For a set of n disjoint line segments S in R-2, the visibility testing problem (VTP) is to test whether the query point p sees a query segment s is an element of S. For this configuration, the visibility counting prob...
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For a set of n disjoint line segments S in R-2, the visibility testing problem (VTP) is to test whether the query point p sees a query segment s is an element of S. For this configuration, the visibility counting problem (VCP) is to preprocess S such that the number of visible segments in S from any query point p can be computed quickly. In this paper, we solve VTP in expected logarithmic query time using quadratic preprocessing time and space. Moreover, we propose a (1 + delta)-approximation algorithm for VCP using at most quadratic preprocessing time and space. The query time of this method is O-epsilon (1/delta(2) root n) where O-epsilon (f (n)) = O (f (n)n(epsilon)) and epsilon > 0 is an arbitrary constant number. (C) 2015 Elsevier B.V. All rights reserved.
We present a parallel implementation of the randomized approximation algorithm for packing and covering linear programs presented by Koufogiannakis and Young (2007). Their approach builds on ideas of the sublinear tim...
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We present a parallel implementation of the randomized approximation algorithm for packing and covering linear programs presented by Koufogiannakis and Young (2007). Their approach builds on ideas of the sublinear time algorithm of Grigoriadis and Khachiyan's (Oper Res Lett 18(2):53-58, 1995) and Garg and Konemann's (SIAM J Comput 37(2):630-652, 2007) non-uniform-increment amortization scheme. With high probability it computes a feasible primal and dual solution whose costs are within a factor of of the optimal cost. In order to make their algorithm more parallelizable we also implemented a deterministic version of the algorithm, i.e. instead of updating a single random entry at each iteration we updated deterministically many entries at once. This slowed down a single iteration of the algorithm but allowed for larger step-sizes which lead to fewer iterations. We use NVIDIA's parallel computing architecture CUDA for the parallel environment. We report a speedup between one and two orders of magnitude over the times reported by Koufogiannakis and Young (2007).
Recently, Cauchie et al. presented an adaptive Hough transform-based algorithm to successfully solve the center-detection problem which is an important issue in many real-world problems. This paper presents a fast ran...
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Recently, Cauchie et al. presented an adaptive Hough transform-based algorithm to successfully solve the center-detection problem which is an important issue in many real-world problems. This paper presents a fast randomized algorithm to solve the same problem. With similar memory requirement and accuracy, the computational complexity analysis and comparison show that our proposed algorithm performs much better in terms of efficiency. We have tested our algorithm on 13 real images. Experimental results indicated that our algorithm has 38% execution-time improvement over Cauchie et al.'s algorithm. The extension of the proposed algorithm to detect multiple centers is also addressed. (C) 2010 Elsevier Ltd. All rights reserved.
This paper addresses the issues of conservativeness and computational complexity of robust control. A new probabilistic robust control method is proposed to design a high performance controller. The key of the new met...
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This paper addresses the issues of conservativeness and computational complexity of robust control. A new probabilistic robust control method is proposed to design a high performance controller. The key of the new method is that the uncertainty set is divided into two parts: r-subset and the complementary set of r-subset. The contributions of the new method are as follows: (i) a deterministic robust controller is designed for r-subset, so it has less conservative than those designed by using deterministic robust control method for the full set;and (ii) the probabilistic robustness of the designed controller is evaluated just for the complementary set of r-subset but not for the full set, so the computational complexity of the new method is reduced. Given expected probability robustness, a pertinent probabilistic robust controller can be designed by adjusting the norm boundary of r-subset. The effectiveness of the proposed method is verified by the simulation example.
We consider auctions of indivisible items to unit-demand bidders with budgets. This setting was suggested as an expressive model for single sponsored search auctions. Prior work presented mechanisms that compute bidde...
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We consider auctions of indivisible items to unit-demand bidders with budgets. This setting was suggested as an expressive model for single sponsored search auctions. Prior work presented mechanisms that compute bidder-optimal outcomes and are truthful for a restricted set of inputs, i.e., inputs in so-called general position. This condition is easily violated. We provide the first mechanism that is truthful in expectation for all inputs and achieves for each bidder no worse utility than the bidder-optimal outcome. Additionally we give a complete characterization for which inputs mechanisms that compute bidder-optimal outcomes are truthful. (C) 2015 Elsevier B.V. All rights reserved.
