly moving points

Naoki Katoh, Takeshi Tokuyama, Kazuo Iwano

研究成果: Conference contribution

8 被引用数 (Scopus)

抄録

The authors investigate the upper bounds on the numbers of transitions of minimum and maximum spanning trees (MinST and MaxST for short) for linearly moving points. Suppose that one is given a set of n points in general d-dimensional space, S=(p1,p2,..., pn), and that all points move along different straight lines at different but fixed speeds, i.e., the position of pi is a linear function of a real parameter. They investigate the numbers of transitions of MinST and MaxST when t increases from - infinity to + infinity. They assume that the dimension d is a fixed constant. Since there are O(n2) distances among n points, there are naively O(n4) transitions of MinST and MaxST. They improve these trivial upper bounds for L1 and L/sub infinity / distance metrics. Let cp(n, min) (resp. cp(n, max)) be the number of maximum possible transitions of MinST (resp. MaxST) in Lp metric for n linearly moving points. They give the following results; c1(n, min)=O(n5/2a(n)), c/sub infinity /(n, min)=O(n5/2a(n)), c1(n, max)=O(nn) and c/sub infinity /(n, max)=O(n2) where O(n) is the inverse Ackermann function. They also investigate two restricted cases.

本文言語English
ホスト出版物のタイトルProceedings - 33rd Annual Symposium on Foundations of Computer Science, FOCS 1992
出版社IEEE Computer Society
ページ396-405
ページ数10
ISBN(電子版)0818629002
DOI
出版ステータスPublished - 1992
イベント33rd Annual Symposium on Foundations of Computer Science, FOCS 1992 - Pittsburgh, United States
継続期間: 1992 10月 241992 10月 27

出版物シリーズ

名前Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
1992-October
ISSN(印刷版)0272-5428

Conference

Conference33rd Annual Symposium on Foundations of Computer Science, FOCS 1992
国/地域United States
CityPittsburgh
Period92/10/2492/10/27

ASJC Scopus subject areas

  • コンピュータ サイエンス(全般)

引用スタイル