The main problem considered is the method of choosing step coefficients in first-order stochastic approximation algorithms for system identification. The proposed method increases the efficency of the Saridis and Stei...
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The main problem considered is the method of choosing step coefficients in first-order stochastic approximation algorithms for system identification. The proposed method increases the efficency of the Saridis and Stein algorithm [4].
Consideration is given to the problem of determining the minimum-weight perfect matching of an even number of points on a plane, i.e., determining how to match the points in pairs so as to minimize the sum of the dist...
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Consideration is given to the problem of determining the minimum-weight perfect matching of an even number of points on a plane, i.e., determining how to match the points in pairs so as to minimize the sum of the distances between the matched points. An optimizing algorithm exists for this problem, whose practical importance lies in finding the optimal sequence of drawing edges of a connected graph by a mechanical plotter. The high degree of complexity of the algorithm renders it impractical. A linear approximation algorithm is presented. It gives results closer to those of the complex algorithms when dealing with an average case rather than the worst case.
Gradient techniques which use a weighting matrix to accelerate convergence are shown to be bilinear in the neighborhood of the extremum, while the gradient method itself behaves as a linear system. An investigation of...
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Gradient techniques which use a weighting matrix to accelerate convergence are shown to be bilinear in the neighborhood of the extremum, while the gradient method itself behaves as a linear system. An investigation of their reachable sets at the extremum provides a basis for explaining the improved performance experienced in practice. Using concepts from bilinear control theory, two new algorithms are designed which achieve further improvements in performance.
This paper is a summary of the author's Ph.D. thesis in Mathematics supervised by Giancarlo Bigi and Antonio Frangioni, and defended on 23 June 2008 at the Universita di Pisa. The thesis is written in English and ...
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This paper is a summary of the author's Ph.D. thesis in Mathematics supervised by Giancarlo Bigi and Antonio Frangioni, and defended on 23 June 2008 at the Universita di Pisa. The thesis is written in English and available from http://***/di/groups/optimize. The work deals with outer approximation algorithms for solving an alternative equivalent formulation and a novel generalization of canonical DC (difference of convex) programs. The thesis develops an in-depth investigation of structural properties of both problems, and of the impact of approximations onto the quality of approximate optimal solutions. It also propose hierarchies of conditions guaranteeing convergence and develops several different implementable algorithms for canonical DC programs and its novel generalization, respectively.
Maximum Satisfiability Problem (MAX SAT) is one of the most natural optimization problems. Since it is known to Le NP-hard, approximation algorithms have been considered. The aim of this survey is to show recent devel...
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Maximum Satisfiability Problem (MAX SAT) is one of the most natural optimization problems. Since it is known to Le NP-hard, approximation algorithms have been considered. The aim of this survey is to show recent developments of approximation algorithms for MAX SAT.
In recent years, data examples have been at the core of several different approaches to schema-mapping design. In particular, Gottlob and Senellart introduced a framework for schema-mapping discovery from a single dat...
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In recent years, data examples have been at the core of several different approaches to schema-mapping design. In particular, Gottlob and Senellart introduced a framework for schema-mapping discovery from a single data example, in which the derivation of a schema mapping is cast as an optimization problem. Our goal is to refine and study this framework in more depth. Among other results, we design a polynomial-time log(n)-approximation algorithm for computing optimal schema mappings from a given set of data examples (where nis the combined size of the given data examples) for a restricted class of schema mappings;moreover, we show that this approximation ratio cannot be improved. In addition to the complexity-theoretic results, we implemented the aforementioned log(n)-approximation algorithm and carried out an experimental evaluation in a real-world mapping scenario.
The exposure of a path p in a sensor field is a measure of the likelihood that an object traveling along p is detected by at least one sensor from a network of sensors, and is formally defined as an integral over all ...
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The exposure of a path p in a sensor field is a measure of the likelihood that an object traveling along p is detected by at least one sensor from a network of sensors, and is formally defined as an integral over all points x of p of the sensibility (the strength of the signal coming from x) times the element of path length. The minimum exposure path (MEP) problem is, given a pair of points x and y inside a sensor field, to find a path between x and y of minimum exposure. In this article we introduce the first rigorous treatment of the problem, designing an approximation algorithm for the MEP problem with guaranteed performance characteristics. Given a convex polygon P of size n with O(n) sensors inside it and any real number epsilon > 0, our algorithm finds a path in P whose exposure is within an 1 + epsilon factor of the exposure of the MEP, in time O(n/epsilon(2)psi log n), where. is a geometric characteristic of the field. We also describe a framework for a faster implementation of our algorithm, which reduces the time by a factor of approximately Theta(1/epsilon), while keeping the same approximation ratio.
