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检索条件"主题词=Approximation algorithm"

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An approximation algorithm for the Smallest Color-Spanning Circle Problem 21st

An Approximation Algorithm for the Smallest Color-Spanning C...

引用

21st International Computing and Combinatorics Conference (COCOON)

作者： Wang, Yin Xu, Yinfeng Xi An Jiao Tong Univ Sch Management Xian 710049 Peoples R China State Key Lab Mfg Syst Engn Xian 710049 Peoples R China

ISBN: (纸本)9783319213989;9783319213972

To find a minimum radius circle in which at least one point of each color lies inside, we have researched the smallest enclosing circle problem for n points with m different colors. The former research proposed a pi-approximation algorithm with a running time O(n(2) + nm log m). In this paper, we construct a color-spanning set for each point and find the smallest enclosing circle to cover all points of each color-spanning set. The approach to find each color-spanning set is based on the nearest neighbor points which have different colors. An approximation algorithm to compute the minimum diameter of the enclosing circle is proposed with the time of O(nm log n + n log m) at most. The approximation ratio of our algorithm is less than 2. In conclusion, both approximation ratio and complexity are improved by our proposed algorithm.

关键词： Computational geometry Colored set approximation algorithm The minimum diameter color-spanning set problem

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An Improved approximation algorithm for Knapsack Median Using Sparsification 23rd

An Improved Approximation Algorithm for Knapsack Median Usin...

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23rd Annual European Symposium on algorithms (ESA) as part of ALGO Conference

作者： Byrka, Jaroslaw Pensyl, Thomas Rybicki, Bartosz Spoerhase, Joachim Srinivasan, Aravind Khoa Trinh Univ Warsaw Inst Comp Sci PL-00325 Warsaw Poland Univ Maryland Dept Comp Sci College Pk MD 20742 USA Univ Maryland Instute Adv Comp Studies College Pk MD 20742 USA

ISBN: (纸本)9783662483503;9783662483497

Knapsack median is a generalization of the classic k-median problem in which we replace the cardinality constraint with a knapsack constraint. It is currently known to be 32-approximable. We improve on the best known algorithms in several ways, including adding randomization and applying sparsification as a preprocessing step. The latter improvement produces the first LP for this problem with bounded integrality gap. The new algorithm obtains an approximation factor of 17.46. We also give a 3.05 approximation with small budget violation.

关键词： approximation algorithm combinatorial optimization randomized algorithm facility-location problems

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FPT approximation algorithm for Scheduling with Memory Constraints 22nd

FPT Approximation Algorithm for Scheduling with Memory Const...

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22nd International Conference on Parallel and Distributed Computing (Euro-Par)

作者： Angel, Eric Chevalier, Cedric Ledoux, Franck Morais, Sebastien Regnault, Damien Univ Evry IBISC Evry France CEA DAM DIF F-91297 Arpajon France

ISBN: (纸本)9783319436593;9783319436586

In this paper we study a scheduling problem motivated by performing intensive numerical simulations on large meshes. In order to run the simulation as fast as possible, we must allocate computations on different processors such that the makespan is minimized, but also take care of the limited memory on each processor. We present a dynamic programming based algorithm that ensures that both of these objectives are satisfied, within a ratio of 1 + epsilon. Our algorithm is fixed-parameter tractable (FPT) with respect to the path-width of the graph. For sake of readability, the algorithm is presented for two identical machines, but it can be generalized for a fixed number of unrelated processors.

关键词： Scheduling approximation algorithm Dynamic programming Fixed-parameter tractable

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A Log-Linear (2+5/6)-approximation algorithm for Parallel Machine Scheduling with a Single Orthogonal Resource 27th

A Log-Linear (2+5/6)-Approximation Algorithm for Parallel Ma...

引用

27th International European Conference on Parallel and Distributed Computing (Euro-Par)

作者： Naruszko, Adrian Przybylski, Bartlomiej Rzadca, Krzysztof Univ Warsaw Inst Informat Warsaw Poland

ISBN: (纸本)9783030856656;9783030856649

As the gap between compute and I/O performance tends to grow, modern High-Performance Computing (HPC) architectures include a new resource type: an intermediate persistent fast memory layer, called burst buffers. This is just one of many kinds of renewable resources which are orthogonal to the processors themselves, such as network bandwidth or software licenses. Ignoring orthogonal resources while making scheduling decisions just for processors may lead to unplanned delays of jobs of which resource requirements cannot be immediately satisfied. We focus on a classic problem of makespan minimization for parallel-machine scheduling of independent sequential jobs with additional requirements on the amount of a single renewable orthogonal resource. We present an easily-implementable log-linear algorithm that we prove is 25/6-approximation. In simulation experiments, we compare our algorithm to standard greedy list-scheduling heuristics and show that, compared to LPT, resource-based algorithms generate significantly shorter schedules.

