Two-variable linear programming is a fundamental problem in computational geometry. Sequentially, this problem was solved optimally in linear time by Megiddo and Dyer using the elegant prune-and-search technique. In p...
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Two-variable linear programming is a fundamental problem in computational geometry. Sequentially, this problem was solved optimally in linear time by Megiddo and Dyer using the elegant prune-and-search technique. In parallel, the previously best known deterministic algorithm on the EREW PRAM for this problem takes O(log n log log n) time and O(n) work. In this paper, we present a faster parallel deterministic two-variable linear programming algorithm, which takes O(log n log* n) time and O(n) work on the EREW PRAM. Our algorithm is based on an interesting parallel prune-and-search technique, and makes use of new geometric observations which can be viewed as generalizations of those used by Megiddo and Dyer's sequential algorithms. Our parallel prune-and-search technique also leads to efficient EREW PRAM algorithm for the weighted selection problem, and is likely to be useful in solving other problems. (C) 2002 Elsevier Science B.V. All rights reserved.
Servo error pre-compensation and feedrate optimization are often performed independently to improve the accuracy and speed of manufacturing machines. However, this independent approach leads to unnecessary trade-offs ...
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Servo error pre-compensation and feedrate optimization are often performed independently to improve the accuracy and speed of manufacturing machines. However, this independent approach leads to unnecessary trade-offs between productivity and quality in manufacturing. This paper proposes a novel linear programming approach for combined servo error pre-compensation and feedrate optimization, subject to contour error (tolerance) and kinematic constraints. The incorporation of servo error pre-compensation into feedrate optimization allows for faster motions without violating tolerance constraints. Experiments carried out on a 3D printer and precision motion stage are respectively used to demonstrate up to 43% and 47% reduction in cycle time without compromising part quality using the proposed approach compared with the independent approach.
Numerical implementations of optimization algorithms often use parameters whose values are not strictly determined by the derivation of the algorithm, but must fall in some appropriate range of values. This work descr...
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Numerical implementations of optimization algorithms often use parameters whose values are not strictly determined by the derivation of the algorithm, but must fall in some appropriate range of values. This work describes how fully logic can be used to "control" such parameters to improve algorithm performance. This concept is shown with the use of sequential linear programming (SLP) due to its simplicity in implementation. The algorithm presented in this paper implements heuristics to improve the behavior of SLP based on current iterate values of design constraints and changes in search direction. Fuzzy logic is used to implement the heuristics in a form similar to what a human observer would do. AR efficient algorithm, known as the infeasible primal-dual path-following interior-point method is used for solving the sequence of LP problems. Four numerical examples are presented to show that the proposed SLP algorithm consistently performs better than the standard SLP algorithm.
It is an NP-complete problem to find several figures from a given set of figures and make their sum equal to a designated figure. In this paper, the linear programming model is used to model it, and its Excel solution...
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For a given family of spatially coupled codes, we prove that the linear programming (LP) threshold on the binary-symmetric channel (BSC) of the tail-biting graph cover ensemble is the same as the LP threshold on the B...
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This paper presents a new idea to solve fractional differential equations and fractional optimal control problems. The fractional derivative is defined in the Grunwald-Letnikov sense. The method is based on the linear...
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This paper presents a new idea to solve fractional differential equations and fractional optimal control problems. The fractional derivative is defined in the Grunwald-Letnikov sense. The method is based on the linear programming problem. In this paper, by using first the concept of fractional derivatives, we will suggest a method where an equation with a fractional derivative is changed to a linear programming problem, and by solving it the fractional derivative will be obtained. Actually this suggested method is based on the minimization of total error. Some numerical examples are provided to confirm the accuracy of the proposed method.
Joint object matching, also known as multi-image matching, namely, the problem of finding consistent partial maps among all pairs of objects within a collection, is a crucial task in many areas of computer vision. Thi...
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Joint object matching, also known as multi-image matching, namely, the problem of finding consistent partial maps among all pairs of objects within a collection, is a crucial task in many areas of computer vision. This problem subsumes bipartite graph matching and graph partitioning as special cases and is NP-hard, in general. We develop scalable linear programming (LP) relaxations with theoretical performance guarantees for joint object matching. We start by proposing a new characterization of consistent partial maps;this in turn enables us to formulate joint object matching as an integer linear programming (ILP) problem. To construct strong LP relaxations, we study the facial structure of the convex hull of the feasible region of this ILP, which we refer to as the joint matching polytope. We present an exponential family of facet-defining inequalities that can be separated in strongly polynomial time, hence obtaining a partial characterization of the joint matching polytope that is both tight and cheap to compute. To analyze the theoretical performance of the proposed LP relaxations, we focus on permutation group synchronization, an important special case of joint object matching. We show that under the random corruption model for the input maps, a simple LP relaxation, that is, an LP containing only a very small fraction of the proposed facet-defining inequalities, recovers the ground truth with high probability if the corruption level is below 40%. Finally, via a preliminary computational study on synthetic data, we show that the proposed LP relaxations outperform a popular SDP relaxation both in terms of recovery and tightness.
The primary methods of assessing the reliability of distribution networks comprise analytic and simulation methods. However, both approaches require the identification and computation of network topology, which preclu...
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The primary methods of assessing the reliability of distribution networks comprise analytic and simulation methods. However, both approaches require the identification and computation of network topology, which precludes their expression in explicit, continuous functions, consequently impeding the incorporation of reliability constraints into planning and operational optimization models. To tackle this restriction, the present work puts forth a novel linear-programming-based reliability assessment method that is mathematically formulated, considering distribution automation (DA) and distributed generations (DGs), consisting of both conventional and renewable energy sources. In this paper, the clustering method and the scenario-based method are used to model DGs. Next, a mixed integer linear programming (MILP) model, considering the DA and DGs with the System Average Interruption Duration Index (SAIDI) as the optimization objective, is proposed. Finally, the feasibility and effectiveness of the proposed method are verified in a 37-node distribution network system.
Ellipsoids that contain all optimal dual slack solutions and those that contain all optimal primal solutions and that are independent of the algorithm used are derived. Based upon these ellipsoids, two criteria each f...
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Ellipsoids that contain all optimal dual slack solutions and those that contain all optimal primal solutions and that are independent of the algorithm used are derived. Based upon these ellipsoids, two criteria each for detecting optimal basic and nonbasic variables prior to optimality in interior-point methods are obtained. Using these results, we then derive a sufficient condition for a linear program to be feasible.
We describe the code PCx, a primal-dual interior-point code for linear programming. Information is given about problem formulation and the underlying algorithm, along with instructions for installing, invoking, and us...
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We describe the code PCx, a primal-dual interior-point code for linear programming. Information is given about problem formulation and the underlying algorithm, along with instructions for installing, invoking, and using the code. Computational results on standard test problems are reported.
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