For a given set of n colored points with k colors in the plane, we study the problem of computing the smallest color-spanning axis-parallel square. First, for a dynamic set of colored points on the real line, we propose a dynamic structure with O(log2 n) update time per insertion and deletion for maintaining the smallest color-spanning interval. Next, we use this result to compute the smallest color-spanning square. Although we show there could be Ω(kn) minimal color-spanning squares, our algorithm runs in O(nlog2 n) time and O(n) space. © 2013 Springer-Verlag.
CITATION STYLE
Khanteimouri, P., Mohades, A., Abam, M. A., & Kazemi, M. R. (2013). Computing the smallest color-spanning axis-parallel square. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 8283 LNCS, pp. 634–643). https://doi.org/10.1007/978-3-642-45030-3_59
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