Maximal Neighborhood Search and Rigid Interval Graphs

Q3 Mathematics

Journal of Graph Algorithms and Applications Pub Date : 2013-01-01 DOI:10.7155/jgaa.00293

Peng Li, Yaokun Wu

引用次数: 2

Abstract

A rigid interval graph is an interval graph which has only one clique tree. In 2009, Panda and Das show that all connected unit interval graphs are rigid interval graphs. Generalizing the two classic graph search algorithms, Lexicographic Breadth-First Search (LBFS) and Maximum Cardinality Search (MCS), Corneil and Krueger propose in 2008 the so-called Maximal Neighborhood Search (MNS) and show that one sweep of MNS is enough to recognize chordal graphs. We develop the MNS properties of rigid interval graphs and characterize this graph class in several dierent ways. This allows us obtain several linear time multi-sweep MNS algorithms for recognizing rigid interval graphs and unit interval graphs, generalizing a corresponding 3-sweep LBFS algorithm for unit interval graph recognition designed by Corneil in 2004. For unit interval graphs, we even present a new linear time 2-sweep MNS certifying recognition algorithm.

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最大邻域搜索与刚性区间图

刚性区间图是只有一个团树的区间图。2009年，Panda和Das证明了所有连通的单位区间图都是刚性区间图。Corneil和Krueger在2008年推广了两种经典的图搜索算法，字典宽度优先搜索(LBFS)和最大基数搜索(MCS)，提出了所谓的最大邻域搜索(MNS)，并表明一次扫描MNS就足以识别弦图。我们发展了刚性区间图的MNS性质，并以几种不同的方式描述了这类图。这使得我们获得了几种用于识别刚性区间图和单位区间图的线性时间多扫描MNS算法，并推广了Corneil在2004年设计的用于单位区间图识别的相应3扫描LBFS算法。对于单位间隔图，我们甚至提出了一种新的线性时间2扫描MNS认证识别算法。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Graph Algorithms and Applications Mathematics-Geometry and Topology

CiteScore

1.20

自引率

0.00%

发文量

审稿时长

50 weeks

期刊介绍： The Journal of Graph Algorithms and Applications (JGAA) is a peer-reviewed scientific journal devoted to the publication of high-quality research papers on the analysis, design, implementation, and applications of graph algorithms. JGAA is supported by distinguished advisory and editorial boards, has high scientific standards and is distributed in electronic form. JGAA is a gold open access journal that charges no author fees. Topics of interest for JGAA include but are not limited to: Design and analysis of graph algorithms: exact and approximation graph algorithms; centralized and distributed graph algorithms; static and dynamic graph algorithms; internal- and external-memory graph algorithms; sequential and parallel graph algorithms; deterministic and randomized graph algorithms. Experiences with graph and network algorithms: animations; experimentations; implementations. Applications of graph and network algorithms: biomedical informatics; computational biology; computational geometry; computer graphics; computer-aided design; computer and interconnection networks; constraint systems; databases; economic networks; graph drawing; graph embedding and layout; knowledge representation; multimedia; social networks; software engineering; telecommunication networks; user interfaces and visualization; VLSI circuits.