Interval Stabbing Problems in Small Integer Ranges

  • Jens M. Schmidt
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5878)


Given a set I of n intervals, a stabbing query consists of a point q and asks for all intervals in I that contain q. The Interval Stabbing Problem is to find a data structure that can handle stabbing queries efficiently. We propose a new, simple and optimal approach for different kinds of interval stabbing problems in a static setting where the query points and interval ends are in {1,...,O(n)}.


interval stabbing interval intersection static discrete point enclosure 


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  1. 1.
    Alstrup, S., Brodal, G.S., Rauhe, T.: New data structures for orthogonal range searching. In: FOCS 2000, pp. 198–207 (2000)Google Scholar
  2. 2.
    Andersson, A., Hagerup, T., Nilsson, S., Raman, R.: Sorting in linear time? In: STOC 1995, pp. 427–436 (1995)Google Scholar
  3. 3.
    Beame, P., Fich, F.E.: Optimal bounds for the predecessor problem. In: STOC 1999: Proceedings of the 31st annual ACM symposium on Theory of computing, pp. 295–304. ACM, New York (1999)CrossRefGoogle Scholar
  4. 4.
    Bentley, J.L.: Solutions to Klee’s rectangle problems. Tech. report, Carnegie-Mellon Univ., Pittsburgh, PA (1977)Google Scholar
  5. 5.
    Chazelle, B.: Filtering search: A new approach to query answering. SIAM J. Comput. 15(3), 703–724 (1986)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Edelsbrunner, H.: Dynamic data structures for orthogonal intersection queries. Tech. Report F59, Inst. Informationsverarb, Tech. Univ. Graz (1980)Google Scholar
  7. 7.
    Gabow, H.N., Bentley, J.L., Tarjan, R.E.: Scaling and related techniques for geometry problems. In: STOC 1984: Proceedings of the 16th annual ACM symposium on Theory of computing, pp. 135–143 (1984)Google Scholar
  8. 8.
    McCreight, E.M.: Efficient algorithms for enumerating intersecting intervals and rectangles. Tech. Report CSL-80-9, Xerox Palo Alto Res. Center, CA (1980)Google Scholar
  9. 9.
    McCreight, E.M.: Priority search trees. SIAM Journal on Computing 14(2), 257–276 (1985)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Jens M. Schmidt
    • 1
  1. 1.Freie UniversitätBerlinGermany

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