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On some geometric problems of color-spanning sets. (English) Zbl 1329.68263

Atallah, Mikhail (ed.) et al., Frontiers in algorithmics and algorithmic aspects in information and management. Joint international conference, FAW-AAIM 2011, Jinhua, China, May 28–31, 2011. Proceedings. Berlin: Springer (ISBN 978-3-642-21203-1/pbk). Lecture Notes in Computer Science 6681, 113-124 (2011).
Summary: In this paper we study several geometric problems of color-spanning sets: given \(N\) points with \(M\) colors in the plane, choosing \(M\) points with distinct colors such that some geometric properties of those \(M\) points are minimized or maximized. The geometric properties studied in this paper are the maximum diameter, the largest closest pair, and the minimum planar spanning tree. We give an \(O(N \log N)\) expected time algorithm for the maximum diameter problem. For the largest closest pair and the minimum planar spanning tree problems, we give hardness proofs.
For the entire collection see [Zbl 1214.68006].

MSC:

68U05 Computer graphics; computational geometry (digital and algorithmic aspects)
68Q17 Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.)
68W05 Nonnumerical algorithms
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