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GENETIC AND combinatorial algorithms FOR OPTIMAL SIZING AND PLACEMENT OF ACTIVE POWER FILTERS

INTERNATIONAL JOURNAL OF APPLIED MATHEMATICS AND COMPUTER SCIENCE 2015年第2期25卷 269-279页

作者： Maciazek, Marcin Grabowski, Dariusz Pasko, Marian Silesian Tech Univ Inst Elect Engn & Comp Sci Ul Akad 10 PL-44100 Gliwice Poland

The paper deals with cost effective compensator placement and sizing. It becomes one of the most important problems in contemporary electrical networks, in which voltage and current waveform distortions increase year-by-year reaching or even exceeding limit values. The suppression of distortions could be carried out by means of three types of compensators, i.e., passive filters, active power filters and hybrid filters. So far, passive filters have been more popular mainly because of economic reasons, but active and hybrid filters have some advantages which should cause their wider application in the near future. Active power filter placement and sizing could be regarded as an optimization problem. A few objective functions have been proposed for this problem. In this paper we compare solutions obtained by means of combinatorial and genetic approaches. The theoretical discussion is followed by examples of active power filter placement and sizing.

关键词： power quality optimization active power filters harmonics genetic algorithms combinatorial algorithms

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Purely combinatorial approximation algorithms for maximum k-vertex cover in bipartite graphs

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DISCRETE OPTIMIZATION 2018年 27卷 26-56页

作者： Bonnet, Edouard Escoffier, Bruno Paschos, Vangelis Th. Stamoulis, Georgios Middlesex Univ Dept Comp Sci London England UPMC Univ Paris 6 CNRS Sorbonne Univ LIP6UMR 7606 Paris France PSL Res Univ Univ Paris Dauphine CNRS UMR 7243LAMSADE F-75016 Paris France Maastricht Univ Dept Data Sci & Knowledge Engn Maastricht Netherlands

We study the polynomial time approximation of the NP-hard MAX k-VERTEX COVER problem in bipartite graphs and propose purely combinatorial approximation algorithms . The main result of the paper is a simple combinatorial algorithm and a computer-assisted analysis of its approximation guarantee giving strong evidence that the worst approximation ratio achieved is bounded below by 0.821. We also study two simpler strategies with provable approximation ratios of 2/3 and 34/47 approximate to 0.72 respectively that already beat the only such known algorithm, namely the greedy approach which guarantees ratio (1-1/e) approximate to 0.632. Our principal motivation is to bring a satisfactory answer in the following question: to what extent combinatorial methods for MAX k-VERTEX COVEr compete with linear programming ones? (C) 2017 Elsevier B.V. All rights reserved.

关键词： Approximation algorithms combinatorial algorithms Non linear program Graph algorithms Maximum coverage

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The smallest enclosing ball of balls:: combinatorial structure and algorithms

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INTERNATIONAL JOURNAL OF COMPUTATIONAL GEOMETRY & APPLICATIONS 2004年第4-5期14卷 341-378页

作者： Fischer, K Gärtner, B ETH Inst Theoret Informat CH-8092 Zurich Switzerland

We develop algorithms for computing the exact smallest enclosing ball of a set of n balls in d-dimensional space. Unlike previous methods, we explicitly address small cases (n less than or equal to d + 2), derive the necessary primitive operations and show that they can efficiently be realized with rational arithmetic. An implementation (along with a fast and robust floating-point version) is available as part of the CGAL library. We show that Welzl's randomized linear-time algorithm for computing the ball spanned by a set of points fails to work for balls. Consequently, the existing adaptations of the method to the ball case are incorrect. In solving the small cases we may assume that the ball centers are affinely independent. Via a geometric transformation and suitable generalization, it fits into the combinatorial model of unique sink orientations whose rich structure has recently received considerable attention. One consequence is that Welzl's algorithm does work for small instances;moreover, there is a variety of pivoting methods for unique sink orientations which have the potential of being fast in practice even for high dimensions. As a by-product, we show that the problem of finding the smallest enclosing ball of balls with a fixed point on the boundary is equivalent to the problem of finding the minimum-norm point in the convex hull of a union of balls.

关键词： smallest enclosing ball minimum bounding sphere combinatorial algorithms unique sink orientation inversion transform

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The smallest enclosing ball of balls:: combinatorial structure and algorithms 03

The smallest enclosing ball of balls:: Combinatorial structu...

