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25
Finding graph matchings in data streams
 APPROXRANDOM
, 2005
"... Abstract. We present algorithms for finding large graph matchings in the streaming model. In this model, applicable when dealing with massive graphs, edges are streamedin in some arbitrary order rather than 1 ..."
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Cited by 56 (10 self)
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Abstract. We present algorithms for finding large graph matchings in the streaming model. In this model, applicable when dealing with massive graphs, edges are streamedin in some arbitrary order rather than 1
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 51 (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].
Engineering a Scalable High Quality Graph Partitioner
 24TH IEEE INTERNATIONAL PARALLAL AND DISTRIBUTED PROCESSING SYMPOSIUM (IPDPS
, 2010
"... We describe an approach to parallel graph partitioning that scales to hundreds of processors and produces a high solution quality. For example, for many instances from Walshaw’s benchmark collection we improve the best known partitioning. We use the well known framework of multilevel graph partiti ..."
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Cited by 29 (17 self)
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We describe an approach to parallel graph partitioning that scales to hundreds of processors and produces a high solution quality. For example, for many instances from Walshaw’s benchmark collection we improve the best known partitioning. We use the well known framework of multilevel graph partitioning. All components are implemented by scalable parallel algorithms. Quality improvements compared to previous systems are due to better prioritization of edges to be contracted, better approximation algorithms for identifying matchings, better local search heuristics, and perhaps most notably, a parallelization of the FM local search algorithm that works more locally than previous approaches.
Greedy in Approximation Algorithms
 PROC. OF ESA
, 2006
"... The objective of this paper is to characterize classes of problems for which a greedy algorithm finds solutions provably close to optimum. To that end, we introduce the notion of kextendible systems, a natural generalization of matroids, and show that a greedy algorithm is a 1factor approximatio ..."
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Cited by 24 (1 self)
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The objective of this paper is to characterize classes of problems for which a greedy algorithm finds solutions provably close to optimum. To that end, we introduce the notion of kextendible systems, a natural generalization of matroids, and show that a greedy algorithm is a 1factor approximation for these systems. Many seemly unrelated k problems fit in our framework, e.g.: bmatching, maximum profit scheduling and maximum asymmetric TSP. In the second half of the paper we focus on the maximum weight bmatching problem. The problem forms a 2extendible system, so greedy gives us a 1factor solution which runs in 2 O(m log n) time. We improve this by providing two linear time approximation algorithms for the problem: a 1 2factor algorithm that runs in O(bm) time, and a `2 3 − ǫ ´factor algorithm which runs in expected O ` bm log 1 ´ time.
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.
Improved Distributed Approximate Matching
"... We present improved algorithms for finding approximately optimal matchings in both weighted and unweighted graphs. For unweighted graphs, we give an algorithm providing (1 − ɛ)approximation in O(log n) time for any constant ɛ> 0. This result improves on the classical 1approximation due 2 to Isr ..."
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Cited by 20 (3 self)
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We present improved algorithms for finding approximately optimal matchings in both weighted and unweighted graphs. For unweighted graphs, we give an algorithm providing (1 − ɛ)approximation in O(log n) time for any constant ɛ> 0. This result improves on the classical 1approximation due 2 to Israeli and Itai. As a byproduct, we also provide an improved algorithm for unweighted matchings in bipartite graphs. In the context of weighted graphs, we give another algorithm which provides ( 1 − ɛ) approximation in general 2 graphs in O(log n) time. The latter result improves on the − ɛ)approximation in O(log n) time. known ( 1 4
Weighted Isotonic Regression under the L1 Norm
"... Isotonic regression, the problem of finding values that best fit given observations and conform to specific ordering constraints, has found many applications in biomedical research and other fields. When the constraints form a partial ordering, solving the problem under the L1 error measure takes O( ..."
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Cited by 9 (0 self)
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Isotonic regression, the problem of finding values that best fit given observations and conform to specific ordering constraints, has found many applications in biomedical research and other fields. When the constraints form a partial ordering, solving the problem under the L1 error measure takes O(n 3) when there are n observations. The analysis of largescale microarray data, which is one of the important tools in biology, using isotonic regression is hence expensive. This is because in microarray analysis, the same procedure is used for studying the fit of tens of thousands of genes to a given partial order. Fast estimation for the fitting error is therefore highly desired to reduce the number of regression instances through pruning. In this paper, we present approximation algorithms to the isotonic regression problem under the L1 error measure. We relate the problem to an edge packing problem and in the special case when the observations are not weighted, we relate it to a weighted matching problem.
Scaling algorithms for approximate and exact maximum weight matching
, 2011
"... The maximum cardinality and maximum weight matching problems can be solved in time Õ(m √ n), a bound that has resisted improvement despite decades of research. (Here m and n are the number of edges and vertices.) In this article we demonstrate that this “m √ n barrier ” is extremely fragile, in the ..."
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Cited by 9 (0 self)
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The maximum cardinality and maximum weight matching problems can be solved in time Õ(m √ n), a bound that has resisted improvement despite decades of research. (Here m and n are the number of edges and vertices.) In this article we demonstrate that this “m √ n barrier ” is extremely fragile, in the following sense. For any ɛ> 0, we give an algorithm that computes a (1 − ɛ)approximate maximum weight matching in O(mɛ −1 log ɛ −1) time, that is, optimal linear time for any fixed ɛ. Our algorithm is dramatically simpler than the best exact maximum weight matching algorithms on general graphs and should be appealing in all applications that can tolerate a negligible relative error. Our second contribution is a new exact maximum weight matching algorithm for integerweighted bipartite graphs that runs in time O(m √ n log N). This improves on the O(Nm √ n)time and O(m √ n log(nN))time algorithms known since the mid 1980s, for 1 ≪ log N ≪ log n. Here N is the maximum integer edge weight. 1
Approximating weighted matchings in parallel
"... revised Version Abstract. algorithm for the weighted matching problem in graphs with an approximation ratio of (1 − ɛ). This improves the previously best approximation ratio of − ɛ) of an NC algorithm for this problem. ..."
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revised Version Abstract. algorithm for the weighted matching problem in graphs with an approximation ratio of (1 − ɛ). This improves the previously best approximation ratio of − ɛ) of an NC algorithm for this problem.
LinearTime Approximation for Maximum Weight Matching
"... The maximum cardinality and maximum weight matching problems can be solved in Ã(mân) time, a bound that has resisted improvement despite decades of research. (Here m and n are the number of edges and vertices.) In this article, we demonstrate that this âm â n barrier â can be bypassed by ap ..."
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Cited by 5 (1 self)
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The maximum cardinality and maximum weight matching problems can be solved in Ã(mân) time, a bound that has resisted improvement despite decades of research. (Here m and n are the number of edges and vertices.) In this article, we demonstrate that this âm â n barrier â can be bypassed by approximation. For any É> 0, we give an algorithm that computes a (1 â É)approximate maximum weight matching in O(mÉâ1 log Éâ1) time, that is, optimal linear time for any fixed É. Our algorithm is dramatically simpler than the best exact maximum weight matching algorithms on general graphs and should be appealing in all applications that can tolerate a negligible relative error.