TY - JOUR
T1 - Finding the largest empty disk containing a query point
AU - Kaplan, Haim
AU - Sharir, Micha
N1 - Funding Information:
∗Work on this paper was partially supported by the Israeli Centers of Research Excellence (I-CORE) program (Center No. 4/11). Work by Haim Kaplan was also supported by Grant 2006/204 from the U.S.–Israel Binational Science Foundation, and by Grant 822/10 from the Israel Science Fund. Work by Micha Sharir was also supported by NSF Grant CCR-08-30272, by Grant 2006/194 from the U.S.–Israel Binational Science Foundation, by Grant 338/09 from the Israel Science Fund, and by the Hermann Minkowski–MINERVA Center for Geometry at Tel Aviv University. A preliminary version of this paper appeared in Ref. 10.
PY - 2013
Y1 - 2013
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84904346242&partnerID=8YFLogxK
U2 - 10.1142/S021819591360008X
DO - 10.1142/S021819591360008X
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AN - SCOPUS:84904346242
SN - 0218-1959
VL - 23
SP - 335
EP - 355
JO - International Journal of Computational Geometry and Applications
JF - International Journal of Computational Geometry and Applications
IS - 4-5
ER -