We consider the Scenario Convex Program (SCP) for two classes of optimization problems that are not tractable in general: Robust Convex Programs (RCPs) and Chance-Constrained Programs (CCPs). We establish a probabilis...
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We consider the Scenario Convex Program (SCP) for two classes of optimization problems that are not tractable in general: Robust Convex Programs (RCPs) and Chance-Constrained Programs (CCPs). We establish a probabilistic bridge from the optimal value of SCP to the optimal values of RCP and CCP in which the uncertainty takes values in a general, possibly infinite dimensional, metric space. We then extend our results to a certain class of non-convex problems that includes, for example, binary decision variables. In the process, we also settle a measurability issue for a general class of scenario programs, which to date has been addressed by an assumption. Finally, we demonstrate the applicability of our results on a benchmark problem and a problem in fault detection and isolation.
We consider the problem of determining the smallest square into which a given set of rectangular items can be packed without overlapping. We present an ILP model, an exact approach based on the iterated execution of a...
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We consider the problem of determining the smallest square into which a given set of rectangular items can be packed without overlapping. We present an ILP model, an exact approach based on the iterated execution of a two-dimensional packing algorithm, and a randomized metaheuristic. Such approaches are valid both for the case where the rectangles have fixed orientation and the case where they can be rotated by 90 degrees. We computationally evaluate the performance and the limits of the proposed approaches on a large set of instances, including a number of classical benchmarks from the literature, for both cases above, and for the special case where the items are squares. (C) 2015 Elsevier Ltd. All rights reserved.
Given a set of sites in the plane, their order-k Voronoi diagram partitions the plane into regions such that all points within one region have the same k nearest sites. The order-k abstract Voronoi diagram is defined ...
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ISBN:
(纸本)9783319130750;9783319130743
Given a set of sites in the plane, their order-k Voronoi diagram partitions the plane into regions such that all points within one region have the same k nearest sites. The order-k abstract Voronoi diagram is defined in terms of bisecting curves satisfying some simple combinatorial properties, rather than the geometric notions of sites and distance, and it represents a wide class of order-k concrete Voronoi diagrams. In this paper we develop a randomized divide-and-conquer algorithm to compute the order-k abstract Voronoi diagram in expected O(kn(1+epsilon)) operations. For solving small sub-instances in the divide-and-conquer process, we also give two sub-algorithms with expected O(k(2)n log n) and O(n 2 2 a(n) log n) time, respectively. This directly implies an O(kn(1+epsilon))-time algorithm for several concrete order-k instances such as points in any convex distance, disjoint line segments and convex polygons of constant size in the L-p norm, and others.
An algorithm is presented that probabilistically computes the exact inverse of a nonsingular n x n integer matrix A using (n(3)(log parallel to A parallel to + log kappa(A)))(1+o(1)) bit operations. Here, parallel to ...
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An algorithm is presented that probabilistically computes the exact inverse of a nonsingular n x n integer matrix A using (n(3)(log parallel to A parallel to + log kappa(A)))(1+o(1)) bit operations. Here, parallel to A parallel to = max(ij) |A(ij)| denotes the largest entry in absolute value, kappa(A) := n parallel to A(-1)parallel to parallel to A parallel to is the condition number of the input matrix, and the "+ o(1)" in the exponent indicates a missing factor c(1)(log n)(c2)(loglog parallel to A parallel to)(c3) for positive real constants c(1), c(2), c(3). A variation of the algorithm is presented for polynomial matrices that computes the inverse of a nonsingular nxn matrix whose entries are polynomials of degree d over a field using (n(3)d)(1+o(1)) field operations. Both algorithms are randomized of the Las Vegas type: failure may be reported with probability at most 1/2, and if failure is not reported, then the output is certified to be correct in the same running time bound.
Knapsack median is a generalization of the classic k-median problem in which we replace the cardinality constraint with a knapsack constraint. It is currently known to be 32-approximable. We improve on the best known ...
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ISBN:
(纸本)9783662483503;9783662483497
Knapsack median is a generalization of the classic k-median problem in which we replace the cardinality constraint with a knapsack constraint. It is currently known to be 32-approximable. We improve on the best known algorithms in several ways, including adding randomization and applying sparsification as a preprocessing step. The latter improvement produces the first LP for this problem with bounded integrality gap. The new algorithm obtains an approximation factor of 17.46. We also give a 3.05 approximation with small budget violation.
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