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19th ACM Symposium on Computational Geometry

作者： Fischer, K Gärtner, B ETH Inst Theoret Informat CH-8092 Zurich Switzerland

ISBN: (纸本)9781581136630

关键词： smallest enclosing ball minimum bounding sphere combinatorial algorithms unique sink orientation inversion transform

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Optimal blocks for maximizing the transaction fee revenue of Bitcoin miners

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JOURNAL OF combinatorial OPTIMIZATION 2025年第1期49卷 1-27页

作者： Meybodi, Mohsen Alambardar Goharshady, Amir Hooshmandasl, Mohammad Reza Shakiba, Ali Univ Isfahan Fac Math & Stat Dept Appl Math & Comp Sci Esfahan *** Iran Inst Res Fundamental Sci IPM Sch Comp Sci Tehran 193955746 Iran Hong Kong Univ Sci & Technol Dept Comp Sci & Math Clear Water Bay Hong Kong Peoples R China Univ Mohaghegh Ardabili Dept Comp Sci Ardebil Iran Univ New South Wales Sydney Australia

In this work, we consider a combinatorial optimization problem with direct applications in blockchain mining, namely finding the most lucrative blocks for Bitcoin miners, and propose optimal algorithmic solutions. Our experiments show that our algorithms increase the miners' revenues by more than a million dollars per month. Modern blockchains reward their miners in two ways: (i) a base reward for each block that is mined, and (ii) the transaction fees of those transactions that are included in the mined block. The base reward is fixed by the respective blockchain's protocol and is not under the miner's control. Hence, for a miner who wishes to maximize earnings, the fundamental problem is to form a valid block with maximal total transaction fees and then try to mine it. Moreover, in many protocols, including Bitcoin itself, the base reward halves at predetermined intervals, hence increasing the importance of maximizing transaction fees and mining an optimal block. This problem is further complicated by the fact that transactions can be prerequisites of each other or have conflicts (in case of double-spending). In this work, we consider the problem of forming an optimal block, i.e. a valid block with maximal total transaction fees, given a set of unmined transactions. On the theoretical side, we first formally model our problem as an extension of Knapsack and then show that, unlike classical Knapsack, our problem is strongly NP-hard. We also show a hardness-of-approximation result. As such, there is no hope in solving it efficiently for general instances. However, we observe that its real-world instances are quite sparse, i.e. the transactions have very few dependencies and conflicts. Using this fact, and exploiting three well-known graph sparsity parameters, namely treedepth, treewidth and pathwidth, we present exact linear-time parameterized algorithms that are applicable to the real-world instances and obtain optimal results. On the practical side, we provide an

关键词： Discrete optimization combinatorial algorithms Blockchain

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Review of combinatorial problems induced by spatial forest harvesting planning

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DISCRETE APPLIED MATHEMATICS 2006年第5期154卷 867-879页

作者： Weintraub, A Murray, AT Univ Chile Dept Ind Engn Santiago Chile Ohio State Univ Dept Geog Columbus OH 43210 USA

In the last two decades forest planning and management has become very much focused on spatially oriented decisions, due to the introduction of spatial details, such as road building, and environmental concerns, like wildlife protection, biodiversity, reducing erosion and improving water quality. This has led to modeling transformations and extensions in planning forest activities, as mixed integer decision variables are necessary to account for spatial restrictions. These new models are much harder to solve due to the added combinatorial complexity. In this paper, we discuss issues of modeling spatial criteria, as well as algorithms that have been developed to solve them, both heuristic and exact. We present these results as they have evolved in a state-of-the-art structure. (c) 2005 Elsevier B.V. All rights reserved.

关键词： spatial forestry environment combinatorial algorithms

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An exact combinatorial algorithm for minimum graph bisection

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MATHEMATICAL PROGRAMMING 2015年第2期153卷 417-458页

作者： Delling, Daniel Fleischman, Daniel Goldberg, Andrew V. Razenshteyn, Ilya Werneck, Renato F. Microsoft Res Silicon Valley Mountain View CA 94043 USA Cornell Univ Sch Operat Res & Informat Engn Ithaca NY USA MIT Comp Sci & Artificial Intelligence Lab Cambridge MA 02139 USA

We present a novel exact algorithm for the minimum graph bisection problem, whose goal is to partition a graph into two equally-sized cells while minimizing the number of edges between them. Our algorithm is based on the branch-and-bound framework and, unlike most previous approaches, it is fully combinatorial. We introduce novel lower bounds based on packing trees, as well as a new decomposition technique that contracts entire regions of the graph while preserving optimality guarantees. Our algorithm works particularly well on graphs with relatively small minimum bisections, solving to optimality several large real-world instances (with up to millions of vertices) for the first time.

