Online chasing problems for regular polygons

Authors:
Hiroshi Fujiwara;Kazuo Iwama;Kouki Yonezawa
Affiliations:
Department of Informatics, Kwansei Gakuin University, 2-1 Gakuen, Sanda 669-1337, Japan;School of Informatics, Kyoto University, Yoshida-Honmachi, Kyoto 606-8501, Japan;Meme Media Laboratory, Hokkaido University Kita 13, Nishi 8, Kita-ku, Sapporo 060-8628, Japan
Venue:
Information Processing Letters
Year:
2008

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Abstract

We consider a server location problem with only one server to move. In this paper we assume that a request is given as a region and that the service can be done anywhere inside the region. Namely, for each request an online algorithm chooses an arbitrary point in the region and moves the server there. Note that if every request is a single point and the server must exactly go there in the given order as conventional server problems, there is no choice for the online player and the problem is trivial. Our main result shows that if the region is a regular n-gon, the competitive ratio of the greedy algorithm is 1/sin@p2n for odd n, and 1/sin@pn for even n. In particular for a square region, the greedy algorithm turns out to be optimal.