34,607 research outputs found

    Quantum search algorithms on a regular lattice

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    Quantum algorithms for searching one or more marked items on a d-dimensional lattice provide an extension of Grover's search algorithm including a spatial component. We demonstrate that these lattice search algorithms can be viewed in terms of the level dynamics near an avoided crossing of a one-parameter family of quantum random walks. We give approximations for both the level-splitting at the avoided crossing and the effectively two-dimensional subspace of the full Hilbert space spanning the level crossing. This makes it possible to give the leading order behaviour for the search time and the localisation probability in the limit of large lattice size including the leading order coefficients. For d=2 and d=3, these coefficients are calculated explicitly. Closed form expressions are given for higher dimensions

    Algorithms Applied to Global Optimisation – Visual Evaluation

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    Evaluation and assessment of various search and optimisation algorithms is subject of large research efforts. Particular interest of this study is global optimisation and presented approach is based on observation and visual evaluation of Real-Coded Genetic Algorithm, Particle Swarm Optimisation, Differential Evolution and Free Search, which are briefly described and used for experiments. 3D graphical views, generated by visualisation tool VOTASA, illustrate essential aspects of global search process such as divergence, convergence, dependence on initialisation and utilisation of accidental events. Discussion on potential benefits of visual analysis, supported with numerical results, which could be used for comparative assessment of other methods and directions for further research conclude presented study

    HEURISTICS OPTIMISATION OF NUMERICAL FUNCTIONS

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    The article presents an investigation of heuristic behaviour of search algorithms applied to numerical problems. The aim is to compare the abilities of Particle Swarm Optimisation, Differential Evolution and Free Search to adapt to variety of search spaces without the need for constant re-tuning of algorithms parameters. The article focuses on several advanced characteristics of Free Search and attempts to clarify specifics of its behaviour. The achieved experimental results are presented and discussed

    Free Search and Particle Swarm Optimisation applied to Non-constrained Test

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    This article presents an evaluation of Particle Swarm Optimisation (PSO) with variable inertia weight and Free Search (FS) with variable neighbour space applied to nonconstrained numerical test. The objectives are to assess how high convergence speed reflects on adaptation to various test problems and to identify possible balance between convergence speed and adaptation, which allows the algorithms to complete successfully the process of search on heterogeneous tasks with limited computational resources within a reasonable finite time and with acceptable for engineering purposes precision. Modification strategies of both algorithms are compared in terms of their ability for search space exploration. Five numerical tests are explored. Achieved experimental results are presented and analysed

    Solving satisfiability problems by fluctuations: The dynamics of stochastic local search algorithms

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    Stochastic local search algorithms are frequently used to numerically solve hard combinatorial optimization or decision problems. We give numerical and approximate analytical descriptions of the dynamics of such algorithms applied to random satisfiability problems. We find two different dynamical regimes, depending on the number of constraints per variable: For low constraintness, the problems are solved efficiently, i.e. in linear time. For higher constraintness, the solution times become exponential. We observe that the dynamical behavior is characterized by a fast equilibration and fluctuations around this equilibrium. If the algorithm runs long enough, an exponentially rare fluctuation towards a solution appears.Comment: 21 pages, 18 figures, revised version, to app. in PRE (2003

    Monte Carlo Methods for Top-k Personalized PageRank Lists and Name Disambiguation

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    We study a problem of quick detection of top-k Personalized PageRank lists. This problem has a number of important applications such as finding local cuts in large graphs, estimation of similarity distance and name disambiguation. In particular, we apply our results to construct efficient algorithms for the person name disambiguation problem. We argue that when finding top-k Personalized PageRank lists two observations are important. Firstly, it is crucial that we detect fast the top-k most important neighbours of a node, while the exact order in the top-k list as well as the exact values of PageRank are by far not so crucial. Secondly, a little number of wrong elements in top-k lists do not really degrade the quality of top-k lists, but it can lead to significant computational saving. Based on these two key observations we propose Monte Carlo methods for fast detection of top-k Personalized PageRank lists. We provide performance evaluation of the proposed methods and supply stopping criteria. Then, we apply the methods to the person name disambiguation problem. The developed algorithm for the person name disambiguation problem has achieved the second place in the WePS 2010 competition
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