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approximation algorithms for network design with metric costs

SIAM JOURNAL ON DISCRETE MATHEMATICS 2007年第3期21卷 612-636页

作者： Cheriyan, Joseph Vetta, Adrian Univ Waterloo Dept Combinator & Optimizat Waterloo ON N2L 3G1 Canada McGill Univ Sch Comp Sci Dept Math & Stat Montreal PQ H3A 2A7 Canada

We study undirected networks with edge costs that satisfy the triangle inequality. Let n denote the number of nodes. We present an O(1)-approximation algorithm for a generalization of the metric-cost subset k-node-connectivity problem. Our approximation guarantee is proved via lower bounds that apply to the simple edge-connectivity version of the problem, where the requirements are for edge-disjoint paths rather than for openly node-disjoint paths. A corollary is that, for metric costs and for each k = 1, 2,..., n - 1, there exists a k-node connected graph whose cost is within a factor of 22 of the cost of any simple k-edge connected graph. Based on our O( 1)- approximation algorithm, we present an O(log r(max))-approximation algorithm for the metric-cost node-connectivity survivable network design problem, where rmax denotes the maximum requirement over all pairs of nodes. Our results contrast with the case of edge costs of 0 or 1, where Kortsarz, Krauthgamer, and Lee. [SIAM J. Comput., 33 (2004), pp. 704-720] recently proved, assuming NP not subset of DTIME(n(polylog(n))), a hardness-of-approximation lower bound of 2(log1-epsilon) (n) for the subset k-node-connectivity problem, where epsilon denotes a small positive number.

关键词： approximation algorithm linear programming relaxation network design vertex-connectivity edge-connectivity

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APPROXIMATING A BEHAVIOURAL PSEUDOMETRIC WITHOUT DISCOUNT FOR PROBABILISTIC SYSTEMS

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LOGICAL METHODS IN COMPUTER SCIENCE 2008年第2期4卷

作者： Van Breugel, Franck Sharma, Babita Worrell, James York Univ Toronto ON M3J 1P3 Canada IBM Corp Toronto Lab Markham ON L6G 1C7 Canada Univ Oxford Comp Lab Oxford OX1 3QD England

Desharnais, Gupta, Jagadeesan and Panangaden introduced a family of behavioural pseudometrics for probabilistic transition systems. These pseudometrics are a quantitative analogue of probabilistic bisimilarity. Distance zero captures probabilistic bisimilarity. Each pseudometric has a discount factor, a real number in the interval (0, 1]. The smaller the discount factor, the more the future is discounted. If the discount factor is one, then the future is not discounted at all. Desharnais et al. showed that the behavioural distances can be calculated up to any desired degree of accuracy if the discount factor is smaller than one. In this paper, we show that the distances can also be approximated if the future is not discounted. A key ingredient of our algorithm is Tarski's decision procedure for the first order theory over real closed fields. By exploiting the Kantorovich-Rubinstein duality theorem we can restrict to the existential fragment for which more efficient decision procedures exist.

关键词： probabilistic transition system behavioural pseudometric probabilistic bisimilarity approximation algorithm

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On the Minimum Common Integer Partition Problem

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ACM TRANSACTIONS ON algorithmS 2008年第1期5卷 1-18页

作者： Chen, Xin Liu, Lan Liu, Zheng Jiang, Tao Google Inc Search Qual Dept Mountain View CA USA Nanyang Technol Univ Sch Phys & Math Sci Singapore Singapore Univ Calif Riverside Dept Comp Sci & Engn Riverside CA 92521 USA

We introduce a new combinatorial optimization problem in this article, called the minimum common integer partition (MCIP) problem, which was inspired by computational biology applications including ortholog assignment and DNA fingerprint assembly. A partition of a positive integer n is a multiset of positive integers that add up to exactly n, and an integer partition of a multiset S of integers is defined as the multiset union of partitions of integers in S. Given a sequence of multisets S-1, S-2, ... , S-k of integers, where k >= 2, we say that a multiset is a common integer partition if it is an integer partition of every multiset S-i, 1 <= i <= k. The MCIP problem is thus defined as to find a common integer partition of S-1, S-2, ... , S-k with the minimum cardinality, denoted as MCIP(S-1, S-2, ... , S-k). It is easy to see that the MCIP problem is NP-hard, since it generalizes the well-known subset sum problem. We can in fact show that it is APX-hard. We will also present a 5/4-approximation algorithm for the MCIP problem when k = 2, and a 3k(k-1)/3k-2-approximation algorithm for k >= 3.

