当前位置: X-MOL 学术arXiv.cs.DM › 论文详情
U-Bubble Model for Mixed Unit Interval Graphs and its Applications: The MaxCut Problem Revisited
arXiv - CS - Discrete Mathematics Pub Date : 2020-02-19 , DOI: arxiv-2002.08311
Jan Kratochvíl; Tomáš Masařík; Jana Novotná

Interval graphs, intersection graphs of segments on a real line (intervals), play a key role in the study of algorithms and special structural properties. Unit interval graphs, their proper subclass, where each interval has a unit length, has also been extensively studied. We study mixed unit interval graphs; a generalization of unit interval graphs where each interval has still a unit length, but intervals of more than one type (open, closed, semi-closed) are allowed. This small modification captures a much richer class of graphs. In particular, mixed unit interval graphs are not claw-free, compared to unit interval graphs. Heggernes, Meister, and Papadopoulos defined a representation of unit interval graphs called the bubble model which turned out to be useful in algorithm design. We extend this model to the class of mixed unit interval graphs. The original bubble model was used by Boyaci, Ekim, and Shalom for proving the polynomiality of the MaxCut problem on unit interval graphs. However, we found a significant mistake in the proof which seems to be hardly repairable. Moreover, we demonstrate the advantages of such a model by providing a subexponential-time algorithm solving the MaxCut problem on mixed unit interval graphs using our extended version of the bubble model. In addition, it gives us a polynomial-time algorithm for specific mixed unit interval graphs; that improves a state-of-the-art result even for unit interval graphs. We further provide a better algorithmic upper-bound on the clique-width of mixed unit interval graphs. Clique-width is one of the most general structural graph parameters, where a large group of natural problems is still solvable in the tracktable time when an efficient representation is given. Unfortunately, the exact computation of the clique-width representation is NP-hard. Therefore, good upper-bounds on clique-width are highly appreciated.
更新日期:2020-02-20

 

全部期刊列表>>
向世界展示您的会议墙报和演示文稿
全球疫情及响应:BMC Medicine专题征稿
欢迎探索2019年最具下载量的化学论文
新版X-MOL期刊搜索和高级搜索功能介绍
化学材料学全球高引用
ACS材料视界
x-mol收录
自然科研论文编辑服务
南方科技大学
南方科技大学
西湖大学
中国科学院长春应化所于聪-4-8
复旦大学
课题组网站
X-MOL
深圳大学二维材料实验室张晗
中山大学化学工程与技术学院
试剂库存
天合科研
down
wechat
bug