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Quantum query complexity of some graph problems
 Proceedings of the 31st International Colloquium on Automata, Lanaguages, and Programming
, 2004
"... Quantum algorithms for graph problems are considered, both in the adjacency matrix model and in an adjacency listlike array model. We give almost tight lower and upper bounds for the bounded error quantum query complexity of Connectivity, Strong Connectivity, Minimum Spanning Tree, and Single Sourc ..."
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Cited by 40 (3 self)
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Quantum algorithms for graph problems are considered, both in the adjacency matrix model and in an adjacency listlike array model. We give almost tight lower and upper bounds for the bounded error quantum query complexity of Connectivity, Strong Connectivity, Minimum Spanning Tree, and Single Source Shortest Paths. For example we show that the query complexity of Minimum Spanning Tree is in Θ(n 3/2) in the matrix model and in Θ ( √ nm) in the array model, while the complexity of Connectivity is also in Θ(n 3/2) in the matrix model, but in Θ(n) in the array model. The upper bounds utilize search procedures for finding minima of functions under various conditions.
Engineering an External Memory Minimum Spanning Tree Algorithm
 IN PROC. 3RD IFIP INTL. CONF. ON THEORETICAL COMPUTER SCIENCE
, 2004
"... We develop an external memory algorithm for computing minimum spanning trees. The algorithm is considerably simpler than previously known external memory algorithms for this problem and needs a factor of at least four less I/Os for realistic inputs. Our implementation indicates that this algorithm ..."
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Cited by 14 (3 self)
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We develop an external memory algorithm for computing minimum spanning trees. The algorithm is considerably simpler than previously known external memory algorithms for this problem and needs a factor of at least four less I/Os for realistic inputs. Our implementation indicates that this algorithm processes graphs only limited by the disk capacity of most current machines in time no more than a factor 2–5 of a good internal algorithm with sufficient memory space.
Minimum Spanning Tree Based Clustering Algorithms
"... The minimum spanning tree clustering algorithm is known to be capable of detecting clusters with irregular boundaries. In this paper, we propose two minimum spanning tree based clustering algorithms. The first algorithm produces a kpartition of a set of points for any given k. The algorithm constru ..."
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Cited by 11 (0 self)
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The minimum spanning tree clustering algorithm is known to be capable of detecting clusters with irregular boundaries. In this paper, we propose two minimum spanning tree based clustering algorithms. The first algorithm produces a kpartition of a set of points for any given k. The algorithm constructs a minimum spanning tree of the point set and removes edges that satisfy a predefined criterion. The process is repeated until k clusters are produced. The second algorithm partitions a point set into a group of clusters by maximizing the overall standard deviation reduction, without a given k value. We present our experimental results comparing our proposed algorithms to kmeans and EM. We also apply our algorithms to image color clustering and compare our algorithms to the standard minimum spanning tree clustering algorithm. 1.
A Practical Minimum Spanning Tree Algorithm Using the Cycle Property
 IN 11TH EUROPEAN SYMPOSIUM ON ALGORITHMS (ESA), NUMBER 2832 IN LNCS
, 2003
"... We present a simple new (randomized) algorithm for computing minimum spanning trees that is more than two times faster than the best previously known algorithms (for dense, "difficult" inputs). It is of conceptual interest that the algorithm uses the property that the heaviest edge in a cycle can be ..."
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Cited by 9 (2 self)
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We present a simple new (randomized) algorithm for computing minimum spanning trees that is more than two times faster than the best previously known algorithms (for dense, "difficult" inputs). It is of conceptual interest that the algorithm uses the property that the heaviest edge in a cycle can be discarded. Previously this has only been exploited in asymptotically optimal algorithms that are considered impractical. An additional advantage is...
Embedding a Chained LinKernighan Algorithm into a Distributed Algorithm
 In: MIC’2005 – 6th Metaheuristics International Conference
, 2004
"... The Chained LinKernighan algorithm (CLK) is one of the best heuristics to solve Traveling Salesman Problems (TSP). In this paper a distributed algorithm is proposed, were nodes in a network locally optimize TSP instances by using the CLK algorithm. Within an Evolutionary Algorithm (EA) networkbase ..."
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Cited by 3 (2 self)
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The Chained LinKernighan algorithm (CLK) is one of the best heuristics to solve Traveling Salesman Problems (TSP). In this paper a distributed algorithm is proposed, were nodes in a network locally optimize TSP instances by using the CLK algorithm. Within an Evolutionary Algorithm (EA) networkbased framework the resulting tours are modified and exchanged with neighboring nodes. We show that the distributed variant finds better tours compared to the original CLK given the same amount of computation time. For instance fl3795, the original CLK got stuck in local optima in each of 10 runs, whereas the distributed algorithm found optimal tours in each run requiring less than 10 CPU minutes per node on average in an 8 node setup. For instance sw24978, the distributed algorithm had an average solution quality of 0.050 % above the optimum, compared to CLK’s average solution of 0.119 % above the optimum given the same total CPU time (10 4 seconds). Considering the best tours of both variants for this instance, the distributed algorithm is 0.033 % above the optimum and the CLK algorithm 0.099%.