关键词： Subset sum integer partition NP-hard approximation algorithm computational biology combinatorial optimization

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Approximate Distance Oracles for Geometric Spanners

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ACM TRANSACTIONS ON algorithmS 2008年第1期4卷 10-10页

作者： Gudmundsson, Joachim Levcopoulos, Christos Narasimhan, Giri Smid, Michiel Natl ICT Australia Ltd Eveleigh NSW 1430 Australia Lund Univ Dept Comp Sci S-22100 Lund Sweden Florida Int Univ Sch Comp & Informat Sci Miami FL 33199 USA Carleton Univ Sch Comp Sci Ottawa ON K1S 5B6 Canada

Given an arbitrary real constant epsilon > 0, and a geometric graph G in d-dimensional Euclidean space with n points, O(n) edges, and constant dilation, our main result is a data structure that answers (1 + epsilon)-approximate shortest-path-length queries in constant time. The data structure can be constructed in O( n log n) time using O( n log n) space. This represents the first data structure that answers (1 + epsilon)-approximate shortest-path queries in constant time, and hence functions as an approximate distance oracle. The data structure is also applied to several other problems. In particular, we also show that approximate shortest-path queries between vertices in a planar polygonal domain with "rounded" obstacles can be answered in constant time. Other applications include query versions of closest-pair problems, and the efficient computation of the approximate dilations of geometric graphs. Finally, we show how to extend the main result to answer (1 + epsilon)-approximate shortest-path-length queries in constant time for geometric spanner graphs with m = omega(n) edges. The resulting data structure can be constructed in O(m + n log n) time using O(n log n) space.

关键词： Shortest paths geometric graphs approximation algorithm computational geometry spanners

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Are approximation algorithms for consensus clustering worthwhile?

Are approximation algorithms for consensus clustering worthw...

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7th SIAM International Conference on Data Mining

作者： Bertolacci, Michael Wirth, Anthony Univ Melbourne Dept Comp Sci & Software Engn Melbourne Vic 3010 Australia

ISBN: (纸本)9780898716306

Consensus clustering has emerged as one of the principal clustering problems in the data mining community. In recent years the theoretical computer science community has generated a number of approximation algorithms for consensus clustering and similar problems. These algorithms run in polynomial time, with performance guaranteed to be at most a certain factor worse than optimal. We investigate the feasibility of the approximation algorithms, in an attempt to link data-mining and theoretical research. On realistic data sets, algorithms with quadratic running times are impractical. Unfortunately these and even worse running times are typical of approximation algorithms. To circumvent this, we sample from the data, run the "slow" algorithms on the sample, and then build a consensus clustering from the seed sample clustering, using a range of techniques. These unsampling techniques are in fact almost as good at creating consensus partitionings as the approximation and data-mining algorithms themselves. We find that one of the latest approximation algorithms is not only fast and effective, but also easy to describe, making it an ideal choice.

关键词： consensus clustering approximation algorithm linear programming mining with constraints

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approximation algorithm for Weighted Weak Vertex Cover

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Journal of Computer Science & Technology 2004年第6期19卷 782-786页

作者： YongZhang HongZhu DepartmentofComputerScienceandEngineering FudanUniversityShanghai200433P.R.China LaboratoryforIntelligentInformationProcessing FudanUniversityShanghai200433P.R.China

The problem of efficiently monitoring the network flow is regarded as the problem to find out the minimum weighted weak vertex cover set for a given graphG=(V,E). In this paper, we give an approximation algorithm to solve it, which has the approximation ratio lnd+1, whered is the maximum degree of the vertex in graphG, and improve the previous work. Keywords weak vertex cover - NP-hard - approximation algorithm Note This work is supported by the Ministry of Science and Technology of China (Grant No.2001CCA03000), the National Natural Science Foundation of China (Grant No.60273045), and the Shanghai Science and Technology Development Foundation (Grant No.025115032).

