Results 1  10
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20
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 ..."
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Cited by 36 (7 self)
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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.
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 ..."
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Cited by 33 (13 self)
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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.
Perfect sorting by reversals is not always difficult
 IEEE/ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS
, 2007
"... We propose new algorithms for computing pairwise rearrangement scenarios that conserve the combinatorial structure of genomes. More precisely, we investigate the problem of sorting signed permutations by reversals without breaking common intervals. We describe a combinatorial framework for this prob ..."
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Cited by 26 (11 self)
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We propose new algorithms for computing pairwise rearrangement scenarios that conserve the combinatorial structure of genomes. More precisely, we investigate the problem of sorting signed permutations by reversals without breaking common intervals. We describe a combinatorial framework for this problem that allows us to characterize classes of signed permutations for which one can compute, in polynomial time, a shortest reversal scenario that conserves all common intervals. In particular, we define a class of permutations for which this computation can be done in linear time with a very simple algorithm that does not rely on the classical HannenhalliPevzner theory for sorting by reversals. We apply these methods to the computation of rearrangement scenarios between permutations obtained from 16 synteny blocks of the X chromosomes of the human, mouse, and rat.
A simple lineartime modular decomposition algorithm for graphs, using order extension
, 2004
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Hole and Antihole Detection in Graphs
, 2004
"... In this paper, we study the problems of detecting holes and antiholes in general undirected graphs and present algorithms for them, which, for a graph on n vertices and m edges, run in O(n + m²) time and require O(nm) space; we thus provide a solution to the open problem posed by Hayward, Spinrad, a ..."
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Cited by 9 (3 self)
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In this paper, we study the problems of detecting holes and antiholes in general undirected graphs and present algorithms for them, which, for a graph on n vertices and m edges, run in O(n + m²) time and require O(nm) space; we thus provide a solution to the open problem posed by Hayward, Spinrad, and Sritharan in [12] asking for an O(n^4) time algorithm for finding holes in arbitrary graphs. The key element of the algorithms is a special type of depthfirst search traversal which proceeds along P4 s (i.e., chordless paths on four vertices) of the input graph. We also describe a different approach which allows us to detect antiholes in graphs that do not contain chordless cycles on 5 vertices in O(n + m²) time requiring O(n +m) space. Our algorithms are simple and can be easily used in practice. Additionally, we show how our detection algorithms can be augmented so that they return a hole or an antihole whenever such a structure is detected in the input graph; the augmentation takes O(n +m) time and space.
A simple linear time algorithm for cograph recognition
 Discrete Applied Mathematics
, 2005
"... www.elsevier.com/locate/dam ..."
C.: Drawing graphs using modular decomposition
 Graph Drawing. Volume LNCS 3843
, 2005
"... In this paper we present an algorithm for drawing an undirected graph G that takes advantage of the structure of the modular decomposition tree of G. Specifically, our algorithm works by traversing the modular decomposition tree of the input graph G on n vertices and m edges in a bottomup fashion u ..."
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Cited by 7 (1 self)
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In this paper we present an algorithm for drawing an undirected graph G that takes advantage of the structure of the modular decomposition tree of G. Specifically, our algorithm works by traversing the modular decomposition tree of the input graph G on n vertices and m edges in a bottomup fashion until it reaches the root of the tree, while at the same time intermediate drawings are computed. In order to achieve aesthetically pleasing results, we use grid and circular placement techniques, and utilize an appropriate modification of a wellknown spring embedder algorithm. It turns out, that for some classes of graphs, our algorithm runs in O(n + m) time, while in general, the running time is bounded in terms of the processing time of the spring embedder algorithm. The result is a drawing that reveals the structure of the graph G and preserves certain aesthetic criteria.
Homogeneity vs. adjacency: generalising some graph decomposition algorithms
 In 32nd International Workshop on GraphTheoretic Concepts in Computer Science (WG), volume 4271 of LNCS
, 2006
"... Abstract. In this paper, a new general decomposition theory inspired from modular graph decomposition is presented. Our main result shows that, within this general theory, most of the nice algorithmic tools developed for modular decomposition are still efficient. This theory not only unifies the usu ..."
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Cited by 6 (2 self)
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Abstract. In this paper, a new general decomposition theory inspired from modular graph decomposition is presented. Our main result shows that, within this general theory, most of the nice algorithmic tools developed for modular decomposition are still efficient. This theory not only unifies the usual modular decomposition generalisations such as modular decomposition of directed graphs and of 2structures, but also decomposition by star cutsets. 1
Algorithms for P4comparability graph recognition and acyclic P4  transitive orientation
, 2004
"... Abstract: We consider two problems pertaining to P4comparability graphs, namely, the problem of recognizing whether a simple undirected graph is a P4comparability graph and the problem of producing an acyclic P4transitive orientation of a P4comparability graph. These problems have been considere ..."
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Cited by 6 (6 self)
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Abstract: We consider two problems pertaining to P4comparability graphs, namely, the problem of recognizing whether a simple undirected graph is a P4comparability graph and the problem of producing an acyclic P4transitive orientation of a P4comparability graph. These problems have been considered by Hoàng and Reed who described O(n 4) and O(n 5)time algorithms for their solution respectively, where n is the number of vertices of the input graph. Faster algorithms have recently been presented by Raschle and Simon, and by Nikolopoulos and Palios; the time complexity of these algorithms for either problem is O(n + m 2), where m is the number of edges of the graph. In this paper, we describe O(n m)time and O(n + m)space algorithms for the recognition and the acyclic P4transitive orientation problems on P4comparability graphs. The algorithms rely on properties of the P4components of a graph, which we establish, and on the efficient construction of the P4components by means of the BFStrees of the complement of the graph rooted at each of its vertices, without however explicitly computing the complement. Both algorithms are simple and use simple data structures. Keywords: Perfectly orderable graph, comparability graph, P4comparability graph, P4component, recognition, P4transitive orientation. 1.
On the Structure of (P_5,Gem)Free Graphs
, 2002
"... We give a complete structure description of (P 5 ,gem)free graphs. By the results of a related paper, this implies bounded clique width for this graph class. Hereby, as usual, the P 5 is the induced path with five vertices a; b; c; d; e and four edges ab; bc; cd; de, and the gem consists of a P ..."
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Cited by 5 (3 self)
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We give a complete structure description of (P 5 ,gem)free graphs. By the results of a related paper, this implies bounded clique width for this graph class. Hereby, as usual, the P 5 is the induced path with five vertices a; b; c; d; e and four edges ab; bc; cd; de, and the gem consists of a P 4 a; b; c; d with edges ab; bc; cd plus a universal vertex e adjacent to a; b; c; d.