The face pairing graph of a 3-manifold triangulation is a 4-valent graph denoting which tetrahedron faces are identified with which others. We present a series of properties that must be satisfied by the face pairing ...
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The face pairing graph of a 3-manifold triangulation is a 4-valent graph denoting which tetrahedron faces are identified with which others. We present a series of properties that must be satisfied by the face pairing graph of a closed minimal P-2-irreducible triangulation. In addition we present constraints upon the combinatorial structure of such a triangulation that can be deduced from its face pairing graph. These results are then applied to the enumeration of closed minimal P-2-irreducible 3-manifold triangulations, leading to a significant improvement in the performance of the enumeration algorithm. Results are offered for both orientable and non-orientable triangulations.
We present an algorithm that generates all (inclusion-wise) minimal feedback vertex sets of a directed graph G = (V.E). The feedback vertex sets of G are generated with a polynomial delay of O(\V\(2)(\V\ + \E\)). We f...
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We present an algorithm that generates all (inclusion-wise) minimal feedback vertex sets of a directed graph G = (V.E). The feedback vertex sets of G are generated with a polynomial delay of O(\V\(2)(\V\ + \E\)). We further show that the underlying technique can be tailored to generate all minimal solutions for the undirected case and the directed feedback arc set problem, both with a polynomial delay of O(\V\ \E\ (\V\ + \E\). Finally, we prove that computing the number of minimal feedback arc sets is #P-hard. (C) 2002 Elsevier Science B.V. All rights reserved.
A nonlinear integer programming model for the optimal design of a series/parallel reliability system is presented, together with an enumeration algorithm for its solution and an example. The algorithm is based on an e...
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A nonlinear integer programming model for the optimal design of a series/parallel reliability system is presented, together with an enumeration algorithm for its solution and an example. The algorithm is based on an efficient procedure for solving the continuous relaxation of the mathematical model. (C) 2001 Elsevier Science Inc. All rights reserved.
We present an efficient algorithm which computes the set of minimal separators of a graph in O(n3) time per separator, thus gaining a factor of n2 on the current best-time algorithms for this problem. Our process is b...
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A new method for extracting drainage systems from Digital Elevation Models (DEMs) is presented. The main algorithm of the proposed method performs a skeletonization process of the set of elevations in the DEM and prod...
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A new method for extracting drainage systems from Digital Elevation Models (DEMs) is presented. The main algorithm of the proposed method performs a skeletonization process of the set of elevations in the DEM and produces a skeleton of flow paths. An enumeration algorithm performs the removal of loops from the initial flow path. A preprocess for filling depressions is described as is the necessary postprocessing for determining the drainage network through depressions. The new method does not suffer from any of the maladies of former methods described in the literature, such as flow cutoffs, loops of flow, and basin flooding. The new method is tested on several real-world DEMs and produced connected, complete, and loopless networks.
enumeration of spanning trees of an undirected graph is one of the graph problems that has received much attention in the literature. In this paper a new enumeration algorithm based on the idea of contractions of the ...
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enumeration of spanning trees of an undirected graph is one of the graph problems that has received much attention in the literature. In this paper a new enumeration algorithm based on the idea of contractions of the graph is presented. The worst-case time complexity of the algorithm isO(n+m+nt) wheren is the number of vertices,m the number of edges, andt the number of spanning trees in the graph. The worst-case space complexity of the algorithm isO(n 2). Computational analysis indicates that the algorithm requires less computation time than any other of the previously best-known algorithms.
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