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检索条件"主题词=approximation algorithms"

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approximation algorithms for finding protected links to keep small diameter against link failures

Approximation algorithms for finding protected links to keep...

引用

3rd IEEE International Conference on Intelligent Networking and CollaborativeSystems, INCoS 2011

作者： Imagawa, Koji Fujimura, Takeshi Miwa, Hiroyoshi Graduate School of Science and Technology Kwansei Gakuin University Hyogo 669-1337 Japan

ISBN: (纸本)9780769545790

High reliability and performance are needed as the Internet becomes an important social infrastructure. Network delay is one of measures of performance of network. As delay between two nodes correlates roughly with the distance between them, the diameter of the network which is the maximum distance of all two nodes must be small. In addition, it is necessary to keep small network delay against network failures. Therefore, critical links whose failures significantly degrade the performance must be protected by rapid recovery so that failures cannot be detected over the IP layer. The number of these protected links must be small to restrict investment cost of facilities and operational cost for Internet service providers. Consequently, it is important to find the smallest number of links to be protected so that the diameter of a network is not more than a given integer even if a limited number of non-protected links fail. It was proved by the authors that this problem is NP-hard when the number of the simultaneous link failures, k, is more than or equal to three, and it can be solved in polynomial time when k is restricted to one. However, it was not known whether the problem is NP-hard or not when k = 2. Furthermore, no approximation algorithm was known for the NP-hard cases. In this paper, we solve these unsolved issues of this problem. First, we prove that the problem is NP-hard even if k = 2. Second, we present approximation algorithms with the approximation ratio of a fixed constant for the NP-hard cases. These results make clear the computational complexity of this problem theoretically and give the useful network design algorithms also from the practical viewpoints. © 2011 IEEE.

关键词： approximation algorithms

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approximation algorithms for independent sets in map graphs 6th

Approximation algorithms for independent sets in map graphs

引用

6th Annual International Conference on Computing and Combinatorics, COCOON 2000

作者： Chen, Zhi-Zhong Department of Mathematical Sciences Tokyo Denki University Hatoyama Saitama350-0394 Japan

ISBN: (纸本)3540677879

This paper presents polynomial-time approximation algorithms for the problem of computing a maximum independent set in a given map graph G with or without weights on its vertices. If G is given together with a map, then a ratio of 1+ δ can be achieved in O(n2) time for any given constant δ > 0, no matter whether each vertex of G is given a weight or not. In case G is given without a map, a ratio of 4 can be achieved in O(n7) time if no vertex is given a weight, while a ratio of O(log n) can be achieved in O(n7 log n) time otherwise. Behind the design of our algorithms are several fundamental results for map graphs;these results can be used to design good approximation algorithms for coloring and vertex cover in map graphs, and may nd applications to other problems on map graphs as well. © Springer-Verlag Berlin Heidelberg 2000.

关键词： approximation algorithms

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approximation algorithms in batch processing 10th

Approximation algorithms in batch processing

引用

10th Annual International Symposium on algorithms and Computation, ISAAC 1999

作者： Deng, Xiaotie Poon, Chung Keung Zhang, Yuzhong Department of Computer Science City University of Hong Kong Hong Kong Institute of Operations Research Qufu Normal University Qufu Shandong China

ISBN: (纸本)3540669167

We study the scheduling of a set of jobs, each characterised by a release (arrival) time and a processing time, for a batch processing machine capable of running (at most) a fixed number of jobs at a time. When the job release times and processing times are known a-priori and the inputs are integers, we obtained an algorithm for finding a schedule with the minimum makespan. The running time is pseudo-polynomial when the number of distinct job release times is constant. We also obtained a fully polynomial time approximation scheme when the number of distinct job release times is constant, and a polynomial time approximation scheme when that number is arbitrary. When nothing is known about a job until it arrives, i.e., the on-line setting, we proved a lower bound of (5 + 1)/2 on the competitive ratio of any approximation algorithm. This bound is tight when the machine capacity is unbounded. © Springer-Veriag Berlin Heidelberg 1999.

关键词： approximation algorithms

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approximation algorithms for multi-budgeted network design problems 1

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22nd International Colloquium on Structural Information and Communication Complexity, SIROCCO 2015

作者： Stamoulis, Georgios LAMSADE PSL* Research University Université Paris-Dauphine CNRS UMR 7243 France Universitá della svizzera Italiana Lugano Switzerland

ISBN: (数字)9783319252582

ISBN: (纸本)9783319252575

We study the multi-budgeted version of the Survivable Network Design Problem [3] where, besides the usual connectivity requirements between pairs of points, we also need to satisfy a set of linear constraints (the budgets). For this case, we provide a polynomial time (3,3) bi-criteria approximation algorithm for the problem which is based on combinatorial properties of the extreme point solutions of the natural linear relaxation of the problem. © Springer International Publishing Switzerland 2015.

