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A Simple Approximation Algorithm for the Weighted Matching Problem
 Information Processing Letters
, 2003
"... We present a linear time approximation algorithm with a performance ratio of 1/2 for nding a maximum weight matching in an arbitrary graph. Such a result is already known and is due to Preis [7]. ..."
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Cited by 53 (4 self)
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We present a linear time approximation algorithm with a performance ratio of 1/2 for nding a maximum weight matching in an arbitrary graph. Such a result is already known and is due to Preis [7].
A lineartime approximation algorithm for weighted matchings in graphs
 ACM TRANSACTIONS ON ALGORITHMS
, 2005
"... Approximation algorithms have so far mainly been studied for problems that are not known to have polynomial time algorithms for solving them exactly. Here we propose an approximation algorithm for the weighted matching problem in graphs which can be solved in polynomial time. The weighted matching p ..."
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Cited by 23 (0 self)
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Approximation algorithms have so far mainly been studied for problems that are not known to have polynomial time algorithms for solving them exactly. Here we propose an approximation algorithm for the weighted matching problem in graphs which can be solved in polynomial time. The weighted matching problem is to find a matching in an edge weighted graph that has maximum weight. The first polynomialtime algorithm for this problem was given by Edmonds in 1965. The fastest known algorithm for the weighted matching problem has a running time of O(nm + n² log n). Many real world problems require graphs of such large size that this running time is too costly. Therefore, there is considerable need for faster approximation algorithms for the weighted matching problem. We present a lineartime approximation algorithm for the weighted matching problem with a performance ratio arbitrarily close to 2/1. This improves the previously best performance ratio of 3/2. Our algorithm is not only of theoretical interest, but because it is easy to implement and the constants involved are quite small it is also useful in practice.
WEIGHTED MATCHING IN THE SEMISTREAMING MODEL
, 2008
"... We reduce the best known approximation ratio for finding a weighted matching of a graph using a onepass semistreaming algorithm from 5.828 to 5.585. The semistreaming model forbids random access to the input and restricts the memory to O(n · polylog n) bits. It was introduced by Muthukrishnan in ..."
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Cited by 13 (1 self)
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We reduce the best known approximation ratio for finding a weighted matching of a graph using a onepass semistreaming algorithm from 5.828 to 5.585. The semistreaming model forbids random access to the input and restricts the memory to O(n · polylog n) bits. It was introduced by Muthukrishnan in 2003 and is appropriate when dealing with massive graphs.
Improving performance and availability of services hosted on IaaS clouds with structural constraintaware virtual machine placement
 in IEEE SCC
, 2011
"... Abstract—The increasing popularity of modern virtualizationbased datacenters continues to motivate both industry and academia to provide answers to a large variety of new and challenging questions. In this paper we aim to answer focusing on one such question: how to improve performance and availabil ..."
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Abstract—The increasing popularity of modern virtualizationbased datacenters continues to motivate both industry and academia to provide answers to a large variety of new and challenging questions. In this paper we aim to answer focusing on one such question: how to improve performance and availability of services hosted on IaaS clouds. Our system, structural constraintaware virtual machine placement (SCAVP), supports three types of constraints: demand, communication and availability. We formulate SCAVP as an optimization problem and show its hardness. We design a hierarchical placement approach with four approximation algorithms that efficiently solves the SCAVP problem for large problem sizes. We provide a formal model for the application (to better understand structural constraints) and the datacenter (to effectively capture capabilities), and use the two models as inputs to the placement problem. We evaluate SCAVP in a simulated environment to illustrate the efficiency and importance of the proposed approach.
9 Linear Time Approximation Algorithms for Degree Constrained Subgraph Problems
"... Summary. Many realworld problems require graphs of such large size that polynomial time algorithms are too costly as soon as their runtime is superlinear. Examples include problems in VLSIdesign or problems in bioinformatics. For such problems the question arises: What is the best solution that ca ..."
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Summary. Many realworld problems require graphs of such large size that polynomial time algorithms are too costly as soon as their runtime is superlinear. Examples include problems in VLSIdesign or problems in bioinformatics. For such problems the question arises: What is the best solution that can be obtained in linear time? We survey linear time approximation algorithms for some classical problems from combinatorial optimization, e.g. matchings and branchings. For many combinatorial optimization problems arising from realworld applications, efficient, i.e., polynomial time algorithms are known for computing an optimum solution. However, there exist several applications for which the input size can easily exceed 10 9. In such cases polynomial time algorithms with a runtime that is quadratic
www.stacsconf.org WEIGHTED MATCHING IN THE SEMISTREAMING MODEL
"... Abstract. We reduce the best known approximation ratio for finding a weighted matching of a graph using a onepass semistreaming algorithm from 5.828 to 5.585. The semistreaming model forbids random access to the input and restricts the memory to O(n · polylog n) bits. It was introduced by Muthukr ..."
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Abstract. We reduce the best known approximation ratio for finding a weighted matching of a graph using a onepass semistreaming algorithm from 5.828 to 5.585. The semistreaming model forbids random access to the input and restricts the memory to O(n · polylog n) bits. It was introduced by Muthukrishnan in 2003 and is appropriate when dealing with massive graphs. hal00255934, version 1 14 Feb 2008 1.