On minimum and maximum spanning trees of linearly moving points

Naoki Katoh, Takeshi Tokuyama, Kazuo Iwano

Research output: Chapter in Book/Report/Conference proceedingConference contribution

9 Citations (Scopus)

Abstract

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.

Original languageEnglish
Title of host publicationProceedings - 33rd Annual Symposium on Foundations of Computer Science, FOCS 1992
PublisherIEEE Computer Society
Pages396-405
Number of pages10
ISBN (Electronic)0818629002
DOIs
Publication statusPublished - 1992
Event33rd Annual Symposium on Foundations of Computer Science, FOCS 1992 - Pittsburgh, United States
Duration: 1992 Oct 241992 Oct 27

Publication series

NameProceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
Volume1992-October
ISSN (Print)0272-5428

Conference

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

ASJC Scopus subject areas

  • Computer Science(all)

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