Random Sequential Covering of a Sphere with Identical Spherical Caps

Teruhisa Sugimoto¹ and Masaharu Tanemura²

¹Department of Statistical Science, The Graduate University for Advanced Studies, 4-6-7 Minami-Azabu, Minato-ku, Tokyo 106-8569, Japan
²The Institute of Statistical Mathematics; Department of Statistical Science, The Graduate University for Advanced Studies, 4-6-7 Minami-Azabu, Minato-ku, Tokyo 106-8569, Japan

(Received August 31, 2001; Accepted October 15, 2001)

Keywords: Sphere, Covering, Spherical Cap, Minkowski Set

Abstract. The coverage problem on the sphere is studied. We consider the sequential covering of identical spherical caps, so that none of them contains the center of another one. Set of the center points of such caps is said to form a Minkowski set. We give an algorithm of random sequential covering under the condition of Minkowski set.