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¥ 42.2 6.2折 ¥ 68 全新
库存14件
作者张晓岩,张赞波[著]
出版社科学出版社
ISBN9787030495020
出版时间2017-01
版次1
装帧平装
开本小16开
定价68元
货号R_8880472
上书时间2022-01-31
这项研究工作主要介绍几年我们从组合优化、算法、计算复杂性及结构图论领域的图划分问题和与匹配问题相关的系列问题中选择出的若干重要问题的研究成果。全书内容共分为七章,对全书的结构、各部分的关联和主要结体介绍,其余六章内容均可独立成篇(已发表在重要SCI学术期刊上),其中前三章主要介绍若干顶点划分问题的计算复杂性和算法分析,后三章主要对与匹配问题相关的若干重要图论问行结构研究,其中匹配问题也可看作是一种边划分问题。
This work is our selected results of research on graph partitioning and matching problems in the field of theoretical computer science and structural graph theory in recent years. After an introductory chapter, the reader will find six chapters, each of which is written as a self-contained content. In the first part of the work, Chapter 2 through 4, we concentrate on the complexity, inapproximability, approximation algorithms and on-line algorithms of some graph vertex partitioning problems. In the second part of the work, Chapter 5 through 7, we focus on the structural properties of some graph problems related to matching wluch can be regarded as edge partitioning problems. We refer to the listed chapters for the details of the results.
Chapter 1 contains a short general introduction to the topics of the book and gives an overview of the main results, together with some motivation and connections to and relationships with older results. Specific terminology and notation can be found juefore each of the topic8.
In Chapter 2, we first investigate the computational complexity of problems of determining the minimum number of monochromatic cliques or rainbow cycles that, respectively, partition the vertex set V(G) of a graph G. We show that the minimum monochromatic clique partition problem is APX-hard on K4 -free graphs and monochromatic-K4 -free graphs, and APX-complete on monochromatic-K4 - free graphs in which the size of a max:imum monochromatic clique iounded by a constant. We also show that the minimum rainbow cycle partition problem is NP-complete, even if the input graph G is triangle-free. Moreover, for the weighted version of the minimum monochromatic clique partition problem on monochromatic-K4 -free graphs, we derive an approximation algorithm with (tight) approximation guarantee In |V (G)|+1.
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