Traveling salesman games with the Monge property
, 2001
"... Several works indicate the relationship between wellsolved combinatorial optimization problems and the core nonemptiness of cooperative games associated with them. In this note, we consider the core of traveling salesman games. We show that the core of traveling salesman games in which the dist ..."
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Cited by 2 (0 self)
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Several works indicate the relationship between wellsolved combinatorial optimization problems and the core nonemptiness of cooperative games associated with them. In this note, we consider the core of traveling salesman games. We show that the core of traveling salesman games in which the distance matrix is a Monge matrix is nonempty. This is the first result for traveling salesman games related with a wellsolved structure. Moreover, we show that the problem of testing the core nonemptiness of a given traveling salesman game is NPhard.
Codings and operators in two genetic algorithms for the leafconstrained minimum spanning tree problem
 International Journal of Applied Mathematics and Computer Science
, 2004
"... The features of an evolutionary algorithm that most determine its performance are the coding by which its chromosomes represent candidate solutions to its target problem and the operators that act on that coding. Also, when a problem involves constraints, a coding that represents only valid solution ..."
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Cited by 2 (1 self)
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The features of an evolutionary algorithm that most determine its performance are the coding by which its chromosomes represent candidate solutions to its target problem and the operators that act on that coding. Also, when a problem involves constraints, a coding that represents only valid solutions and operators that preserve that validity represent a smaller search space and result in a more effective search. Two genetic algorithms for the leafconstrained minimum spanning tree problem illustrate these observations. Given a connected, weighted, undirected graph G with n vertices and a bound ℓ, this problem seeks a spanning tree on G with at least ℓ leaves and minimum weight among all such trees. A greedy heuristic for the problem begins with an unconstrained minimum spanning tree on G, then economically turns interior vertices into leaves until their number reaches ℓ. One genetic algorithm encodes candidate trees with Prüfer strings decoded via the Blob Code. The second GA uses strings of length n−ℓ that specify trees ’ interior vertices. Both GAs apply operators that generate only valid chromosomes. The latter represents and searches a much smaller space. In tests on 65 instances of the problem, both Euclidean and with weights chosen randomly, the BlobCoded GA cannot compete with the greedy heuristic, but the subsetcoded GA consistently identifies leafconstrained spanning trees of lower weight than the greedy heuristic does, particularly on the random instances.
Automated Selection of Modelling Coordinates for Forward Dynamic Analysis of Multibody Systems
"... I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public. Mathieu Léger ii Modelling mechanical systems using symbo ..."
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Cited by 1 (1 self)
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I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public. Mathieu Léger ii Modelling mechanical systems using symbolic equations can provide many advantages over the more widelyused numerical methods of modelling these systems. The use of symbolic equations produces more efficient models, which can be used for many purposes such as realtime simulation and control. However, the number, complexity, and computational efficiency of these equations is highly dependent on which coordinate set was used to model the system. One method of modelling a mechanism’s topology and formulating its symbolic equations is to model the system using a graphtheoretical approach. This approach models mechanisms using a linear graph, from which spanning trees can be used to define a mech
PATCHBASED IMAGE SEGMENTATION OF SATELLITE IMAGERY USING MINIMUM SPANNING TREE CONSTRUCTION
"... We present a method for hierarchical image segmentation and feature extraction. This method builds upon the combination of the detection of image spectral discontinuities using Canny edge detection and the image Laplacian, followed by the construction of a hierarchy of segmented images of successive ..."
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We present a method for hierarchical image segmentation and feature extraction. This method builds upon the combination of the detection of image spectral discontinuities using Canny edge detection and the image Laplacian, followed by the construction of a hierarchy of segmented images of successively reduced levels of details. These images are represented as sets of polygonized pixel patches (polygons) attributed with spectral and structural characteristics. This hierarchy forms the basis for objectoriented image analysis. To build fine levelofdetail representation of the original image, seed partitions (polygons) are built upon a triangular mesh composed of irregular sized triangles, whose spatial arrangement is adapted to the image content. This is achieved by building the triangular mesh on the top of the detected spectral discontinuities that form a network of constraints for the Delaunay triangulation. A polygonized image is represented as a spatial network in the form of a graph with vertices which correspond to the polygonal partitions and graph edges reflecting pairwise partitions relations. Image graph partitioning is based on the iterative graph contraction using Boruvka's Minimum Spanning Tree algorithm. An important characteristic of the approach is that the agglomeration of partitions is constrained by the detected spectral discontinuities; thus the shapes of agglomerated partitions are more likely to correspond to the outlines of realworld objects. 1.