关键词： approximation algorithms

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approximation algorithms for Maximum Weighted Throughput on Unrelated Machines 26

Approximation Algorithms for Maximum Weighted Throughput on ...

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26th International Conference on approximation algorithms for Combinatorial Optimization Problems, APPROX 2023 and the 27th International Conference on Randomization and Computation, RANDOM 2023

作者： Karakostas, George Kolliopoulos, Stavros G. Department of Computing & Software McMaster University Hamilton Canada Department of Informatics and Telecommunications National and Kapodistrian University of Athens Greece

ISBN: (纸本)9783959772969

We study the classic weighted maximum throughput problem on unrelated machines. We give a (1 − 1/e − Ε)-approximation algorithm for the preemptive case. To our knowledge this is the first ever approximation result for this problem. It is an immediate consequence of a polynomial-time reduction we design, that uses any ρ-approximation algorithm for the single-machine problem to obtain an approximation factor of (1 − 1/e)ρ − Ε for the corresponding unrelated-machines problem, for any Ε > 0. On a single machine we present a PTAS for the non-preemptive version of the problem for the special case of a constant number of distinct due dates or distinct release dates. By our reduction this yields an approximation factor of (1 − 1/e) − Ε for the non-preemptive problem on unrelated machines when there is a constant number of distinct due dates or release dates on each machine. © 2023 Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. All rights reserved.

关键词： approximation algorithms

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approximation algorithms for a point-to-surface registration problem in medical navigation

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1st International Frontiers in Algorithmics Workshop, FAW 2007

作者： Dimitrov, Darko Knauer, Christian Kriegel, Klaus Stehn, Fabian Institut für Informatik Freie Universität Berlin

ISBN: (纸本)9783540738138

We present two absolute error approximation algorithms for a point-to-surface registration problem in 3D with applications in medical navigation systems. For a given triangulated or otherwise dense sampled surface S, a small point set P ⊂ 3 and an error bound μ we present two algorithms for computing the set T of rigid motions, so that the directed Hausdorff distance of P transformed by any of these rigid motions to S is at most the Hausdorff distance of the best semioptimal1 matching plus the user chosen error bound μ. Both algorithms take advantage of so called characteristic points Sc ⊂ S and Pc ⊂ P P which are used to reduce the search space significantly. We restrict our attention to scenarios with |Pc| = 2. The algorithms are implemented and compared with respect to their efficiency in different settings. © Springer-Verlag Berlin Heidelberg 2007.

关键词： approximation algorithms

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approximation algorithms for the bandwidth minimization problem for caterpillar graphs 2

Approximation algorithms for the bandwidth minimization prob...

引用

2nd IEEE Symposium on Parallel and Distributed Processing, SPDP 1990

作者： Haralambides, J. Makedon, F. Monien, B. Computer Science Program University of Texas at Dallas RichardsonTX75083-0688 United States Dept.of Math and C.S. University of Paderborn Warburger Strasse Paderborn4790 Germany

ISBN: (纸本)0818620870

The bandwidth minimization problem (BMP) is the problem, given a graph G and an integer k, to map the vertices of G to distinct positive integers, so that no edge of G has its endpoints mapped to integers that differ by more than k. There is no known approximation algorithm for this problem, even for the case of trees. The authors present two different approximation algorithms for the BMP for the case of special graphs, called caterpillars. The BMP for caterpillars is related to multiprocessor scheduling. It has been shown to be NP-complete, even for degree-3 trees. The authors first algorithm, gives an O(log n) times optimal algorithm, where n is the number of nodes of the caterpillar. It is based on the idea of level algorithms. The second algorithm gives an square root n times approximation. It is based on a greedy approach and outperforms the first one up to a certain value n=n0 due to the constants involved. © 1990 IEEE.

关键词： approximation algorithms

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approximation algorithms for Vertex-Connectivity Augmentation on the Cycle 19th

Approximation Algorithms for Vertex-Connectivity Augmentatio...

