Taking a walk in a planar arrangement

Research output: Contribution to journalConference articlepeer-review


We present a randomized algorithm for computing portions of an arrangement of n arcs in the plane, each pair of which intersect in at most t points. We use this algorithm to perform online walks inside such an arrangement (i.e., compute all the faces that a curve, given in an online manner, crosses), and to compute a level in an arrangement, both in an output-sensitive manner. The expected running time of the algorithm is O(λt+2(m + n) log n), where m is the number of intersections between the walk and the given arcs. No similarly efficient algorithm is known for the general case of arcs. For the case of lines and for certain restricted cases involving line segments, our algorithm improves the best known algorithm of [15] by almost a logarithmic factor.

Original languageEnglish (US)
Pages (from-to)100-110
Number of pages11
JournalAnnual Symposium on Foundations of Computer Science - Proceedings
StatePublished - 1999
Externally publishedYes
EventProceedings of the 1999 IEEE 40th Annual Conference on Foundations of Computer Science - New York, NY, USA
Duration: Oct 17 1999Oct 19 1999

ASJC Scopus subject areas

  • Hardware and Architecture


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