TY - JOUR
T1 - Computing the smallest k-enclosing circle and related problems
AU - Efrat, Alon
AU - Sharir, Micha
AU - Ziv, Alon
N1 - Funding Information:
*Work on this paper by the second author has been supported by NSF Grant CCR-91-22103, and by grants from the U.S.-Israeli Binational Science Foundation, the G.I.F., the German-Israeli Foundation for Scientific Research and Development, and the Fund for Basic Research administered by the Israeli Academy of Sciences. * Corresponding author.
PY - 1994/7
Y1 - 1994/7
N2 - We present an efficient algorithm for solving the "smallest k-enclosing circle" (kSC) problem: Given a set of n points in the plane and an integer k ≤ n, find the smallest disk containing k of the points. We present two solutions. When using O(nk) storage, the problem can be solved in time O(nk log2 n). When only O(n log n) storage is allowed, the running time is O(nk log2 n log n/k). We also extend our technique to obtain efficient solutions of several related problems (with similar time and storage bounds). These related problems include: finding the smallest homothetic copy of a given convex polygon P which contains k points from a given planar set, and finding the smallest disk intersecting k segments from a given planar set of non-intersecting segments.
AB - We present an efficient algorithm for solving the "smallest k-enclosing circle" (kSC) problem: Given a set of n points in the plane and an integer k ≤ n, find the smallest disk containing k of the points. We present two solutions. When using O(nk) storage, the problem can be solved in time O(nk log2 n). When only O(n log n) storage is allowed, the running time is O(nk log2 n log n/k). We also extend our technique to obtain efficient solutions of several related problems (with similar time and storage bounds). These related problems include: finding the smallest homothetic copy of a given convex polygon P which contains k points from a given planar set, and finding the smallest disk intersecting k segments from a given planar set of non-intersecting segments.
KW - Geometric optimization
KW - Smallest enclosing circle
UR - http://www.scopus.com/inward/record.url?scp=38149145977&partnerID=8YFLogxK
U2 - 10.1016/0925-7721(94)90003-5
DO - 10.1016/0925-7721(94)90003-5
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AN - SCOPUS:38149145977
SN - 0925-7721
VL - 4
SP - 119
EP - 136
JO - Computational Geometry: Theory and Applications
JF - Computational Geometry: Theory and Applications
IS - 3
ER -