In the last few years line-sweep has become the standard method to solve problems that involve computing some property of a set of planar objects. In this paper we argue that at least for sets of orthogonal objects di...
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In the last few years line-sweep has become the standard method to solve problems that involve computing some property of a set of planar objects. In this paper we argue that at least for sets of orthogonal objects divide-and-conquer is competitive, if a suitable representation of the objects is used. We support this claim by sketching three (new) time-optimal divide-and-conquer algorithms to solve the line segment intersection problem, the measure problem and the contour problem, respectively. It turns out that divide-and-conquer requires simpler supporting data structures while line-sweep permits an easier reduction to a one-dimensional problem.
Suppose we are given a graph with nodes characterized by amounts of supplies and demands of multiple commodities. The amounts of commodities stored at nodes (supplies) are given by positive numbers while those of dema...
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Suppose we are given a graph with nodes characterized by amounts of supplies and demands of multiple commodities. The amounts of commodities stored at nodes (supplies) are given by positive numbers while those of demands at nodes are given by negative numbers. To meet demands we send commodities from nodes to neighbors by using vehicles, one at each node, with some loading capacity moving to and from neighbors. In this paper we adopt a one-way transportation model in which we just send commodities from a node to one of its neighbors along an *** we choose one neighbor at each node, we have a set of trips which naturally define a graph such that each connected component has at most one cycle, which is known as a pseudoforest. We present a linear-time algorithm for deciding whether there is a set of trips that meet all demands using one-way multi-commodity transportations on a pseudoforest with node degrees bounded by a *** the algorithm, we first present an efficient algorithm for finding an optimal set of one-way one-commodity trips that minimize the maximum unmet demand on a pseudoforest, and then extend the idea to a multi-commodity problem on a pseudoforest with node degrees bounded by a constant.
To solve unpunctual delivery, low assembly line utilization and unbalanced production in the assembly shop scheduling of an automotive electronic components enterprise, the model of multi-model multiple assembly line ...
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To solve unpunctual delivery, low assembly line utilization and unbalanced production in the assembly shop scheduling of an automotive electronic components enterprise, the model of multi-model multiple assembly line mixed-lines assembling by turns was constructed and the model was solved by designing a series of optimal algorithms. In view of meeting the punctual delivery period, improving the utilization of assembly lines and the order fulfillment rate, the scheduling model was constructed different from the majority of similar models. The virtual sequence, a new neighborhood structure to avoid the adjustment in cycling improvement, was defined and combined with the scheduling rules and heuristics strategy to design three algorithms for solving the model. The performance of presented algorithms were analyzed and compared with the original scheduling results. The performance comparison results demonstrate the virtual tabu (Vtr-Tabu) algorithm can apply in the small and medium scale scheduling problem with better performance than other two. And the performance variation curves of three algorithms with the increasing of single parameter were analyzed. The computational results verify the effectiveness of the presented model and algorithms in improving delivery, the assembly line utilization and the order fulfillment rate.
Although the number of artificial neural network and machine learning architectures is growing at an exponential pace, more attention needs to be paid to theoretical guarantees of asymptotic convergence for novel, non...
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Although the number of artificial neural network and machine learning architectures is growing at an exponential pace, more attention needs to be paid to theoretical guarantees of asymptotic convergence for novel, nonlinear, high-dimensional adaptive learning algorithms. When properly understood, such guarantees can guide the algorithm development and evaluation process and provide theoretical validation for a particular algorithm design. For many decades, the machine learning community has widely recognized the importance of stochastic approximation theory as a powerful tool for identifying explicit convergence conditions for adaptive learning machines. However, the verification of such conditions is challenging for multidisciplinary researchers not working in the area of stochastic approximation theory. For this reason, this letter presents a new stochastic approximation theorem for both passive and reactive learning environments with assumptions that are easily verifiable. The theorem is widely applicable to the analysis and design of important machine learning algorithms including deep learning algorithms with multiple strict local minimizers, Monte Carlo expectation-maximization algorithms, contrastive divergence learning in Markov fields, and policy gradient reinforcement learning.
The suffix tree data structure has been intensively described, studied and used in the eighties and nineties, its linear-time construction counterbalancing his space-consuming requirements. An equivalent data structur...