关键词： weak vertex cover NP-hard approximation algorithm

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approximation algorithm for Bottleneck Steiner Tree Problem in the Euclidean Plane

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Journal of Computer Science & Technology 2004年第6期19卷 791-794页

作者： Zi-MaoLi Da-MingZhu Shao-HanMa SchoolofComputerScienceandTechnology ShandongUniversityJinan250061P.R.China

A special case of the bottleneck Steiner tree problem in the Euclidean plane was considered in this paper. The problem has applications in the design of wireless communication networks, multifacility location, VLSI routing and network routing. For the special case which requires that there should be no edge connecting any two Steiner points in the optimal solution, a 3-restricted Steiner tree can be found indicating the existence of the performance ratio root2. In this paper, the special case of the problem is proved to be NP-hard and cannot be approximated within ratio root2. First a simple polynomial time approximation algorithm with performance ratio root3 is presented. Then based on this algorithm and the existence of the 3-restricted Steiner tree, a polynomial time approximation algorithm with performance ratio-root2 + epsilon is proposed, for any epsilon > 0.

关键词： bottleneck Steiner tree approximation algorithm performance ratio algorithm design and analysis

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Scheduling jobs on a single machine with inventory operations

Scheduling jobs on a single machine with inventory operation...

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第七届运筹学及其应用国际研讨会

作者： Bao-Qiang Fan Guo-Chun Tang Shu-Xia Zhang Department of Mathematics Ludong University Institute of Management Engineering Shanghai Second Polytechnic University Department of Watercraft CommandňZhenjiang Watercraft College

In the classical scheduling problems, it is always assumed that jobs would be delivery immediately when they are completed. However, in many production-distribution systems, the jobs are required to be delivered by their due date but completed times. Then those jobs completed ahead of their due dates must be stored. In this paper, we consider the single machine scheduling problem with inventory operations. The objective is to minimize makespan subject to minimize ∑Uj . We show the problem is strongly NP-hard. A polynomial 2-approximation scheme for the problem is presented and a special case of the problem, in which each job is one unit in size, is provided an optimal algorithm.

关键词： scheduling strongly NP-hard approximation algorithm performance ratio makespan

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A performance guaranteed distributed multicast algorithm for long-lived directional communications in WANETs 08

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Proceedings of the 15th international conference on High performance computing

作者： Song Guo Minyi Guo Victor Leung School of Computer Science and Engineering University of Aizu Aizu-Wakamatsu Fukushima Japan Department of Electrical and Computer Engineering University of British Columbia Vancouver British Columbia Canada

ISBN: (纸本)9783540898931

We consider the lifetime optimization problem for multicasting inwireless ad hoc networks, in which each node is equipped with a directional antennaand has limited energy supplies. In this paper, we propose a new distributedalgorithm, whose performance in terms of providing long-lived multicasttree is guaranteed by our theoretical analysis. We prove that its approximationratio is bounded by a finite number. In particular, the derived upper bound in aclosed form shows that the algorithm can achieve global optimal in some *** real performance of this new proposed algorithm is also evaluated usingsimulation studies and the experimental results show that it outperforms otherdistributed algorithms.

关键词： approximation algorithm directional antenna energy efficiency multicast wireless ad hoc network

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A New Nature-inspired algorithm for Load Balancing

A New Nature-inspired Algorithm for Load Balancing

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The 11th IEEE International Conference on Communications Systems(第11届电子和电气工程师协会国际通信系统会议)(IEEE ICCS 2008)

作者： Xiang Feng Francis C.M.Lau Dianxun Shuai Department of Computer Science East China University of Science and Technology Shanghai China 200237 Department of Computer Science The University of Hong Kong Hong Kong Department of Computer Science East China University of Science and Technology Shanghai China 20023

The classical Load Balancing Problem (LBP) is to map tasks to processors so as to minimize the maximum load. Solving the LBP successfully would lead to better utilization of resources and better performance. The LBP has been proven to be NP-hard, thus generating the exact solutions in a tractable amount of time becomes infeasible when the problems become *** present a new nature-inspired approximation algorithm based on the Particle Mechanics (PM) model to compute in parallel approximate *** solutions for LBPs. Just like other Nature-inspired algorithms (NAs) drawing from observations of physical processes that occur in nature, the PM algorithm is inspired by physical models of particle kinematics and dynamics. The PM algorithm maps the classical LBP to the movement of particles in a *** by a corresponding mathematical model in which all particles move according to certain *** rules until reaching a stable state. By anti-mapping the stable state, the solution to LBP can be obtained.

关键词： Load balancing approximation algorithm nature-inspired algorithm particle mechanics model distributed and parallel algorithm.

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