Polynomial-time approximation scheme for a Euclidean problem on a cycle covering of a graph

被引：0

作者：

Khachai, M. Yu. ^{[1
]}

Neznakhina, E. D. ^{[2
]}

机构：

[1] Yeltsin Ural Fed Univ, Russian Acad Sci, Ural Branch, Inst Math & Mech,Phys Mat Sci, Ekaterinburg, Russia

[2] Yeltsin Ural Fed Univ, Russian Acad Sci, Ural Branch, Inst Math & Mech, Ekaterinburg, Russia

来源：

TRUDY INSTITUTA MATEMATIKI I MEKHANIKI URO RAN | 2014年 / 20卷 / 04期

关键词：

NP-hard problem; polynomial-time approximation scheme (PTAS); traveling salesman problem (TSP); cycle covering of size k;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the Min-k-SCCP problem on a partition of a complete weighted digraph into k vertex-disjoint cycles of minimum total weight. This problem is a natural generalization of the known Traveling salesman problem (TSP) and has a number of applications in operations research and data analysis. We show that the problem is strongly NP-hard and preserves intractability even in the geometric statement. For a metric special case of the problem, a new polynomial 2-approximation algorithm is proposed. For the Euclidean Min-2-SCCP, a polynomial-time approximation scheme based on Arora's approach is built.

引用

页码：297 / 311

页数：15

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