Finding the largest empty disk containing a query point

Research output: Contribution to journalArticlepeer-review


Let P be a set of n points in the plane. We present an efficient algorithm for preprocessing P, so that, for a given query point q, we can quickly report the largest disk that contains q but its interior is disjoint from P. The storage required by the data structure is O(n log n), the preprocessing cost is O(n log2 n), and a query takes O(log2 n) time. We also present an alternative solution with an improved query cost and with slightly worse storage and preprocessing requirements.

Original languageEnglish
Pages (from-to)335-355
Number of pages21
JournalInternational Journal of Computational Geometry and Applications
Issue number4-5
StatePublished - 2013


Dive into the research topics of 'Finding the largest empty disk containing a query point'. Together they form a unique fingerprint.

Cite this