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New Results on Three-Sided Skyline Range Counting and Reporting

Authors Suruchi Kushwaha , Yakov Nekrich

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LIPIcs.SWAT.2026.27.pdf
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Subject Classification

ACM Subject Classification
  • Theory of computation → Data structures design and analysis
Keywords
  • Data Structures
  • Range Searching
  • Skyline Queries

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Abstract

In the orthogonal skyline range counting (resp. reporting) problem we store the set of points P in a data structure so that for any query range Q the number of points (resp. the list of all points) on the skyline of Q∩ P can be found efficiently. In this paper we study two-dimensional range counting and reporting problems in the case when the query range is bounded on three sides. 
We describe a linear-space data structure that answers top-open three-sided skyline counting queries in O(log log N) time, where N is the number of points stored in the data structure. We also show that bottom-open three-sided skyline counting queries are as difficult as general four-sided queries and any data structure that uses O(Nlog^c N) space for a constant c requires Ω(log N/log log N) time to answer such queries. 
Next, we turn to skyline color range queries. In this variant of the problem each point in P is assigned a color and we must count (resp. report) the distinct colors of point on the skyline of Q∩ P. We describe an O(N)-space data structure that answers top-open three-sided color counting queries in O(log N/log log N) time. Finally, we study top-open three-sided skyline color reporting in the EM model and describe a data structure that uses linear space and answers queries in O(k/B+1) I/Os where k is the number of colors on the skyline. This is the first external-memory data structure with optimal query cost and space usage for this problem.

Cite As Get BibTex

Suruchi Kushwaha and Yakov Nekrich. New Results on Three-Sided Skyline Range Counting and Reporting. In 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 370, pp. 27:1-27:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.SWAT.2026.27

Author Details

Suruchi Kushwaha
  • Michigan Technological University, Houghton, MI, USA
Yakov Nekrich
  • Michigan Technological University, Houghton, MI, USA

References

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