The area of research on probabilistic and randomized methods for analysis and design of uncertain systems is fairly recent and is focused both on algorithmic as well as theoretical developments. In this paper a framew...
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The area of research on probabilistic and randomized methods for analysis and design of uncertain systems is fairly recent and is focused both on algorithmic as well as theoretical developments. In this paper a framework for randomization-based control design is presented and applied to a Mini-UAV platform. The proposed approach makes use of random search and uncertainty randomization for controller synthesis and probabilistic robustness analysis. Several structured uncertain parameters, related to the plant and to the operating conditions, are taken into account to design a robust flight control system. A selection criterion, based on estimated probability and its degradation function, is proposed in order to match stability and performance metrics fulfillment. Computational issues associated to the specific application, integration of a priori domain knowledge and human designer interaction with automated design are also addressed. (C) 2009 Elsevier Ltd. All rights reserved.
In this paper we present a sublinear-time (1 + epsilon)-approximation randomized algorithm to estimate the weight of the minimum spanning tree of an n-point metric space. The running time of the algorithm is (O) over ...
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In this paper we present a sublinear-time (1 + epsilon)-approximation randomized algorithm to estimate the weight of the minimum spanning tree of an n-point metric space. The running time of the algorithm is (O) over tilde (n/epsilon(O(1))). Since the full description of an n-point metric space is of size Theta(n(2)), the complexity of our algorithm is sublinear with respect to the input size. Our algorithm is almost optimal as it is not possible to approximate in o(n) time the weight of the minimum spanning tree to within any factor. We also show that no deterministic algorithm can achieve a B-approximation in o(n(2)/B-3) time. Furthermore, it has been previously shown that no o(n(2)) algorithm exists that returns a spanning tree whose weight is within a constant times the optimum.
The scenario optimization method developed in [5] is a theoretically sound and practically effective technique for solving in a probabilistic setting robust convex optimization problems arising in systems and control ...
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The scenario optimization method developed in [5] is a theoretically sound and practically effective technique for solving in a probabilistic setting robust convex optimization problems arising in systems and control design, that would otherwise be hard to tackle via standard deterministic techniques. In this note, we explore some further aspects of the scenario methodology, and present two results pertaining to the tightness of the sample complexity bounds. We also state a new theorem that enables the user to make a-priori probabilistic claims on the scenario solution, with one level of probability only.
A Boolean function is symmetric if it is invariant under all permutations of its arguments;it is quasi-symmetric if it is symmetric with respect to the arguments on which it actually depends. We present a test that ac...
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A Boolean function is symmetric if it is invariant under all permutations of its arguments;it is quasi-symmetric if it is symmetric with respect to the arguments on which it actually depends. We present a test that accepts every quasi-symmetric function and, except with an error probability at most delta > 0, rejects every function that differs from every quasi-symmetric function on at least a fraction epsilon > 0 of the inputs. For a function of n arguments, the test probes the function at O ((n/epsilon) log(n/delta)) inputs. Our quasi-symmetry test acquires information concerning the arguments on which the function actually depends. To do this, it employs a generalization of the property testing paradigm that we call attribute estimation. Like property testing, attribute estimation uses random sampling to obtain results that have only "one-sided" errors and that are close to accurate with high probability. (C) 2008 Elsevier B.V. All rights reserved.
We consider the following geometric pattern matching problem: Given two sets of points in the plane, P and Q, and some (arbitrary) delta > 0, find the largest subset B subset of P and a similarity transformation T ...
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We consider the following geometric pattern matching problem: Given two sets of points in the plane, P and Q, and some (arbitrary) delta > 0, find the largest subset B subset of P and a similarity transformation T (translation, rotation and scale) such that h(T(B), Q) < delta, where h(.,.) is the directional Hausdorff distance. This problem stems from real world applications, where d is determined by the practical uncertainty in the position of the points (pixels). We reduce the problem to finding the depth (maximally covered point) of an arrangement of polytopes in transformation space. The depth is the cardinality of B, and the polytopes that cover the deepest point correspond to the points in B. We present an algorithm that approximates the maximum depth with high probability, thus getting a large enough common point set in P and Q. The algorithm is implemented in the GPU framework, thus it is very fast in practice. We present experimental results and compare their runtime with those of an algorithm running on the CPU.
