Results 21  30
of
478
On the Embedding Phase of the Hopcroft and Tarjan Planarity Testing Algorithm
 ALGORITHMICA
, 1994
"... We give a detailed description of the embedding phase of the Hopcroft and Tarjan planarity testing algorithm. The embedding phase runs in linear time. An implementation based on this paper can be found in [MMN93]. ..."
Abstract

Cited by 36 (6 self)
 Add to MetaCart
We give a detailed description of the embedding phase of the Hopcroft and Tarjan planarity testing algorithm. The embedding phase runs in linear time. An implementation based on this paper can be found in [MMN93].
LinearTime Recognition of CircularArc Graphs
 Algorithmica
, 2003
"... A graph G is a circulararc graph if it is the intersection graph of a set of arcs on a circle. That is, there is one arc for each vertex of G, and two vertices are adjacent in G if and only if the corresponding arcs intersect. We give a lineartime algorithm for recognizing this class of graphs. W ..."
Abstract

Cited by 36 (7 self)
 Add to MetaCart
A graph G is a circulararc graph if it is the intersection graph of a set of arcs on a circle. That is, there is one arc for each vertex of G, and two vertices are adjacent in G if and only if the corresponding arcs intersect. We give a lineartime algorithm for recognizing this class of graphs. When G is a member of the class, the algorithm gives a certificate in the form of a set of arcs that realize it.
The Ultimate Interval Graph Recognition Algorithm? (Extended Abstract)
 Proceedings of the Ninth Annual ACMSIAM Symposium on Discrete Algorithms
, 1998
"... ) Derek G. Corneil Stephan Olariu y Lorna Stewart z Summary of Results 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 ..."
Abstract

Cited by 36 (0 self)
 Add to MetaCart
) Derek G. Corneil Stephan Olariu y Lorna Stewart z Summary of Results 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 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 do not use maximal cliques in our algorithm  we rely, instead, on a less wellknown characterization by a linear order of the vertices. 1 Introduction Interval graphs arise naturally in the process of modeling reallife situations, especially those involving time dependencies or other restrictions that are linear...
PC trees and circularones arrangements
 Theoretical Computer Science
"... A 01 matrix has the consecutiveones property if its columns can be ordered so that the ones in every row are consecutive. It has the circularones property if its columns can be ordered so that, in every row, either the ones or the zeros are consecutive. PQ trees are used for representing all cons ..."
Abstract

Cited by 35 (4 self)
 Add to MetaCart
A 01 matrix has the consecutiveones property if its columns can be ordered so that the ones in every row are consecutive. It has the circularones property if its columns can be ordered so that, in every row, either the ones or the zeros are consecutive. PQ trees are used for representing all consecutiveones orderings of the columns of a matrix that has the consecutiveones property. We give an analogous structure, called a PC tree, for representing all circularones orderings of the columns of a matrix that has the circularones property. No such representation has been given previously. In contrast to PQ trees, PC trees are unrooted. We obtain a much simpler algorithm for computing PQ trees that those that were previously available, by adding a zero column, x, to a matrix, computing the PC tree, and then picking the PC tree up by x to root it. 1
Planarizing Graphs  A Survey and Annotated Bibliography
, 1999
"... Given a finite, undirected, simple graph G, we are concerned with operations on G that transform it into a planar graph. We give a survey of results about such operations and related graph parameters. While there are many algorithmic results about planarization through edge deletion, the results abo ..."
Abstract

Cited by 32 (0 self)
 Add to MetaCart
Given a finite, undirected, simple graph G, we are concerned with operations on G that transform it into a planar graph. We give a survey of results about such operations and related graph parameters. While there are many algorithmic results about planarization through edge deletion, the results about vertex splitting, thickness, and crossing number are mostly of a structural nature. We also include a brief section on vertex deletion. We do not consider parallel algorithms, nor do we deal with online algorithms.
SNPs Problems, Complexity and Algorithms
, 2001
"... Single nucleotide polymorphisms (SNPs) are the most frequent form of human genetic variation. They are of fundamental importance for a variety of applications including medical diagnostic and drug design. They also provide the highestresolution genomic fingerprint for tracking disease genes. Th ..."
Abstract

Cited by 32 (10 self)
 Add to MetaCart
Single nucleotide polymorphisms (SNPs) are the most frequent form of human genetic variation. They are of fundamental importance for a variety of applications including medical diagnostic and drug design. They also provide the highestresolution genomic fingerprint for tracking disease genes. This paper is devoted to algorithmic problems related to computational SNPs validation based on genome assembly of diploid organisms. In diploid genomes, there are two copies of each chromosome. A description
Maximum Planar Subgraphs and Nice Embeddings: Practical Layout Tools
 ALGORITHMICA
, 1996
"... ..."
Certifying algorithms for recognizing interval graphs and permutation graphs
 SIAM J. COMPUT
, 2006
"... A certifying algorithm for a problem is an algorithm that provides a certificate with each answer that it produces. The certificate is a piece of evidence that proves that the answer has not been compromised by a bug in the implementation. We give lineartime certifying algorithms for recognition o ..."
Abstract

Cited by 31 (7 self)
 Add to MetaCart
A certifying algorithm for a problem is an algorithm that provides a certificate with each answer that it produces. The certificate is a piece of evidence that proves that the answer has not been compromised by a bug in the implementation. We give lineartime certifying algorithms for recognition of interval graphs and permutation graphs, and for a few other related problems. Previous algorithms fail to provide supporting evidence when they claim that the input graph is not a member of the class. We show that our certificates of nonmembership can be authenticated in O(V) time.
Reversal distance without hurdles and fortresses
 Lecture Notes in Computer Science
, 2004
"... Abstract. This paper presents an elementary proof of the HannenhalliPevzner theorem on the reversal distance of two signed permutations. It uses a single PQtree to encode the various features of a permutation. The parameters called hurdles and fortress are replaced by a single one, whose value is ..."
Abstract

Cited by 30 (3 self)
 Add to MetaCart
Abstract. This paper presents an elementary proof of the HannenhalliPevzner theorem on the reversal distance of two signed permutations. It uses a single PQtree to encode the various features of a permutation. The parameters called hurdles and fortress are replaced by a single one, whose value is computed by a simple and efficient algorithm. 1
Computing common intervals of K permutations, with applications to modular decomposition of graphs
, 2008
"... We introduce a new approach to compute the common intervals of K permutations based on a very simple and general notion of generators of common intervals. This formalism leads to simple and efficient algorithms to compute the set of all common intervals of K permutations, that can contain a quadrat ..."
Abstract

Cited by 30 (13 self)
 Add to MetaCart
We introduce a new approach to compute the common intervals of K permutations based on a very simple and general notion of generators of common intervals. This formalism leads to simple and efficient algorithms to compute the set of all common intervals of K permutations, that can contain a quadratic number of intervals, as well as a linear space basis of this set of common intervals. Finally, we show how our results on permutations can be used for computing the modular decomposition of graphs.