Since the classic determinant computation method Cholesky decomposition may devastate sparsity of matrices and cost cubic steps, it is impractical to apply this method to large-scale symmetric positive-definite matric...
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ISBN:
(数字)9783319325576
ISBN:
(纸本)9783319325576;9783319325569
Since the classic determinant computation method Cholesky decomposition may devastate sparsity of matrices and cost cubic steps, it is impractical to apply this method to large-scale symmetric positive-definite matrices due to limitation of storage and efficiency. Therefore, a randomized algorithm is proposed to calculate log-determinants of symmetric positive-definite matrices via stochastic trace approximations, implemented by weighted L-2 orthogonal polynomial expansions with efficient recursion formulas and matrix-vector multiplications based on the matrix eigenvalue distribution. As Chebyshev expansions have been applied to this problem before, our main contribution is proposing the strategies of weighted function selection based on prior eigenvalue distribution, which generalizes approximating polynomials for this problem and may accelerate computation.
This paper proposes a probabilistic robust control approach for a small unmanned aerial vehicle(UAV) in longitudinal ight. In the proposed method, the stochastic behavior of uncertainty parameters is considered in sol...
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ISBN:
(纸本)9781509009107
This paper proposes a probabilistic robust control approach for a small unmanned aerial vehicle(UAV) in longitudinal ight. In the proposed method, the stochastic behavior of uncertainty parameters is considered in solving a high-performance robust controller of UAV. Compared to deterministic robust control, this solution has two advantages:(a) the controller obtained by the proposed method has xed order;(b) it is less-conservative and more reasonable for controlling ight control systems with bounded uncertainty. Simulation results for an UAV in longitudinal motion are given to show the effectiveness of the proposed approach.
Given a set S of n disjoint line segments in R-2, the visibility counting problem (VCP) is to preprocess S such that the number of segments in S visible from any query point p can be computed quickly. This problem can...
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ISBN:
(纸本)9783319426341;9783319426334
Given a set S of n disjoint line segments in R-2, the visibility counting problem (VCP) is to preprocess S such that the number of segments in S visible from any query point p can be computed quickly. This problem can trivially be solved in logarithmic query time using O(n(4)) preprocessing time and space. Gudmundsson and Morin proposed a 2-approximation algorithm for this problem with a trade-off between the space and the query time. They answer any query in O epsilon(n (1-alpha)) with O epsilon (n(2+2 alpha)) of preprocessing time and space, where alpha is a constant 0 <= alpha <= 1, epsilon > 0 is another constant that can be made arbitrarily small, and O epsilon(f(n)) = O(f( n)n(epsilon)). In this paper, we propose a randomized approximation algorithm for VCP with a tradeoff between the space and the query time. We will show that for an arbitrary constants 0 <= beta <= 2/3 and 0 < delta < 1, the expected preprocessing time, the expected space, and the query time of our algorithm are O( n(4-3 beta) log n), O(n(4-3 beta)), and O(1/delta(3)n(beta) log n), respectively. The algorithm computes the number of visible segments from p, or mp, exactly if m(p) <= (1)/(3)(delta)n(beta) log ***, it computes a ( 1+ delta)-approximation m'(p) with the probability of at least 1- 1/log n, where m(p) <= m'(p) <= ( 1 + delta) m(p).
In this paper, we propose route of interest (ROI) query which allows users to specify their interests with query keywords and returns a route such that (i) its distance is less than a distance threshold and (ii) its r...
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ISBN:
(纸本)9783319399379;9783319399362
In this paper, we propose route of interest (ROI) query which allows users to specify their interests with query keywords and returns a route such that (i) its distance is less than a distance threshold and (ii) its relevance to the query keywords is maximized. ROI query is particularly helpful for tourists and city explorers. For example, a tourist may wish to find a route from a scenic spot to her hotel to cover many artware shops. It is challenging to efficiently answer ROI query due to its NP-hard complexity. Novelly, we propose an adaptive route sampling framework that adaptively computes a route according to a given response time, and gradually improve the quality of the route with time. Moreover, we design a suite of route sampling techniques under this framework. Experiments on real data suggest that our proposed solution can return high quality routes within a short response time.
We study voting models on graphs. In the beginning, the vertices of a given graph have some initial opinion. Over time, the opinions on the vertices change by interactions between graph neighbours. Under suitable cond...
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Given an undirected network G(V, E) and a set of traffic requests R, the minimum power-cost routing problem requires that each R-k is an element of R, be routed along a single path to minimize Sigma(e is an element of...
