Orthogonal Queries in Segments

Takeshi Tokuyama

Research output: Contribution to journalArticlepeer-review


We consider the orthgonal clipping problem in a set of segments: Given a set of n segments in d-dimensional space, we preprocess them into a data structure such that given an orthogonal query window, the segments intersecting it can be counted/reported efficiently. We show that the efficiency of the data structure significantly depends on a geometric discrete parameter K named the projected-image complexity, which becomes Θ (n2) in the worst case but practically much smaller. If we use O(m) space, where K log4d-7 n ≥ m ≥ n log4d-7 n, the query time is O((K/m)1/2 logmax{4,4d-5} n). This is near to an Ω((K/m)1/2) lower bound.

Original languageEnglish
Pages (from-to)229-245
Number of pages17
JournalAlgorithmica (New York)
Issue number2
Publication statusPublished - 1997 Jun
Externally publishedYes


  • Algorithms
  • Clipping
  • Computational geometry
  • Range searching

ASJC Scopus subject areas

  • Computer Science(all)
  • Computer Science Applications
  • Applied Mathematics


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