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The suffix tree data structure has been intensively described, studied and used in the eighties and nineties, its linear-time construction counterbalancing his space-consuming requirements. An equivalent data structure, the suffix array, has been described by Manber and Myers in 1990. This space-economical structure has been neglected during more than a decade, its construction being too slow. Since 2003, several linear-time suffix array construction algorithms have been proposed, and this structure has slowly replaced the suffix tree in many string processing problems. All these constructions are building the suffix array from the text, and any edit operation on the text leads to the construction of a brand new suffix array. In this article, we are presenting an algorithm that modifies the suffix array and the Longest Common Prefix (LCP) array when the text is edited (insertion, substitution or deletion of a letter or a factor). This algorithm is based on a recent four-stage algorithm developed for dynamic Burrows-Wheeler Transforms (BWT). For minimizing the space complexity, we are sampling the Suffix Array, a technique used in BWT-based compressed indexes. We furthermore explain how this technique can be adapted for maintaining a sample of the Extended Suffix Array, containing a sample of the Suffix Array, a sample of the Inverse Suffix Array and the whole LCP array. Our practical experiments show that it operates very well in practice, being quicker than the fastest suffix array construction algorithm. (C) 2009 Published by Elsevier B.V.
In the constructive programming community it is commonplace to see formal developments of textbook algorithms. In the algorithm design community, on the other hand, it may be well known that the textbook solution to a...
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In the constructive programming community it is commonplace to see formal developments of textbook algorithms. In the algorithm design community, on the other hand, it may be well known that the textbook solution to a problem is not the most efficient possible. However, in presenting the more efficient solution, the algorithm designer will usually omit some of the implementation details, thus creating an algorithm gap between the abstract algorithm and its concrete implementation. This is in contrast to the formal development, which usually proceeds all the way to the complete concrete implementation of the less efficient solution. We claim that the algorithm designer is forced to omit some of the details by the relative expressive poverty of the Pascal-like languages typically used to present the solution. The greater expressiveness provided by a functional language would allow the whole story to be told in a reasonable amount of space. In this paper we use a functional language to present the development of a sophisticated algorithm all the way to the final code. We hope to bridge the algorithm gap between abstract and concrete implementations, and thereby facilitate communication between the constructive programming and algorithm design communities. (C) 1999 Elsevier Science B.V. All rights reserved.
In this paper, we study the problems of (approximately) representing a functional curve in 2-D by a set of curves with fewer peaks. Representing a function (or its curve) by certain classes of structurally simpler fun...
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In this paper, we study the problems of (approximately) representing a functional curve in 2-D by a set of curves with fewer peaks. Representing a function (or its curve) by certain classes of structurally simpler functions (or their curves) is a basic mathematical problem. Problems of this kind also find applications in applied areas such as intensity-modulated radiation therapy (IMRT). Let f be an input piece-wise linear functional curve of size n. We consider several variations of the problems. (1) Uphill-downhill pair representation (UDPR): Find two nonnegative piecewise linear curves, one nondecreasing (uphill) and one nonincreasing (downhill), such that their sum exactly or approximately represents f. (2) Unimodal representation (UR): Find a set of unimodal (single-peak) curves such that their sum exactly or approximately represents f. (3) Fewer-peak representation (FPR): Find a piecewise linear curve with at most k peaks that exactly or approximately represents f. Furthermore, for each problem, we consider two versions. For the UDPR problem, we study its feasibility version: Given epsilon > 0, determine whether there is a feasible UDPR solution for f with an approximation error epsilon;its min-epsilon version: Compute the minimum approximation errror c* such that there is a feasible UDPR solution for f with error c*. For the UR problem, we study its min-k version: Given epsilon > 0, find a feasible solution with the minimum number k* of unimodal curves for f with an error epsilon;its min-epsilon version: given k > 0, compute the minimum error epsilon* such that there is a feasible solution with at most k unimodal curves for f with error epsilon*. For the FPR problem, we study its min-k version: Given epsilon > 0, find one feasible curve with the minimum number k* of peaks for f with an error epsilon;its min-epsilon version: given k >= 0, compute the minimum error epsilon* such that there is a feasible curve with at most k peaks for f with error epsilon*. Litt
In the cyclic Towers of Hanoi problem, the discs may only move in a clockwise direction from a source peg to a specified peg subject to the usual restrictions of the standard problem. An iterative solution to the modi...
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In the cyclic Towers of Hanoi problem, the discs may only move in a clockwise direction from a source peg to a specified peg subject to the usual restrictions of the standard problem. An iterative solution to the modified problem is presented. A number of observations that lead to the construction of an iterative algorithm is also discussed.
We theoretically propose a procedure based on a cascading genetic algorithm for the design of aperiodically quasi-phase-matched gratings for frequency conversion of optical ultrafast pulses during difference-frequency...
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We theoretically propose a procedure based on a cascading genetic algorithm for the design of aperiodically quasi-phase-matched gratings for frequency conversion of optical ultrafast pulses during difference-frequency generation. By designing the sequence of a domain inversion grating, different wavelengths at the output idler pulse almost have the same phase response, so femtosecond laser pulses at wavelength 800 nm can be shifted to other wavelengths without group-velocity mismatch. (C) 2007 Optical Society of America.
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