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).
|Number of pages||9|
|Journal||Conference Proceedings of the Annual ACM Symposium on Theory of Computing|
|Publication status||Published - 1997 Jan 1|
|Event||Proceedings of the 1997 29th Annual ACM Symposium on Theory of Computing - El Paso, TX, USA|
Duration: 1997 May 4 → 1997 May 6
ASJC Scopus subject areas