Concatenable segment trees

extended abstract
  • Marc J. van Kreveld
  • Mark H. Overmars
Contributed Papers Graph Algorithms
Part of the Lecture Notes in Computer Science book series (LNCS, volume 349)


In this paper a variant of a segment tree is devised on which, in addition to insertions, deletions and stabbing queries, the operations concatenate and split can be performed efficiently. Insertions, concatenations and splits take O(log n) time, deletions take O(log2n) time, stabbing queries take O(k + log n) time (where k is the number of answers to the query), and the structure uses O(n log n) space to store. The technique is based on a new general data structure that stores sets of objects, the union-copy structure, on which the operations union (of two sets), copy (of a set), insert (of an object in one or more sets), delete (of an object from all sets in which it occurs) and enumerate (of a set) can be performed efficiently.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • Marc J. van Kreveld
    • 1
  • Mark H. Overmars
    • 1
  1. 1.Department of Computer ScienceUniversity of UtrechtUtrechtthe Netherlands

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