Notes on computing peaks in k-levels and parametric spanning trees

N. Katoh; T. Tokuyama

doi:10.1145/378583.378675

Notes on computing peaks in k-levels and parametric spanning trees

N. Katoh, T. Tokuyama

INF - System Information Sciences

Research output: Contribution to conference › Paper › peer-review

5 Citations (Scopus)

Abstract

We give an algorithm to compute all the local peaks in the k-level of an arrangement of n lines in O(n log n) + Õ((kn)^2/3) time. We can also find τ largest peaks in O(n log² n) + Õ((τn)^2/3) time. Moreover, we consider the longest edge in a parametric minimum spanning tree (in other words, a bottleneck edge for connectivity), and give an algorithm to compute the parameter value (within a given interval) maximizing/minimizing the length of the longest edge in MST. The time complexity is Õ(n^8/7k^1/7 + nk^1/3).

Original language	English
Pages	241-248
Number of pages	8
DOIs	https://doi.org/10.1145/378583.378675
Publication status	Published - 2001
Event	17th Annual Symposium on Computational Geometry (SCG'01) - Medford, MA, United States Duration: 2001 Jun 3 → 2001 Jun 5

Other

Other	17th Annual Symposium on Computational Geometry (SCG'01)
Country	United States
City	Medford, MA
Period	01/6/3 → 01/6/5

ASJC Scopus subject areas

Theoretical Computer Science
Geometry and Topology
Computational Mathematics

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AU - Katoh, N.

AU - Tokuyama, T.

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AB - We give an algorithm to compute all the local peaks in the k-level of an arrangement of n lines in O(n log n) + Õ((kn)2/3) time. We can also find τ largest peaks in O(n log2 n) + Õ((τn)2/3) time. Moreover, we consider the longest edge in a parametric minimum spanning tree (in other words, a bottleneck edge for connectivity), and give an algorithm to compute the parameter value (within a given interval) maximizing/minimizing the length of the longest edge in MST. The time complexity is Õ(n8/7k1/7 + nk1/3).

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T2 - 17th Annual Symposium on Computational Geometry (SCG'01)

Y2 - 3 June 2001 through 5 June 2001

ER -

Notes on computing peaks in k-levels and parametric spanning trees

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