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Given an undirected network G(V, E) and a set of traffic requests R, the minimum power-cost routing problem requires that each R-k is an element of R, be routed along a single path to minimize Sigma(e is an element of E)(l(e))(alpha), where l(e) is the traffic load on edge e and alpha is a constant greater than 1. Typically, alpha is an element of (1,3]. This problem is important in optimizing the energy consumption of networks. To address this problem, we propose a randomized oblivious routing algorithm. An oblivious routing algorithm makes decisions independently of the current traffic in the network. This feature enables the efficient implementation of our algorithm in a distributed manner, which is desirable for large-scale high-capacity networks. An important feature of our work is that our algorithm can satisfy the integral constraint, which requires that each traffic request Rk should follow a single path. We prove that, given this constraint, no randomized oblivious routing algorithm can guarantee a competitive ratio bounded by o(vertical bar E vertical bar(alpha-1/alpha+1)). By contrast, our approach provides a competitive ratio of O(vertical bar E vertical bar(alpha-1/alpha+1) log(2 alpha/alpha+1) vertical bar V vertical bar . log(alpha-1) D), where D is the maximum demand of traffic requests. Furthermore, our results also hold for a more general case where the objective is to minimize Sigma(e)(l(e))(p), where p >= I is an arbitrary unknown parameter with a given upper bound alpha >1. The theoretical results established in proving these bounds can be further generalized to a framework of designing and analyzing oblivious integral routing algorithms, which is significant for research on minimizing Sigma(e)(l(e))(alpha) in specific scenarios with simplified problem settings. For instance, we prove that this framework can generate an oblivious integral routing algorithm whose competitive ratio can be bounded by O(log(alpha) vertical bar V vertical bar . log(a
In most wireless sensor network (WSN) applications, data are typically gathered by sensor nodes and reported to a data collection point called sink. To support such a data collection pattern, a tree structure rooted a...
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In most wireless sensor network (WSN) applications, data are typically gathered by sensor nodes and reported to a data collection point called sink. To support such a data collection pattern, a tree structure rooted at the sink is defined. Depending on various factors, including the WSN topology and the availability of resources, the energy consumption of nodes in different paths of the data collection tree may vary largely, thus affecting the overall network lifetime. This paper addresses the problem of lifetime maximization of WSNs based on data collection trees. Specifically, we propose a novel and efficient algorithm, called randomized Switching for Maximizing Lifetime (RaSMaLai), that aims at extending the lifetime of WSNs through load balancing. Given an initial data collection tree, RaSMaLai randomly switches some sensor nodes from their original paths to other paths with lower load. We prove that, under appropriate settings of the operating parameters, RaSMaLai converges with a low time complexity. We further design a distributed version of our algorithm. Through an extensive performance evaluation study that includes simulation of large-scale scenarios and real experiments on a WSN testbed, we show that the proposed RaSMaLai algorithm and its distributed version achieve a longer network lifetime than the state-of-the-art solutions.
We describe a class of adaptive algorithms tor approximating the global minimum of a function defined on a compact subset of R(d) The algorithms are adaptive versions of Monte Carlo search and use a memory of a fixed ...
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We describe a class of adaptive algorithms tor approximating the global minimum of a function defined on a compact subset of R(d) The algorithms are adaptive versions of Monte Carlo search and use a memory of a fixed number of past observations By choosing a large enough memory. the convergence rate can be made to exceed any power of the convergence rate obtained with standard Monte Carlo search (C) 2008 IMACS Published by Elsevier B V All rights reserved
In this paper, we study the Parameterized P-2-Packing problem and Parameterized Co-Path Packing problem from random perspective. For the Parameterized P-2-Packing problem, based on the structure analysis of the proble...
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In this paper, we study the Parameterized P-2-Packing problem and Parameterized Co-Path Packing problem from random perspective. For the Parameterized P-2-Packing problem, based on the structure analysis of the problem and using random partition technique, a randomized parameterized algorithm of running time O*(6.75(k)) is obtained, improving the current best result O*(8(k)). For the Parameterized Co-Path Packing problem, we firstly study the kernel and randomized algorithm for the degree-bounded instance, where each vertex in the instance has degree at most three. A kernel of size 20k and a randomized algorithm of running time O*(2(k)) are given for the Parameterized Co-Path Packing problem with bounded degree constraint. By applying iterative compression technique and based on the randomized algorithm for degree bounded problem, a randomized algorithm of running time O*(3(k)) is given for the Parameterized Co-Path Packing problem.
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