SMALLEST COLOR-SPANNING OBJECT REVISITED-Reference-Cited by-同舟云学术

SMALLEST COLOR-SPANNING OBJECT REVISITED

Published:2009-10 Issue:05 Volume:19 Page:457-478
ISSN:0218-1959
Container-title:International Journal of Computational Geometry & Applications
language:en
Short-container-title:Int. J. Comput. Geom. Appl.

Author:

DAS SANDIP¹,GOSWAMI PARTHA P.²,NANDY SUBHAS C.¹

Affiliation:

1. Advanced Computing and Microelectronics Unit, Indian Statistical Institute, Kolkata 700 108, India

2. Department of Radiophysics and Electronics, University of Calcutta, Kolkata 700 009, India

Abstract

Given a set of n colored points in IR2 with a total of m (3 ≤ m ≤ n) colors, the problem of identifying the smallest color-spanning object of some predefined shape is studied in this paper. We shall consider two different shapes: (i) corridor and (ii) rectangle of arbitrary orientation. Our proposed algorithm for identifying the smallest color-spanning corridor is simple and runs in O(n2 log n) time using O(n) space. A dynamic version of the problem is also studied, where new points may be added, and the narrowest color-spanning corridor at any instance can be reported in O(mn(α(n))2 log m) time. Our algorithm for identifying the smallest color-spanning rectangle of arbitrary orientation runs in O(n3 log m) time and O(n) space.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Computational Mathematics,Computational Theory and Mathematics,Geometry and Topology,Theoretical Computer Science

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218195909003076

Reference10 articles.

1. The K-dense corridor problems

2. Algorithms in Combinatorial Geometry

3. Constructing Belts in Two-Dimensional Arrangements with Applications

4. Smallest k-point enclosing rectangle and square of arbitrary orientation

5. Finding the upper envelope of n line segments in O(n log n) time

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