最大圈分解问题的研究进展-计算机科学

第 44 卷第1 期 Vo l. 44 No. 1

计算机科学

2017 年 1 月 COMPUTER SCIENCE

Ja口.2017

最大圈分解问题的研究进展

罗卫东王建新冯启龙

(中甫大学信息科学与工程学院 长沙 410083)

摘 要 最大圈分解问题最早由 Erdös 和 Pósa 提出，随后研究人员在图论领域和理论计算机科学领域中对其进行了

广泛的探索。最近研究发现，该问题在计算生物学上特别是在构建进化树与分析基因组的研究方面有重要的应用。

主要介绍了该问题的研究现状。首先讨论了该问题在图论方面的研究进展p 随后对该问题的近似算法、参数算法、参

数复杂性与不可近似性进行了分析和讨论;最后给出了该问题的进一步研究方向。

关键词 最大圈分解，图论，近似算法，参数算法，不可近似性，参数复杂性

中图法分类号 TP30 1. 6 文献标识码 A DOI 10. 11896/j. issn. 1002-137X. 2017. 0 1. 001

Survey of Cycle Packing Problem

LUO Wei-dong W ANG Jian-xin FENG Qi-long

(School of Infonnation Science and Engineering ,Central South Universi句， Changsha 410083 ,China)

Abstract Cycle packing problem was first presented by Erdös and Pósa. Since th巳nr巳searchers hav巳 b巳en studying the

problem in graph theory and theoretical computer science. Recently ,researchers find that the problem has improtant ap-

plications in computational biology ,especially for reconstruction of evolutionary trees and genomic analysis. In this pa

per ,an introduction to the research status of this problem was give凡 First and foremost ,some results of cycle packing

problem in graph theory were discussed. Then ,we analyzed and discussed approximation algorithms ,parameterized al

gorithms ,parameterized complexity and inapproximability of the problem. At last ,some further research directions on

this problem were given.

Keywords Cycle packing , Graph theo巧， Approximation algorithms , Parameterized algorithms , Inapproximability