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58
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 93 (12 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 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 37 (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.
On Coloring Unit Disk Graphs
 ALGORITHMICA
, 1994
"... In this paper the coloring problem for unit disk (UD) graphs is considered. UD graphs are the intersection graphs of equal sized disks in the plane. Colorings of UD graphs arise in the study of channel assignment problems in broadcast networks. Improving on a result of Clark, Colbourn and Johnson (1 ..."
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Cited by 37 (0 self)
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In this paper the coloring problem for unit disk (UD) graphs is considered. UD graphs are the intersection graphs of equal sized disks in the plane. Colorings of UD graphs arise in the study of channel assignment problems in broadcast networks. Improving on a result of Clark, Colbourn and Johnson (1990) it is shown that the coloring problem for UD graphs remains NPcomplete for any fixed number of colors k 3. Furthermore, a 3approximation algorithm for the problem is presented which is based on network flow and matching techniques, and it is pointed out how this technique can be applied to more general classes of disk graphs.
Optimal FPGA Module Placement with Temporal Precedence Constraints
 IN PROC. DATE 2001, DESIGN, AUTOMATION AND TEST IN EUROPE
, 2001
"... We consider the optimal placement of hardware modules in space and time for FPGA architectures with reconfiguration capabilities, where modules are modeled as threedimensional boxes in space and time. Using a graphtheoretic characterization of feasible packings, we are able to solve the following p ..."
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Cited by 35 (5 self)
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We consider the optimal placement of hardware modules in space and time for FPGA architectures with reconfiguration capabilities, where modules are modeled as threedimensional boxes in space and time. Using a graphtheoretic characterization of feasible packings, we are able to solve the following problems: (a) Find the minimal execution time of the given problem on an FPGA of fixed size, (b) Find the FPGA of minimal size to accomplish the tasks within a fixed time limit. Furthermore, our approach is perfectly suited for the treatment of precedence constraints for the sequence of tasks, which are present in virtually all practical instances. Additional mathematical structures are developed that lead to a powerful framework for computing optimal solutions. The usefulness is illustrated by computational results.
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 32 (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.
A simple lineartime modular decomposition algorithm for graphs, using order extension
, 2004
"... ..."
The Mutual Exclusion Scheduling Problem for Permutation and Comparability Graphs
, 1998
"... In this paper, we consider the mutual exclusion scheduling problem for comparability graphs. Given an undirected graph G and a fixed constant m, the problem is to find a minimum coloring of G such that each color is used at most m times. The complexity of this problem for comparability graphs was me ..."
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Cited by 13 (1 self)
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In this paper, we consider the mutual exclusion scheduling problem for comparability graphs. Given an undirected graph G and a fixed constant m, the problem is to find a minimum coloring of G such that each color is used at most m times. The complexity of this problem for comparability graphs was mentioned as an open problem by MÃ¶hring (1985) and for permutation graphs (a subclass of comparability graphs) as an open problem by Lonc (1991). We prove that this problem is already NPcomplete for permutation graphs and for each fixed constant m >= 6.
NC algorithms for comparability graphs, interval graphs, and unique perfect matching
 Proc. 5th Conf. Found. Software Technology and Theor. Comput. Sci., volume 206 of Lect. Notes in Comput. Sci
, 1985
"... Laszlo Lovasz recently posed the following problem: \Is there an NC algorithm for testing if a given graph has a unique perfect matching?" We present suchan algorithm for bipartite graphs. We also give NC algorithms for obtaining a transitive orientation of a comparability graph, and an interva ..."
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Cited by 12 (0 self)
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Laszlo Lovasz recently posed the following problem: \Is there an NC algorithm for testing if a given graph has a unique perfect matching?" We present suchan algorithm for bipartite graphs. We also give NC algorithms for obtaining a transitive orientation of a comparability graph, and an interval representation of an interval graph. These enable us to obtain an NC algorithm for nding a maximum matching in an incomparability graph. 1
ResourceConstrained Project Scheduling With Branching Scheme Based On Dynamic Release Dates
, 1999
"... We propose a branchandbound algorithm for resourceconstrained project scheduling where any two of jobs can be linked by arbitrary minimal and maximal time lags. The jobs have to be scheduled nonpreemptively, and while in process, they require several limited resources. The objective is to find a ..."
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Cited by 10 (6 self)
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We propose a branchandbound algorithm for resourceconstrained project scheduling where any two of jobs can be linked by arbitrary minimal and maximal time lags. The jobs have to be scheduled nonpreemptively, and while in process, they require several limited resources. The objective is to find a feasible schedule which minimizes the project makespan. Different branchandbound algorithms have been previously proposed  either based on constraint propagation techniques, or based on the idea to branch over socalled resource conflicts which are resolved by introducing additional precedence constraints. Our approach also follows the latter principle. The new idea is to resolve resource conflicts only locally by a dynamic update of job release dates instead of introducing precedence constraints. This gives rise to a reduction of both computation time and memory requirements in every node of the enumeration tree, however, at the expense of a loss of information. Nevertheless, enriched ...
Scheduling multiprocessor tasks on dedicated processors
 Fachbereich Mathematik /Informatik, Universitat Osnabruck, Osnabruck
, 1995
"... this paper for a detailed description. 7.3.2 An algorithm based on the calculation of partially directed comparability graphs ..."
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Cited by 9 (0 self)
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this paper for a detailed description. 7.3.2 An algorithm based on the calculation of partially directed comparability graphs