关键词： Parallel machines Orthogonal resource Burst buffers Rigid jobs approximation algorithm

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An approximation algorithm for Constructing Multicast Trees with Degree-Dependent Node Costs

An Approximation Algorithm for Constructing Multicast Trees ...

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IEEE Global Telecommunications Conference (GLOBECOM 2010)

作者： Lin, Hwa-Chun Yang, Hsiu-Ming Natl Tsing Hua Univ Dept Comp Sci Hsinchu 30043 Taiwan Natl Tsing Hua Univ Inst Commun Engn Hsinchu 30043 Taiwan

ISBN: (纸本)9781424456383

This paper studies the problem of constructing a minimum-cost multicast tree (or Seiner tree) in which each node is associated with a cost that is dependent on the degree of the node on the multicast tree. The cost of a node may depend on its degree on the multicast tree due to a number of reasons. For example, a node may need to perform various processing for sending messages to each of its neighbors on the multicast tree. Thus, the overhead for processing the messages increases as the number of neighbors increases. This paper devises a novel technique to deal with the degree-dependent node costs and applies the technique to develop an approximation algorithm for the problem. The bound on the cost of the multicast tree constructed by the proposed approximation algorithm is derived.

关键词： approximation algorithm constructing multicast trees degree-dependent node costs multicast communication telecommunication network routing trees (mathematics)

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An Improved approximation algorithm for Spanning Star Forest in Dense Graphs

An Improved Approximation Algorithm for Spanning Star Forest...

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4th Annual International Conference on Combinatorial Optimization and Applications (COCOA)

作者： He, Jing Liang, Hongyu Tsinghua Univ Inst Theoret Comp Sci Beijing 100084 Peoples R China

ISBN: (纸本)9783642174605

A spanning subgraph of a given graph G is called a spanning star forest of G if it is a collection of node-disjoint trees of depth at most 1 (such trees are called stars). The size of a spanning star forest is the number of leaves in all its components. The goal of the spanning star forest problem [12] is to find the maximum-size spanning star forest of a given graph. In this paper, we study this problem in c-dense graphs, where for c is an element of (0,1), a graph of n vertices is called c-dense if it contains at least cn(2)/2 edges [2]. We design a (alpha+ (1 - alpha)root c - epsilon)-approximation algorithm for spanning star forest in c-dense graphs for any epsilon > 0, where alpha = 193/240 is the best known approximation ratio of the spanning star forest problem in general graphs [3]. Thus, our approximation ratio outperforms the best known bound for this problem when dealing with c-dense graphs. We also prove that for any c is an element of (0, 1), there is a constant epsilon = epsilon(c) > 0 such that approximating spanning star forest in c-dense graphs within a factor of 1 - epsilon is NP-hard. We then demonstrate that for weighted versions (both node- and edge- weighted) of this problem, we cannot get any approximation algorithm with strictly better performance guarantee in c-dense graphs than that of the best possible approximation algorithm for general graphs. Finally, we give strong hardness-of-approximation results for a closely related problem, the minimum dominating set problem, in c-dense graphs.

关键词： spanning star forest approximation algorithm dense graphs

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A New approximation algorithm for Vertex Cover Problem

A New Approximation Algorithm for Vertex Cover Problem

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IEEE International Conference on Machine Intelligence Research and Advancement (ICMIRA)

作者： Dahiya, Sonika Guru Gobind Singh Indraprastha Univ USICT Dept CSE IT Delhi 110078 India

ISBN: (纸本)9780769550138

Vertex Cover Problem is one among NP-Complete problems. So neither the proof of existence of a optimal solution algorithm nor the proof of no existence of such solution has been given yet. So it is desirable to try to find a near optimal solution. In this paper we give a brief introduction of existing algorithms and propose a new heuristic algorithm. This new algorithm has polynomial running time and produces a near optimal solution for the unweighted graphs and outperforms compared to the existing approximation algorithms for graph.