This paper addresses the Inner-node Weighted Minimum Spanning Tree Problem (IWMST), which asks for a spanning tree in a graph G = (V. E) (vertical bar V vertical bar = n. vertical bar E vertical bar = m) with the mini...
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This paper addresses the Inner-node Weighted Minimum Spanning Tree Problem (IWMST), which asks for a spanning tree in a graph G = (V. E) (vertical bar V vertical bar = n. vertical bar E vertical bar = m) with the minimum total cost for its edges and non-leaf nodes. This problem is NP-Hard because it contains the connected dominating set problem (CDS) as a special case. Since CDS cannot be approximated with a factor of (1 E)H(A) (A is the maximum degree) unless NP subset of DT I M E/n(O(log log n)) vertical bar [10], we can only expect a poly-logarithmic approximation algorithm for the IWMST problem. To tackle this problem, we first present a general framework for developing poly-logarithmic approximation algorithms. Our framework aims to find a r. rk Inn-approximate Algorithm (k epsilon N and k >= 2) for the IWMST problem. Based on this framework, we further design two polynomial time approximation algorithms. The first one can find a k/k-1 In n-approximate solution in O(mn log n) time, while the second one can compute a 1.5 Inn-approximate solution in O(n(2) Delta(6)) time (Delta is the maximum degree in G). We have also studied the relationships between the IWMST problem and several other similar problems.
Data collection from the sensors in time is an integral part of many applications of wireless sensor networks (WSNs). Vehicles, referred to as Mobile Sinks (SNKs), may be used to collect data from the sensors by visit...
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Data collection from the sensors in time is an integral part of many applications of wireless sensor networks (WSNs). Vehicles, referred to as Mobile Sinks (SNKs), may be used to collect data from the sensors by visiting them. Since the sensors have limited memory, the sensed data needs to be collected by the SNKs within a predefined time interval to avoid memory overflow. Periodic data collection by SNKs becomes even more challenging when the sensors are mobile. Moreover, the presence of obstacles in the area makes the path planning for SNKs even more complicated. In this paper, an optimization problem, referred to as Minimum Mobile Sink Aided Periodic Data Collection (MinSnkDC) problem, is formulated, where the objective is to determine the minimum number of SNKs that collect data for every time period from the mobile sensors in the WSN, while avoiding collision with the obstacles in the area. The problem is proved to be NP-complete. Two constant factor approximation algorithms, namely MinSnkDC and Modified MinSnkDC (M-MinSnkDC), are proposed to solve the problem. From the simulation results, it is evident that M-MinSnkDC can produce a better solution compared to the existing obstacle-aware SNK-based data collection algorithms, while using a small number of SNKs.
This paper describes a general technique that can be used to obtain approximation schemes for various NP-complete problems on planar graphs. The strategy depends on decomposing a planar graph into subgraphs of a form ...
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This paper describes a general technique that can be used to obtain approximation schemes for various NP-complete problems on planar graphs. The strategy depends on decomposing a planar graph into subgraphs of a form we call k-outerplanar. For fixed k, the problems of interest are solvable optimally in linear time on k-outerplanar graphs by dynamic programming. For general planar graphs, if the problem is a maximization problem, such as maximum independent set, this technique gives for each k a linear time algorithm that produces a solution whose size is at least k/(k + 1) optimal. If the problem is a minimization problem, such as minimum vertex cover, it gives for each k a linear time algorithm that produces a solution whose size is at most (k + 1)/k optimal. Taking k = inverted right perpendicular c log log n inverted left perpendicular or k = right perpendicular c log n left perpendicular, where n is the number of nodes and c is some constant, we get polynomial time approximation algorithms whose solution sizes converge toward optimal as n increases. The class of problems for which this approach provides approximation schemes includes maximum independent set, maximum tile salvage, partition into triangles, maximum H-matching, minimum vertex cover, minimum dominating set, and minimum edge dominating set. For these and certain other problems, the proof of solvability on k-outerplanar graphs also enlarges the class of planar graphs for which the problems are known to be solvable in polynomial time.
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