Results 1  10
of
126
A simple 3sweep LBFS algorithm for the recognition of unit interval graphs
 DISCRETE APPLIED MATHEMATICS
, 2003
"... ..."
A foursweep LBFS recognition algorithm for interval graphs
 Submitted. URL: http://math.sjtu.edu.cn/faculty/ykwu/ 4sweepLW.pdf
"... In their 2009 paper, Corneil et al. design a linear time interval graph recognition algorithm based on six sweeps of Lexicographic BreadthFirst Search (LBFS) and prove its correctness. They believe that their corresponding 5sweep LBFS interval graph recognition algorithm is also correct. Thanks to ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
In their 2009 paper, Corneil et al. design a linear time interval graph recognition algorithm based on six sweeps of Lexicographic BreadthFirst Search (LBFS) and prove its correctness. They believe that their corresponding 5sweep LBFS interval graph recognition algorithm is also correct. Thanks
Simple Linear Time Recognition of Unit Interval Graphs
, 1998
"... We present a linear time algorithm for unit interval graph recognition. The algorithm is simple and based on BreadthFirst Search. It is also direct  it does not first recognize the graph as an interval graph. Given a graph G, the algorithm produces an ordering of the vertices of the graph whe ..."
Abstract

Cited by 44 (1 self)
 Add to MetaCart
We present a linear time algorithm for unit interval graph recognition. The algorithm is simple and based on BreadthFirst Search. It is also direct  it does not first recognize the graph as an interval graph. Given a graph G, the algorithm produces an ordering of the vertices of the graph
MultiSweep Graph Traversals and Certifying Algorithms for Interval Graph Recognition
"... Given a family of (unit) intervals on the real line, can we reconstruct its distribution (sort the intervals) from their intersection information? If we have a set of unknown objects as well as their intersection information, can we tell efficiently whether or not these objects can be a family of ..."
Abstract
 Add to MetaCart
ognizing (unit) interval graphs and we can implement these algorithms in linear time when we adopt LBFS as the MNS used. We will introduce the basic idea of multisweep graph search algorithm, some classic work on recognizing (unit) interval graphs as well as our ongoing work on interval graph recognition. Many
The Ultimate Interval Graph Recognition Algorithm? (Extended Abstract)
 PROCEEDINGS OF THE NINTH ANNUAL ACMSIAM SYMPOSIUM ON DISCRETE ALGORITHMS
, 1998
"... An independent set of three vertices is called an asteroidal triple if between every two vertices in the triple there exists a path avoiding the neighbourhood of the third. A graph is asteroidal triplefree (ATfree, for short) if it contains no asteroidal triple. A classic result states that a g ..."
Abstract

Cited by 46 (0 self)
 Add to MetaCart
graph is an interval graph if and only if it is chordal and ATfree. Our main contribution is to exhibit a very simple, lineartime, recognition algorithm for interval graphs involving four sweeps of the wellknown Lexicographic Breadth First Search. Unlike the vast majority of existing algorithms, we
A simple test for interval graphs
 Proc. 18th Int. Workshop (WG '92), GraphTheoretic Concepts in Computer Science
, 1992
"... An interval graph is the intersection graph of a collection of intervals. Interval graphs are a special class of chordal graphs. This class of graphs has a wide range of applications. Several linear time algorithms have been designed to recognize interval graphs. Booth & Lueker first used PQtre ..."
Abstract

Cited by 22 (3 self)
 Add to MetaCart
for these algorithms. Based on graph decomposition, we give a much simpler recognition algorithm in this paper which directly places the intervals without precomputing all maximal cliques. A linear time isomorphism algorithm can be easily derived as a byproduct. Another advantage of our approach is that it can
Fast and simple algorithms for recognizing chordal comparability graphs and interval graphs
 SIAM Journal on Computing
, 1999
"... Abstract. In this paper, we present a lineartime algorithm for substitution decomposition on chordal graphs. Based on this result, we develop a lineartime algorithm for transitive orientation on chordal comparability graphs, which reduces the complexity of chordal comparability recognition from O( ..."
Abstract

Cited by 19 (3 self)
 Add to MetaCart
(n 2)toO(n+m). We also devise a simple lineartime algorithm for interval graph recognition where no complicated data structure is involved. Key words. chordal graph, triangulated graph, interval graph, analysis of algorithms, graph theory, substitution decomposition, modular decomposition, cycle
Certifying LexBFS recognition algorithms for proper inteval graphs and proper interval bigraphs
 SIAM J. Discrete Math
"... Recently, D. Corneil found a simple 3sweep lexicographic breadth first search (LexBFS) algorithm for the recognition of proper interval graphs. We point out how to modify Corneil’s algorithm to make it a certifying algorithm, and then describe a similar certifying 3sweep LexBFS algorithm for the r ..."
Abstract

Cited by 21 (4 self)
 Add to MetaCart
Recently, D. Corneil found a simple 3sweep lexicographic breadth first search (LexBFS) algorithm for the recognition of proper interval graphs. We point out how to modify Corneil’s algorithm to make it a certifying algorithm, and then describe a similar certifying 3sweep LexBFS algorithm
Linear Recognition of Almost (Unit) Interval Graphs
, 2014
"... Give a graph class G and a nonnegative integer k, we use G+kv, G+ke, and G−ke to denote the classes of graphs that can be obtained from some graph in G by adding k vertices, adding k edges, and deleting k edges, respectively. They are called almost (unit) interval graphs if G is the class of (unit) ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
these classes, and in the case of membership, our algorithms provide also a specific (unit) interval graph as evidence. When k is part of the input, all the recognition problems are NPcomplete. Our results imply that all of them are fixedparameter tractable parameterized by k, thereby resolving the long
A Simple Efficient Parallel Algorithms to Recognize Chordal Graphs as Interval Graphs
 Discrete Applied Mathematics
, 1995
"... We present an efficient parallel algorithm that recognizes interval graphs, provided it is known that the given graph is chordal and a representation as a collection of subtrees of a tree is known. The running time is logarithmic and the processor number is linear. 0 Introduction Interval graph ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
, consecutive information retrieval, and gate layout problems (see for example [12, 16]). Linear time sequential algorithms to recognize interval graphs are quiet well known [3, 15]. Still there is a development to simplify the recognition of interval graphs. A parallel algorithms with a linear number
Results 1  10
of
126