Covering points in the plane by k-tours: Towards a polynomial time approximation scheme for general k

Tetsuo Asano, Naoki Katoh, Hisao Tamaki, Takeshi Tokuyama

Research output: Contribution to journalConference articlepeer-review

33 Citations (Scopus)

Abstract

Let P be a set of n points in the plane. A k-tour through P is a tour in the plane that starts and ends at the fixed origin and visits at most k points of P. Our goal is to cover all the points of P by k-tours so as to minimize the total length of the tours. We give a polynomial time approximation scheme (PTAS) for this problem whose running time is (k/ε)O(k/ε(3))+O(n log n). Thus, our scheme remains a PTAS when k has a nearly logarithmic dependence on n. This improves over the previous best known scheme which is a PTAS only when k = O(log log n).

Original languageEnglish
Pages (from-to)275-283
Number of pages9
JournalConference Proceedings of the Annual ACM Symposium on Theory of Computing
Publication statusPublished - 1997 Jan 1
EventProceedings of the 1997 29th Annual ACM Symposium on Theory of Computing - El Paso, TX, USA
Duration: 1997 May 41997 May 6

ASJC Scopus subject areas

  • Software

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