关键词： approximation algorithm approximation ratio degree pendant edge pendant vertex vertex cover vertex cover problem

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AN approximation algorithm TO THE SOURCEWISE GREEN'S FUNCTION IN THE D'ALEMBERT EQUATION FOR THE CIRCULAR WAVEGUIDE 10

AN APPROXIMATION ALGORITHM TO THE SOURCEWISE GREEN'S FUNCTIO...

引用

10th International Conference on Antenna Theory and Techniques (ICATT)

作者： Prijmenko, S. D. Bondarenko, L. A. NSC KIPT Inst Plasma Elect & New Methods Accelerat Kharkov Ukraine

ISBN: (纸本)9781479985579

The approximation algorithm to the tensor Green's function calculation in the D'Alembert equation for the polarization potential in the circular waveguide is proposed. The tensor Green's function is presented in the sourcewise form as the sum of the Green's function for free space and the regular part caused by reflections from the waveguide walls. The circular waveguide is a circular cylinder with a directrix in the form of a circle. The directrix in the form of a circle is approximated by a broken line in the form of an inscribed rectilinear polygon. This approximation allows one to use the method of specular reflections and get the tensor Green's function as an infinite sum of tensor divergent spherical waves with a delta-shaped front. The resulting representation of the Green's function can be used to solve the nonstationary intrinsic boundary-value problems of electrodynamics in the case of a circular waveguide with consideration for the reflections from the walls.

关键词： Sourcewise tensor Green's function circular waveguide D'Alembert equation approximation algorithm specular reflections

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An approximation algorithm for Minimizing the Cloud Carbon Footprint through Workload Scheduling 15

An Approximation Algorithm for Minimizing the Cloud Carbon F...

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15th IEEE International Conference on Cloud Computing (IEEE CLOUD) / IEEE World Congress on Services (IEEE SERVICES)

作者： Bahreini, Tayebeh Tantawi, Asser Youssef, Alaa IBM TJ Watson Res Ctr Yorktown Hts NY 10598 USA

ISBN: (数字)9781665481373

ISBN: (纸本)9781665481373

In this paper, we address the problem of workload scheduling in data centers, while considering the greenness of the power sources. We prove that finding a feasible solution for the problem is NP-hard. Therefore, we develop an LP-based approximation algorithm to solve the problem in polynomial time. The proposed algorithm provides strong approximation bounds on the constraints and the objective of the problem. We conduct an extensive experimental analysis to evaluate the performance of the proposed algorithm using real world data.

关键词： cloud optimization cloud sustainability green computing approximation algorithm resource constraine scheduling

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On an approximation algorithm Combined with D3QN for HDFS Data Block Recovery in Heterogeneous Hadoop Clusters

On an Approximation Algorithm Combined with D3QN for HDFS Da...

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Intelligent Systems Conference

作者： Zhang, Yijie Wu, Chase Q. Hou, Aiqin New Jersey Inst Technol Newark NJ 07102 USA Northwest Univ Xian 710127 Shaanxi Peoples R China

ISBN: (纸本)9783031663284;9783031663291

Hadoop stands as a cornerstone in the realm of big data processing, with its Hadoop Distributed File System (HDFS) serving as a pivotal layer ensuring fault tolerance and high throughput data storage. Through mechanisms such as block replication and cluster-wide distribution, HDFS facilitates parallel computing in higher layers. However, the inherent heterogeneity within Hadoop clusters introduces complexities, particularly concerning the reliability of stored data. The failure of DataNodes within heterogeneous clusters poses a significant risk, potentially leading to data loss and compromising data reliability. Notably, the default block recovery strategy within HDFS overlooks the varying capacities of data nodes and the diverse patterns of data access, rendering it inadequate for heterogeneous environments. To address this gap, we first propose a novel approach for block recovery selection based on dueling double deep Q-networks, augmented with Gaussian Process Regression. We further formulate block recovery placement as an optimization problem in heterogeneous clusters, show its NP-completeness, and design an approximation algorithm that leverages linear programming-based iterative rounding (LPIR-BR), which offers a robust performance guarantee. Extensive experimental results validates the efficacy of LPIR-BR, showcasing its superiority over existing algorithms and affirming the soundness of our theoretical framework.

关键词： Big data Block distribution approximation algorithm Dueling double deep Q-network Hadoop distributed file system Performance bound Reliability

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