TY - GEN

T1 - Optimal cover of points by disks in a simple polygon

AU - Kaplan, Haim

AU - Katz, Matthew J.

AU - Morgenstern, Gila

AU - Sharir, Micha

PY - 2010/11/19

Y1 - 2010/11/19

N2 - Let P be a simple polygon, and let Q be a set of points in P. We present an almost-linear time algorithm for computing a minimum cover of Q by disks that are contained in P. We generalize the algorithm above, so that it can compute a minimum cover of Q by homothets of any fixed compact convex set of constant description complexity that are contained in P. This improves previous results of Katz and Morgenstern [20]. We also consider the disk-cover problem when Q is contained in a (not too wide) annulus, and present a nearly linear algorithm for this case too.

AB - Let P be a simple polygon, and let Q be a set of points in P. We present an almost-linear time algorithm for computing a minimum cover of Q by disks that are contained in P. We generalize the algorithm above, so that it can compute a minimum cover of Q by homothets of any fixed compact convex set of constant description complexity that are contained in P. This improves previous results of Katz and Morgenstern [20]. We also consider the disk-cover problem when Q is contained in a (not too wide) annulus, and present a nearly linear algorithm for this case too.

UR - http://www.scopus.com/inward/record.url?scp=78249265643&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-15775-2_41

DO - 10.1007/978-3-642-15775-2_41

M3 - Conference contribution

AN - SCOPUS:78249265643

SN - 3642157742

SN - 9783642157745

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 475

EP - 486

BT - Algorithms, ESA 2010 - 18th Annual European Symposium, Proceedings

T2 - 18th Annual European Symposium on Algorithms, ESA 2010

Y2 - 6 September 2010 through 8 September 2010

ER -