Note: On finding a large number of 3D points with a small diameter

Authors:
Minghui Jiang
Affiliations:
Department of Computer Science, Utah State University, Logan, UT 84322-4205, USA
Venue:
Discrete Applied Mathematics
Year:
2007

Citing 4
Cited 0

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Abstract

Given a set S of n points in R^3, we wish to decide whether S has a subset of size at least k with Euclidean diameter at most r. It is unknown whether this decision problem is NP-hard. The two closely related optimization problems, (i) finding a largest subset of diameter at most r, and (ii) finding a subset of the smallest diameter of size at least k, were recently considered by Afshani and Chan. For maximizing the size, they presented several polynomial-time algorithms with constant approximation factors, the best of which has a factor of @p/arccos13