关键词： Bisection Branch-and-bound Graph partition combinatorial algorithms

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High performance combinatorial algorithm design on the Cell Broadband Engine processor

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PARALLEL COMPUTING 2007年第10-11期33卷 720-740页

作者： Bader, David A. Agarwal, Virat Madduri, Kamesh Kang, Seunghwa Georgia Inst Technol Atlanta GA 30332 USA

The Sony-Toshiba-IBM Cell Broadband Engine (Cell/B.E.) is a heterogeneous multicore architecture that consists of a traditional microprocessor (PPE) with eight SIMD co-processing units (SPEs) integrated on-chip. While the Cell/B.E. processor is architected for multimedia applications with regular processing requirements, we are interested in its performance on problems with non-uniform memory access patterns. In this article, we present two case studies to illustrate the design and implementation of parallel combinatorial algorithms on Cell/B.E.: we discuss list ranking, a fundamental kernel for graph problems, and zlib, a data compression and decompression library. List ranking is a particularly challenging problem to parallelize on current cache-based and distributed memory architectures due to its low computational intensity and irregular memory access patterns. To tolerate memory latency on the Cell/B.E. processor, we decompose work into several independent tasks and coordinate computation using the novel idea of Software-Managed threads (SM-Threads). We apply this generic SPE work-partitioning technique to efficiently implement list ranking, and demonstrate substantial speedup in comparison to traditional cache-based microprocessors. For instance, on a 3.2 GHz IBM QS20 Cell/B.E. blade, for a random linked list of I million nodes, we achieve an overall speedup of 8.34 over a PPE-only implementation. Our second case study, zlib, is a data compression/decompression library that is extensively used in both scientific as well as general purpose computing. The core kernels in the zlib library are the LZ77 longest subsequence matching algorithm and Huffman data encoding. We design efficient parallel algorithms for these combinatorial kernels, and exploit concurrency at multiple levels on the Cell/B.E. processor. We also present a Cell/B.E. optimized implementation of gzip, a popular file-compression application based on the zlib library. For our Cell/B.E. implementati

关键词： combinatorial algorithms Cell Broadband Engine processor multicore list ranking zlib parallel algorithms graph algorithms performance novel architectures

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Sequential and indexed two-dimensional combinatorial template matching allowing rotations

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THEORETICAL COMPUTER SCIENCE 2005年第1-2期347卷 239-275页

作者： Fredriksson, K Navarro, G Ukkonen, E Univ Chile Dept Comp Sci Ctr Web Res Santiago Chile Univ Joensuu Dept Comp Sci FIN-80101 Joensuu Finland Univ Helsinki Dept Comp Sci FIN-00014 Helsinki Finland

We present new and faster algorithms to search for a two-dimensional pattern in a two-dimensional text allowing any rotation of the pattern. This has applications such as image databases and computational biology. We consider the cases of exact and approximate matching under several matching models, using a combinatorial approach that generalizes string matching techniques. We focus on sequential algorithms, where only the pattern can be preprocessed, as well as on indexed algorithms, where the text is preprocessed and an index built on it. On sequential searching we derive average-case lower bounds and then obtain optimal average-case algorithms for all the matching models. At the same time, these algorithms are worst-case optimal. On indexed searching we obtain search time polylogarithmic on the text size, as well as sublinear time in general for approximate searching. (c) 2005 Elsevier B.V. All rights reserved.

关键词： template matching combinatorial algorithms image processing string matching

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A combinatorial algorithm for the maximum lifetime data gathering with aggregation problem in sensor networks

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COMPUTER COMMUNICATIONS 2009年第15期32卷 1655-1665页

作者： Kalpakis, Konstantinos Tang, Shilang Univ Maryland Baltimore Cty Dept Comp Sci & Elect Engn Baltimore MD 21250 USA

Performing tasks energy efficiently in a wireless sensor network (WSN) is a critical issue for the successful deployment and operation of such networks. Gathering data from all the sensors to a base station, especially with in-network aggregation, is an important problem that has received a lot of attention recently. The Maximum Lifetime Data Gathering with Aggregation (MLDA) problem deals with maximizing the system lifetime T so that we can perform T rounds of data gathering with in-network aggregation, given the initial available energy of the sensors. A solution of value T to the MLDA problem consists of a collection of aggregation trees together with the number of rounds each such tree should be used in order to achieve lifetime T. We describe a combinatorial iterative algorithm for finding an optimal continuous solution to the MLDA problem that consists of up to n - 1 aggregation trees and achieves lifetime T-o, which depends on the network topology and initial energy available at the sensors. We obtain an alpha-approximate optimal integral solution by simply rounding down the optimal continuous solution, where alpha = (T-o - n + 1)/T-o Since in practice T-o >> n, alpha approximate to 1. We get asymptotically optimal integral solutions to the MLDA problem whenever the optimal continuous solution is omega(n). Furthermore, we demonstrate the efficiency and effectiveness of the proposed algorithm via extensive experimental results. (C) 2009 Elsevier B.V. All rights reserved.

关键词： Wireless sensor networks Lifetime maximization combinatorial algorithms Linear programming

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