We improve the previous results by Aronov and Har-Peled (SODA'05) and Kaplan and Sharir (SODA'06) and present a randomized data structure of O(n) expected size which can answer 3D approximate halfspace range c...
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We improve the previous results by Aronov and Har-Peled (SODA'05) and Kaplan and Sharir (SODA'06) and present a randomized data structure of O(n) expected size which can answer 3D approximate halfspace range counting queries in O(log n/k) expected time, where k is the actual value of the count. This is the first optimal method for the problem in the standard decision tree model;moreover, unlike previous methods, the new method is Las Vegas instead of Monte Carlo. In addition, we describe new results for several related problems, including approximate Tukey depth queries in 3D, approximate regression depth queries in 2D, and approximate linear programming with violations in low dimensions.
We present an extension of a classical data management subproblem, the page migration. The problem is investigated in dynamic networks, where costs of communication between different nodes may change with time. We con...
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We present an extension of a classical data management subproblem, the page migration. The problem is investigated in dynamic networks, where costs of communication between different nodes may change with time. We construct asymptotically optimal online algorithms for this problem, both in deterministic and randomized scenarios. (C) 2008 Elsevier B.V.
We give a randomized algorithm that determines if a given graph has a simple path of length at least k in O(2(k) . poly(n)) time. Our method extends a recent O(2(3k/2). poly(n)) <= 0 (2.83(k) . poly(n)) algorithm o...
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We give a randomized algorithm that determines if a given graph has a simple path of length at least k in O(2(k) . poly(n)) time. Our method extends a recent O(2(3k/2). poly(n)) <= 0 (2.83(k) . poly(n)) algorithm of Koutis. (C) 2008 Elsevier B.V. All rights reserved.
Consider a given undirected graph G = (V, E) with non-negative edge lengths, a root node r is an element of V, and a set D subset of V of demands with dv representing the units of flow that demand v is an element of D...
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Consider a given undirected graph G = (V, E) with non-negative edge lengths, a root node r is an element of V, and a set D subset of V of demands with dv representing the units of flow that demand v is an element of D wishes to send to the root. We are also given K types of cables, each with a specified capacity and cost per unit length. The single-sink buy-at-bulk (SSBB) problem asks for a low-cost installation of cables along the edges of G, such that the demands can simultaneously send their flow to root r. The problem is studied with and without the restriction that the flow from a node must follow a single path to the root. We are allowed to install zero or more copies of a cable type on each edge. The SSBB problem is NP-hard. In this paper, we present a 153.6-approximation algorithm for the SSBB problem improving the previous best ratio of 216. For the case in which the flow is splittable, we improve the previous best ratio of 76.8 to aK, where aK is less than 67.94 for all K. In particular, alpha(2) < 17.7, alpha(3) < 23.2, alpha(4) < 28.8, and alpha(5) < 34.3. Published by Elsevier B.V.
We confront a practical cutting stock problem from a production plant of plastic rolls. The problem is a variant of the well-known one dimensional cutting stock, with particular constraints and optimization criteria d...
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We confront a practical cutting stock problem from a production plant of plastic rolls. The problem is a variant of the well-known one dimensional cutting stock, with particular constraints and optimization criteria defined by the experts of the company. We start by giving a problem formulation in which optimization criteria have been considered in linear hierarchy according to expert preferences, and then propose a heuristic solution based on a GRASP algorithm. The generation phase of this algorithm solves a simplified version which is rather similar to the conventional one dimensional cutting stock. To do that, we propose a Sequential Heuristic randomized Procedure (SHRP). Then in the repairing phase, the solution of the simplified problem is transformed into a solution to the real problem. For experimental study we have chosen a set of problem instances of com-mon use to compare SHRP with another recent approach. Also, we show by means of examples, how our approach works over instances taken from the real production process.
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