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The NPcompleteness column: an ongoing guide
 Journal of Algorithms
, 1985
"... This is the nineteenth edition of a (usually) quarterly column that covers new developments in the theory of NPcompleteness. The presentation is modeled on that used by M. R. Garey and myself in our book ‘‘Computers and Intractability: A Guide to the Theory of NPCompleteness,’ ’ W. H. Freeman & Co ..."
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Cited by 188 (0 self)
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This is the nineteenth edition of a (usually) quarterly column that covers new developments in the theory of NPcompleteness. The presentation is modeled on that used by M. R. Garey and myself in our book ‘‘Computers and Intractability: A Guide to the Theory of NPCompleteness,’ ’ W. H. Freeman & Co., New York, 1979 (hereinafter referred to as ‘‘[G&J]’’; previous columns will be referred to by their dates). A background equivalent to that provided by [G&J] is assumed, and, when appropriate, crossreferences will be given to that book and the list of problems (NPcomplete and harder) presented there. Readers who have results they would like mentioned (NPhardness, PSPACEhardness, polynomialtimesolvability, etc.) or open problems they would like publicized, should
Modular Decomposition and Transitive Orientation
, 1999
"... A module of an undirected graph is a set X of nodes such for each node x not in X, either every member of X is adjacent to x, or no member of X is adjacent to x. There is a canonical linearspace representation for the modules of a graph, called the modular decomposition. Closely related to modular ..."
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Cited by 90 (14 self)
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A module of an undirected graph is a set X of nodes such for each node x not in X, either every member of X is adjacent to x, or no member of X is adjacent to x. There is a canonical linearspace representation for the modules of a graph, called the modular decomposition. Closely related to modular decomposition is the transitive orientation problem, which is the problem of assigning a direction to each edge of a graph so that the resulting digraph is transitive. A graph is a comparability graph if such an assignment is possible. We give O(n +m) algorithms for modular decomposition and transitive orientation, where n and m are the number of vertices and edges of the graph. This gives linear time bounds for recognizing permutation graphs, maximum clique and minimum vertex coloring on comparability graphs, and other combinatorial problems on comparability graphs and their complements.
Lineartime transitive orientation
 In Proceedings of the Eighth Annual ACMSIAM Symposium on Discrete Algorithms
, 1997
"... The transitive orientation problem is the problem of assigning a direction to each edge of a graph so that the resulting digraph is transitive. A graph is a comparability graph if such an assignment is possible. We describe an O(n + m) algorithm for the transitive orientation problem, where n and m ..."
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Cited by 21 (2 self)
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The transitive orientation problem is the problem of assigning a direction to each edge of a graph so that the resulting digraph is transitive. A graph is a comparability graph if such an assignment is possible. We describe an O(n + m) algorithm for the transitive orientation problem, where n and m are the number of vertices and edges of the graph; full details are given in [IS]. This gives linear time bounds for maximum clique and minimum vertex coloring on comparability graphs, recognition of twodimensional partial orders, permutation graphs, cointerval graphs, and triangulated comparability graphs, and other combinatorial problems on comparability graphs and their complements.
Some Results on Ongoing Research on Parallel Implementation of Graph Algorithms
, 1997
"... In high performance computing, three recognized important points are usability, scalability and portability. No models seemed to satisfy these three steps till recently: a few proposed models try to fulfill the previous goals. Among them, the BSPlike CGM model seemed adapted to us to facilitate the ..."
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Cited by 2 (2 self)
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In high performance computing, three recognized important points are usability, scalability and portability. No models seemed to satisfy these three steps till recently: a few proposed models try to fulfill the previous goals. Among them, the BSPlike CGM model seemed adapted to us to facilitate the way between algorithms design and real implementations. Many algorithms have been designed but few implementations have been carried out to demonstrate the practical relevance of this model. In this article, we propose to test this model actually on an irregular problem. We present the results of implementations of permutation graph algorithms written in two different models: the PRAM and the BSPlike CGM model. These implementation have been made on a CM5 and a PC cluster. We compare the results of these implementations with the performances of sequential code for this problem. With a classical problem in gaph theory, we validate BSPlike CGM model: it is possible to write portable code o...
The Handling of Graphs on PC Clusters: A Coarse Grained Approach
, 2000
"... We study the relationship between the design and analysis of graph algorithms in the coarsed grained parallel models and the behavior of the resulting code on clusters. We conclude that the coarse grained multicomputer model (CGM) is well suited to design competitive algorithms, and that it is there ..."
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We study the relationship between the design and analysis of graph algorithms in the coarsed grained parallel models and the behavior of the resulting code on clusters. We conclude that the coarse grained multicomputer model (CGM) is well suited to design competitive algorithms, and that it is thereby now possible to aim to develop portable, predictable and efficient parallel code for graph problems on clusters.
Feasibility, Portability, . . . Grained Graph Algorithms
, 2000
"... We study the relationship between the design and analysis of graph algorithms in the coarsed grained parallel models and the behavior of the resulting code on todays parallel machines and clusters. We conclude that the coarse grained multicomputer model (CGM) is well suited to design competitive al ..."
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We study the relationship between the design and analysis of graph algorithms in the coarsed grained parallel models and the behavior of the resulting code on todays parallel machines and clusters. We conclude that the coarse grained multicomputer model (CGM) is well suited to design competitive algorithms, and that it is thereby now possible to aim to develop portable, predictable and efficient parallel algorithms code for graph problems.