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73
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 302 (15 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 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.
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 31 (7 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.
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 29 (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.
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 25 (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. 1 Introduction and
Revisiting T. Uno and M. Yagiura’s Algorithm
"... ... 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 19 (5 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.
Extension of Hereditary Classes With Substitutions
, 2001
"... Let G and H be graphs. A substitution of H in G instead of a vertex v 2 V (G) is the graph G(v ! H), which consists of disjoint union of H and G \Gamma v with the additional edgeset fxy : x 2 V (H); y 2 NG (v)g. For a hereditary class of graphs P , the substitutional closure of P is defined as th ..."
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Cited by 13 (9 self)
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Let G and H be graphs. A substitution of H in G instead of a vertex v 2 V (G) is the graph G(v ! H), which consists of disjoint union of H and G \Gamma v with the additional edgeset fxy : x 2 V (H); y 2 NG (v)g. For a hereditary class of graphs P , the substitutional closure of P is defined as the class P consisting of all graphs which can be obtained from graphs in P by repeated substitutions. Let P be an arbitrary hereditary class for which a characterization in terms of forbidden induced subgraphs is known. We propose a method of constructing forbidden induced subgraphs for P . RRR 142001 Page 1 1
The recognizability of sets of graphs is a robust property
"... Once the set of finite graphs is equipped with an algebra structure (arising from the definition of operations that generalize the concatenation of words), one can define the notion of a recognizable set of graphs in terms of finite congruences. Applications to the construction of efficient algorith ..."
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Cited by 13 (9 self)
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Once the set of finite graphs is equipped with an algebra structure (arising from the definition of operations that generalize the concatenation of words), one can define the notion of a recognizable set of graphs in terms of finite congruences. Applications to the construction of efficient algorithms and to the theory of contextfree sets of graphs follow naturally. The class of recognizable sets depends on the signature of graph operations. We consider three signatures related respectively to Hyperedge Replacement (HR) contextfree graph grammars, to Vertex Replacement (VR) contextfree graph grammars, and to modular decompositions of graphs. We compare the corresponding classes of recognizable sets. We show that they are robust in the sense that many variants of each signature (where in particular operations are defined by quantifierfree formulas, a quite flexible framework) yield the same notions of recognizability. We prove that for graphs without large complete bipartite subgraphs, HRrecognizability and VRrecognizability coincide. The same combinatorial condition equates HRcontextfree and VRcontextfree sets of graphs. Inasmuch as possible, results are formulated in the more general framework of relational structures. 1
A simple lineartime modular decomposition algorithm for graphs, using order extension
, 2004
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Algebraic recognizability of languages
 In Proc. 29th Int. Symp. Math. Found. of Comp. Sci. (MFCS’04
, 2004
"... Abstract. Recognizable languages of finite words are part of every computer science cursus, and they are routinely described as a cornerstone for applications and for theory. We would like to briefly explore why that is, and how this wordrelated notion extends to more complex models, such as those ..."
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Cited by 11 (3 self)
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Abstract. Recognizable languages of finite words are part of every computer science cursus, and they are routinely described as a cornerstone for applications and for theory. We would like to briefly explore why that is, and how this wordrelated notion extends to more complex models, such as those developed for modeling distributed or timed behaviors. In the beginning was the Word... Recognizable languages of finite words are part of every computer science cursus, and they are routinely described as a cornerstone for applications and for theory. We would like to briefly explore why that is, and how this wordrelated notion extends to more complex models, such as those developed for modeling distributed or timed behaviors. The notion of recognizable languages is a familiar one, associated with classical theorems by Kleene, Myhill, Nerode, Elgot, Büchi, Schützenberger, etc. It can be approached from several angles: recognizability by automata, recognizability by finite monoids or finiteindex congruences, rational expressions, monadic second