引用

19th International Workshop on approximation and Online algorithms, WAOA 2021

作者： Gálvez, Waldo Sanhueza-Matamala, Francisco Soto, José A. Department of Computer Science Technical University of Munich Munich Germany Departamento de Ingeniería Matemática Universidad de Chile Santiago Chile Centro de Modelamiento Matemático IRL 2807 CNRS Universidad de Chile Santiago Chile

ISBN: (纸本)9783030927011

Given a k-vertex-connected graph G and a set S of extra edges (links), the goal of the k-vertex-connectivity augmentation problem is to find a subset S′ of S of minimum size such that adding S′ to G makes it (k+ 1 ) -vertex-connected. Unlike the edge-connectivity augmentation problem, research for the vertex-connectivity version has been sparse. In this work we present the first polynomial time approximation algorithm that improves the known ratio of 2 for 2-vertex-connectivity augmentation, for the case in which G is a cycle. This is the first step for attacking the more general problem of augmenting a 2-connected graph. Our algorithm is based on local search and attains an approximation ratio of 1.8703. To derive it, we prove novel results on the structure of minimal solutions. © 2021, Springer Nature Switzerland AG.

关键词： approximation algorithms

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approximation algorithms for hamming clustering problems 11

Approximation algorithms for hamming clustering problems

引用

11th Annual Symposium on Combinatorial Pattern Matching, CPM 2000

作者： G Ą Sieniec, Leszek Jansson, Jesper Lingas, Andrzej Dept. of Computer Science University of Liverpool Peach Street LiverpoolL69 7ZF United Kingdom Dept. of Computer Science Lund University Box 118 Lund221 00 Sweden

ISBN: (纸本)3540676333

We study Hamming versions of two classical clustering problems. The Hamming radius p-clustering problem (HRC) for a set S of k binary strings, each of length n, is to find p binary strings of length n that minimize the maximum Hamming distance between a string in S and the closest of the p strings;this minimum value is termed the p-radius of S and is denoted by ϱ: The related Hamming diameter p-clustering problem (HDC) is to split S into p groups so that the maximum of the Hamming group diameters is minimized;this latter value is called the p-diameter of S. First, we provide an integer programming formulation of HRC which yields exact solutions in polynomial time whenever k and p are constant. We also observe that HDC admits straightforward polynomial- time solutions when k = O(log n) or p = 2. Next, by reduction from the corresponding geometric p-clustering problems in the plane under the L1 metric, we show that neither HRC nor HDC can be approximated within any constant factor smaller than two unless P=NP. We also prove that for any Ε > 0 it is NP-hard to split S into at most pk1/7–Ε clusters whose Hamming diameter doesn't exceed the p-diameter. Fur- thermore, we note that by adapting Gonzalez' farthest-point clustering algorithm [6], HRC and HDC can be approximated within a factor of two in time O(pkn). Next, we describe a 2O(pϱ/Ε)kO(p/Ε)n2-time (1+Ε)-approximation algorithm for HRC. In particular, it runs in polynomial time when p = O(1) and ϱ = O(log(k+n)): Finally, we show how to find in O((formula presented) + kn log n + k2 log n)(2ϱk)2/Ε) time a set L of O(p log k) strings of length n such that for each string in S there is at least one string in L within distance (1 + Ε)%, for any constant 0 © Springer-Verlag Berlin Heidelberg 2000.

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approximation algorithms for dynamic storage allocation 4th

Approximation algorithms for dynamic storage allocation

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4th European Symposium on algorithms, ESA 1996

作者： Gergov, Jordan Max-Planck-Institut für Informatik SaarbrückenD-66123 Germany

ISBN: (纸本)3540616802

We present a new O(n log n)-time 5-approximation algorithm for the NP-hard dynamic storage allocation problem (DSA). The two previous approximation algorithms for DSA are based on on-line coloring of interval graphs and have approximation ratios of 6 and 80 [6, 7, 16]. Our result gives an affirmative answer to the important open question of whether the approximation ratio of DSA can be improved below the bound implied by on-line coloring of interval graphs [7, 16]. Our approach is based on the novel concept of a 2-allocation and on the design of an efficient transformation of a 2-allocation to an at most 5/2 times larger memory allocation. For the NP-hard variant of DSA with only two sizes of blocks allowed, we give a simpler 2-approximation algorithm. Further, by means of a tighter analysis of the widely used First Fit strategy, we show how the competitive ratio of on-line DSA can be improved to Θ(max{1, log(nk/M)}) where M, k, and n are upper bounds on the maximum number of simultaneously occupied cells, the maximum number of blocks simultaneously in the storage, and the maximum size of a block. © Springer-Verlag Berlin Heidelberg 1996.

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