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approximate algorithms for the container loading problem

International Transactions in Operational Research 2002年第6期9卷 747-774页

作者： Hifi, M. Université de Picardie Jules Verne France

In this paper we develop several algorithms for solving three–dimensional cutting/packing problems. We begin by proposing an adaptation of the approach proposed in Hifi and Ouafi (1997) for solving two–staged unconstrained two–dimensional cutting problems. We show how the algorithm can be polynomially solved for producing a constant approximation ratio. We then extend this algorithm for developing better approximate algorithms. By using hill–climbing strategies, we construct some heuristics which produce a good trade–off between the computational time and the solution quality. The performance of the proposed algorithms is evaluated on different problem instances of the literature, with different sizes and densities (a total of 144 problem instances). International Federation of Operational Research Societies 2002.

关键词： approximate algorithms Combinatorial optimization Cutting/packing problems Dynamic programming Single knapsack problem

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approximate algorithms for Regulatory Motif Discovery in DNA

Approximate Algorithms for Regulatory Motif Discovery in DNA

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作者： Hasnaa Imad Al-Shaikhli Western Michigan University

学位级别：博士

Motif discovery is the problem of finding common substrings within a set of biological strings. Therefore it can be applied to finding Transcription Factor Binding Sites (TFBS) that have common patterns (motifs). A transcription factor molecule can bind to multiple binding sites in the promoter region of different genes to make these genes co-regulating. The Planted ( ) Motif Problem (PMP) is a classic version of motif discovery where is the motif length and represents the maximum allowed mutation distance. The quorum Planted ( ) Motif Problem (qPMP) is a version of PMP where the motif of length occurs in at least percent of the sequences with up to mismatches. In this thesis we develop the and ) algorithms and evaluate their performance. The ) returns a list of its highest ranked (strongest) motifs. The performance of SMF is compared with the APMotif and MEME algorithms with respect to execution time and prediction accuracy. Several performance metrics are used at both the nucleotide and the site level. The algorithms are tested on simulated datasets. The time comparisons show that SMF is faster than the APMotif and the MEME (ANR) and similar in speed to the MEME (ZOOPS). The MEME algorithm with choice OOPS is the fastest but is not practical if no prior knowledge is available. The prediction accuracy results reveal that the SMF outperforms the APMotif, and performs at the level of the best prediction accuracy of the MEME (with OOPS choice), notwithstanding that the SMF is not given a-priori information. In addition, the SMF is tested on real DNA datasets of orthologous regularity regions from multiple species, without using their related phylogenetic tree. The experiments indicate that the SMF results agree with published motifs. The ) returns a list of highest ranked (strongest) motifs occurring in at least q percent of the data sequences. The algorithm is tested on ChIPSeq (large) data that was sampled using the SamSelect algorithm. In comparison

关键词： motif finding approximate algorithms ChIP-Seq DNA sequences

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(P-1)/(p+1)-approximate algorithms for p-traveling salesmen problems on a tree with minmax objective

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DISCRETE APPLIED MATHEMATICS 1997年第3期75卷 201-216页

作者： Averbakh, I Berman, O UNIV TORONTO FAC MANAGEMENTTORONTOON M5S 1V4CANADA

Suppose p traveling salesmen must visit together all points/nodes of a tree, and the objective is to minimize the maximum of lengths of their tours. For location-allocation problems (where both optimal home locations of the salesmen and their tours must be found), which are NP-complete, fast polynomial heuristics with worst-case relative error (p - 1)/(p + 1) are presented.

关键词： traveling salesman approximate algorithms complexity

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A survey on multi-constrained optimal path computation Exact and approximate algorithms

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COMPUTER NETWORKS 2010年第17期54卷 3081-3107页

作者： Garroppo, Rosario G. Giordano, Stefano Tavanti, Luca Univ Pisa Dip Ingn Informaz I-56122 Pisa Italy

The paper presents a survey on the techniques to solve the multi-constrained optimal path (MCOP) problem Computing the MCOP is a task shared by many research areas from transportation systems to telecommunication networks In the latter the MCOP is often related to the issue of Quality of Service (QoS) routing which consists in finding a route between a couple of nodes that meets a series of QoS requirements such as bounded delay pack et loss and other parameters The MCOP problem has been faced by several authors and a plethora of solving methods is now available In the present work we draw the state of the art of exact and approximate MCOP computation algorithms with particular attention to the networking area We describe and analyse the most representative methods and for each of them we derive the worst case computational complexity In addition we provide the reader with a uniform notation and with the detailed pseudo-code of various algorithms so that the paper can indeed serve as a workable starting point for further studies on the MCOP problem (C) 2010 Elsevier B V All rights reserved

关键词： Multi Constrained Optimal Path (MCOP) Multi Objective Optimal Path (MOOP) Multi Constrained Path (MCP) Restricted Shortest Path (RSP) Quality of Service (QoS) Routing Exact algorithms approximate algorithms

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ASSESSMENT OF approximate algorithms - THE ERROR MEASURES CRUCIAL ROLE

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BIT 1986年第3期26卷 284-294页

作者： KRARUP, J PRUZAN, P UNIV COPENHAGEN INST DATALDIKUDK-2100 COPENHAGEN ODENMARK COPENHAGEN SCH ECON & BUSINESS ADM INST COMP & SYST SCIDATA ANAL SYSTDK-1925 FREDERIKSBERG CDENMARK

Initially, the distinction between exact and approximate algorithms is accounted for. We then consider a broad class of decision problems including the so-called account location ork-plant location problem (kPLP), and show that the choice of an appropriate reference value is critical; even an apparent plausible choice may lead to disputable conclusions.

