کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
414252 680861 2015 15 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
On the approximability of covering points by lines and related problems
ترجمه فارسی عنوان
در تقریب پذیری نقاط پوشش توسط خطوط و مشکلات مرتبط
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر نظریه محاسباتی و ریاضیات
چکیده انگلیسی

Given a set P of n points in the plane, Covering Points by Lines is the problem of finding a minimum-cardinality set LL of lines such that every point p∈Pp∈P is incident to some line ℓ∈Lℓ∈L. As a geometric variant of Set Cover, Covering Points by Lines is still NP-hard. Moreover, it has been proved to be APX-hard, and hence does not admit any polynomial-time approximation scheme unless P = NP. In contrast to the small constant approximation lower bound implied by APX-hardness, the current best approximation ratio for Covering Points by Lines is still O(log⁡n)O(log⁡n), namely the ratio achieved by the greedy algorithm for Set Cover.In this paper, we give a lower bound of Ω(log⁡n)Ω(log⁡n) on the approximation ratio of the greedy algorithm for Covering Points by Lines. We also study several related problems including Maximum Point Coverage by Lines, Minimum-Link Covering Tour, Minimum-Link Spanning Tour, and Min–Max-Turn Hamiltonian Tour. We show that all these problems are either APX-hard or at least NP-hard. In particular, our proof of APX-hardness of Min–Max-Turn Hamiltonian Tour sheds light on the difficulty of Bounded-Turn-Minimum-Length Hamiltonian Tour, a problem proposed by Aggarwal et al. at SODA 1997.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Computational Geometry - Volume 48, Issue 9, October 2015, Pages 703–717
نویسندگان
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