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112
The University of Florida sparse matrix collection
 NA DIGEST
, 1997
"... The University of Florida Sparse Matrix Collection is a large, widely available, and actively growing set of sparse matrices that arise in real applications. Its matrices cover a wide spectrum of problem domains, both those arising from problems with underlying 2D or 3D geometry (structural enginee ..."
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Cited by 538 (19 self)
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The University of Florida Sparse Matrix Collection is a large, widely available, and actively growing set of sparse matrices that arise in real applications. Its matrices cover a wide spectrum of problem domains, both those arising from problems with underlying 2D or 3D geometry (structural engineering, computational fluid dynamics, model reduction, electromagnetics, semiconductor devices, thermodynamics, materials, acoustics, computer graphics/vision, robotics/kinematics, and other discretizations) and those that typically do not have such geometry (optimization, circuit simulation, networks and graphs, economic and financial modeling, theoretical and quantum chemistry, chemical process simulation, mathematics and statistics, and power networks). The collection meets a vital need that artificiallygenerated matrices cannot meet, and is widely used by the sparse matrix algorithms community for the development and performance evaluation of sparse matrix algorithms. The collection includes software for accessing and managing the collection, from MATLAB, Fortran, and C.
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 54 (8 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.
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 ..."
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Cited by 44 (8 self)
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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.
Minimal triangulations of graphs: A survey
 DISCRETE MATHEMATICS
"... Any given graph can be embedded in a chordal graph by adding edges, and the resulting chordal graph is called a triangulation of the input graph. In this paper we study minimal triangulations, which are the result of adding an inclusion minimal set of edges to produce a triangulation. This topic was ..."
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Cited by 37 (3 self)
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Any given graph can be embedded in a chordal graph by adding edges, and the resulting chordal graph is called a triangulation of the input graph. In this paper we study minimal triangulations, which are the result of adding an inclusion minimal set of edges to produce a triangulation. This topic was first studied from the standpoint of sparse matrices and vertex elimination in graphs. Today we know that minimal triangulations are closely related to minimal separators of the input graph. Since the first papers presenting minimal triangulation algorithms appeared in 1976, several characterizations of minimal triangulations have been proved, and a variety of algorithms exist for computing minimal triangulations of both general and restricted graph classes. This survey presents and ties together these results in a unified modern notation, keeping an emphasis on the algorithms.
Efficient and practical algorithms for sequential modular decomposition
, 1999
"... A module of an undirected graph G = (V, E) is a set X of vertices that have the same set of neighbors in V \ X. The modular decomposition is a unique decomposition of the vertices into nested modules. We give a practical algorithm with an O(n + m(m;n)) time bound and a variant with a linear time bou ..."
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Cited by 36 (1 self)
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A module of an undirected graph G = (V, E) is a set X of vertices that have the same set of neighbors in V \ X. The modular decomposition is a unique decomposition of the vertices into nested modules. We give a practical algorithm with an O(n + m(m;n)) time bound and a variant with a linear time bound.
Revisiting T. Uno and M. Yagiura’s Algorithm
, 2005
"... ... of two given permutations of length n in O(n + K) time. Our paper first presents a decomposition approach to obtain a compact encoding for common intervals of d permutations. Then, we revisit T. Uno and M. Yagiura’s algorithm to yield a linear time algorithm for finding this encoding. Besides, w ..."
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Cited by 27 (8 self)
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... of two given permutations of length n in O(n + K) time. Our paper first presents a decomposition approach to obtain a compact encoding for common intervals of d permutations. Then, we revisit T. Uno and M. Yagiura’s algorithm to yield a linear time algorithm for finding this encoding. Besides, we adapt the algorithm to obtain a linear time modular decomposition of an undirected graph, and thereby propose a formal invariantbased proof for all these algorithms.
A simple lineartime modular decomposition algorithm for graphs, using order extension
, 2004
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Graph Decompositions and Factorizing Permutations
 Discrete Mathematics and Theoretical Computer Science
, 1997
"... A factorizing permutation of a given undirected graph is simply a permutation of the vertices in which all decomposition sets appear to be factors. Such a concept seems to play a central role in recent papers dealing with graph decomposition. It is applied here for modular decomposition and we propo ..."
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Cited by 17 (11 self)
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A factorizing permutation of a given undirected graph is simply a permutation of the vertices in which all decomposition sets appear to be factors. Such a concept seems to play a central role in recent papers dealing with graph decomposition. It is applied here for modular decomposition and we propose a linear algorithm that computes the whole decomposition tree when a factorizing permutation is provided. This algorithm can be seen as a common generalization of Ma and Hsu [9, 8] for modular decomposition of chordal graphs and Habib, Huchard and Spinrad [7] for inheritance graphs decomposition. It also suggests many new decomposition algorithms for various notions of graph decompositions.
A survey on Algorithmic Aspects of Modular Decomposition
, 2009
"... The modular decomposition is a technique that applies but is not restricted to graphs. The notion of module naturally appears in the proofs of many graph theoretical theorems. Computing the modular decomposition tree is an important preprocessing step to solve a larger number of combinatorial optimi ..."
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Cited by 16 (2 self)
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The modular decomposition is a technique that applies but is not restricted to graphs. The notion of module naturally appears in the proofs of many graph theoretical theorems. Computing the modular decomposition tree is an important preprocessing step to solve a larger number of combinatorial optimization problems. Since the first polynomial time algorithm in the early 70’s, the algorithmic of the modular decomposition has known an important development. This paper survey the ideas and techniques that arose from this line of research.
On Leaf Powers
"... For an integer k, a tree T is a kleaf root of a finite simple undirected graph G = (V, E) if the set of leaves of T is the vertex set V of G and for any two vertices x, y ∈ V, x ̸ = y, xy ∈ E if and only if the distance of x and y in T is at most k. Then graph G is a kleaf power if it has a kleaf ..."
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Cited by 14 (2 self)
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For an integer k, a tree T is a kleaf root of a finite simple undirected graph G = (V, E) if the set of leaves of T is the vertex set V of G and for any two vertices x, y ∈ V, x ̸ = y, xy ∈ E if and only if the distance of x and y in T is at most k. Then graph G is a kleaf power if it has a kleaf root. G is a leaf power if it is a kleaf power for some k. This notion was introduced and studied by Nishimura, Ragde and Thilikos; it has its background and motivation in computational biology and phylogeny. In this survey, we describe recent results on leaf powers, variants and generalizations. We discuss the relationship between leaf powers and strongly chordal graphs as well as fixed tolerance NeST graphs, describe some subclasses of leaf powers, give the complete inclusion structure of kleaf power classes, and describe various characterizations of 3and 4leaf powers, as well as of distancehereditary 5leaf powers. Finally we discuss two variants of the notion of kleaf power such as (k, ℓ)leaf powers and exact leaf powers, and we generalize leaf powers (of trees) to simplicial powers of graphs. Most of the presented results are part of joint work, mostly with Van Bang Le and Peter Wagner, but also with Christian Hundt, Federico Mancini, R. Sritharan, and Dieter Rautenbach.