关键词： F.2.1 G.1.6 approximate algorithms worst-case analysis location theory

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A simple but NP-hard Problem of Mixed-discrete Programming and its Solution by approximate algorithms

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Optimization 1985年第5期16卷 705-714页

作者： Dempe, S. Technische Hochschule Karl-Marx-Stadt Sektion Mathematik DDR - 9010 PSF 964 Karl-Marx-Stadt Germany

A NP-hard problem (P) of mixed-discrete linear programming is considered which consists in the minimization of a linear objective function subject to a special nonconnected subset of an unbounded polymatroid. For this problem we describe three polynomial approximate algorithms including a greedy algorithm and a fully polynomial approximation scheme solving a special subproblem of (P). © 1985, Taylor & Francis Group, LLC. All rights reserved.

关键词： approximate algorithms Fully polynomial approximation scheme Greedy algorithm Mixed-discrete programming Polynomial algorithms

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Divergence Measures and approximate algorithms for Valuation Based Systems 17th

Divergence Measures and Approximate Algorithms for Valuation...

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17th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU)

作者： Moral, Serafin Univ Granada Dept Comp Sci & Artificial Intelligence Granada Spain

ISBN: (纸本)9783319914794;9783319914787

This paper considers an abstract framework for expressing approximate inference algorithms in valuation based systems. It will provide a definition of a 'more informative' binary relation between representations of information as well as the basic properties of a divergence measure. The approach is illustrated with the cases of probabilistic reasoning (computation of marginal probabilities and most probable explanation) and with inference problems in propositional logic. Examples of divergence measures satisfying the basic properties will be given for these problems. Finally, we will formulate in an abstract way the mean field variational approach and the iterative belief propagation algorithm.

关键词： Valuation based systems Inference problems approximate algorithms Divergence measures Probabilistic Reasoning

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Efficient approximate algorithms for Empirical Variance with Hashed Block Sampling 22

Efficient Approximate Algorithms for Empirical Variance with...

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28th ACM SIGKDD Conference on Knowledge Discovery and Data Mining (KKD)

作者： Chen, Xingguang Zhang, Fangyuan Wang, Sibo Chinese Univ Hong Kong Hong Kong Peoples R China

ISBN: (纸本)9781450393850

Empirical variance is a fundamental concept widely used in data management and data analytics, e.g., query optimization, approximate query processing, and feature selection. A direct solution to derive the empirical variance is scanning the whole data table, which is expensive when the data size is huge. Hence, most current works focus on approximate answers by sampling. For results with approximation guarantees, the samples usually need to be uniformly independent random, incurring high cache miss rates especially in compact columnar style layouts. An alternative uses block sampling to avoid this issue, which directly samples a block of consecutive records fitting page sizes instead of sampling one record each time. However, this provides no theoretical guarantee. Existing studies show that the practical estimations can be inaccurate as the records within a block can be correlated. Motivated by this, we investigate how to provide approximation guarantees for empirical variances with block sampling from a theoretical perspective. Our results shows that if the records stored in a table are 4-wise independent to each other according to keys, a slightly modified block sampling can provide the same approximation guarantee with the same asymptotic sampling cost as that of independent random sampling. In practice, storing records via hash clusters or hash organized tables are typical scenarios in modern commercial database systems. Thus, for data analysis on tables in the data lake or OLAP stores that are exported from such hash-based storage, our strategy can be easily integrated to improve the sampling efficiency. Based on our sampling strategy, we present an approximate algorithm for empirical variance and an approximate top-k algorithm to return the k columns with the highest empirical variance scores. Extensive experiments show that our solutions outperform existing solutions by up to an order of magnitude.

关键词： Empirical Variance Block Sampling approximate algorithms

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approximate algorithms of the Min -max Weighted Distance Problem

Approximate Algorithms of the Min -max Weighted Distance Pro...

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2012 International Conference on Computer Science and Artificial Intelligence(CSAI 2012)

作者： Lin Liu Dayong Wu Department of Mathematics and Physics Zhengzhou Institute of Aeronautical Industrial Management

The location problem is one kind of special type optimized problems .The Min-max weighted distance problem is a new class of location problem, its decision problem is a NP- Complete problem. In this paper, some approximate algorithms are designed, designs a genetic algorithm by some properties of the problem, and gives the design and selection method of crossover operator, mutation operator and reproduction operator.

关键词： Location Polynomial-Time Algorithm approximate algorithms Genetic Algorithm

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approximate algorithms of the Min-max Weighted Distance Problem

Approximate Algorithms of the Min-max Weighted Distance Prob...

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2010 4th International Conference on Intelligent Information Technology Application (IITA2010)

作者： Lin Liu Department of Mathematics and Physics Zhengzhou Institute of Aeronautical Industrial Management Zhengzhou, China Dayong Wu Department of Mathematics and Physics Zhengzhou Institute of Aeronautical Industrial Management Zhengzhou, China

The location problem is one kind of special type optimized problems .The Min-max weighted distance problem is a new class of location problem, its decision problem is a NP-Complete problem. In this paper, some approximate algorithms are designed, designs a genetic algorithm by some properties of the problem, and gives the design and selection method of crossover operator, mutation operator and reproduction operator.

关键词： location polynomial-time algorithm approximate algorithms genetic algorithm

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