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Computing the smallest color-spanning axis-parallel square

Khanteimouri, P ; Sharif University of Technology | 2013

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  1. Type of Document: Article
  2. DOI: 10.1007/978-3-642-45030-3_59
  3. Publisher: 2013
  4. Abstract:
  5. 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
  6. Keywords:
  7. Algorithm ; Color spanning objects ; Computational geometry ; Dynamic structure ; Real line ; Algorithms ; Color
  8. Source: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) ; Volume 8283 , 2013 , Pages 634-643 ; 03029743 (ISSN) ; 9783642450297 (ISBN)
  9. URL: http://link.springer.com/chapter/10.1007%2F978-3-642-45030-3_59