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Optimal Color Range Reporting in One Dimension

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Algorithms – ESA 2013 (ESA 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8125))

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Abstract

Color (or categorical) range reporting is a variant of the orthogonal range reporting problem in which every point in the input is assigned a color. While the answer to an orthogonal point reporting query contains all points in the query range Q, the answer to a color reporting query contains only distinct colors of points in Q. In this paper we describe an O(N)-space data structure that answers one-dimensional color reporting queries in optimal O(k + 1) time, where k is the number of colors in the answer and N is the number of points in the data structure. Our result can be also dynamized and extended to the external memory model.

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Nekrich, Y., Vitter, J.S. (2013). Optimal Color Range Reporting in One Dimension. In: Bodlaender, H.L., Italiano, G.F. (eds) Algorithms – ESA 2013. ESA 2013. Lecture Notes in Computer Science, vol 8125. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40450-4_63

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  • DOI: https://doi.org/10.1007/978-3-642-40450-4_63

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-40449-8

  • Online ISBN: 978-3-642-40450-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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