Results 1  10
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29
A Linear Time Approximation Algorithm for Weighted Matchings in Graphs
, 2003
"... 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 18 (3 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 polynomial time 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+n 2 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 linear time approximation algorithm for the weighted matching problem with a performance ratio arbitrarily close to 2/3
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 16 (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.
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 15 (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.
Transport in dynamical astronomy and multibody problems
 INT. J. OF BIFURCATION AND CHAOS
, 2005
"... We combine the techniques of almost invariant sets (using tree structured box elimination and graph partitioning algorithms) with invariant manifold and lobe dynamics techniques. The result is a new computational technique for computing key dynamical features, including almost invariant sets, resona ..."
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Cited by 11 (7 self)
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We combine the techniques of almost invariant sets (using tree structured box elimination and graph partitioning algorithms) with invariant manifold and lobe dynamics techniques. The result is a new computational technique for computing key dynamical features, including almost invariant sets, resonance regions as well as transport rates and bottlenecks between regions in dynamical systems. This methodology can be applied to a variety of multibody problems, including those in molecular modeling, chemical reaction rates and dynamical astronomy. In this paper we focus on problems in dynamical astronomy to illustrate the power of the combination of these different numerical tools and their applicability. In particular, we compute transport rates between two resonance regions for the three body system consisting of the Sun, Jupiter and a third body (such as an asteroid). These resonance regions are appropriate for certain comets and asteroids.
Approximating Maximum Weight Matching in Nearlinear Time
"... Given a weighted graph, the maximum weight matching problem (MWM) is to find a set of vertexdisjoint edges with maximum weight. In the 1960s Edmonds showed that MWMs can be found in polynomial time. At present the fastest MWM algorithm, due to Gabow and Tarjan, runs in Õ(m √ n) time, where m and n ..."
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Cited by 11 (2 self)
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Given a weighted graph, the maximum weight matching problem (MWM) is to find a set of vertexdisjoint edges with maximum weight. In the 1960s Edmonds showed that MWMs can be found in polynomial time. At present the fastest MWM algorithm, due to Gabow and Tarjan, runs in Õ(m √ n) time, where m and n are the number of edges and vertices in the graph. Surprisingly, restricted versions of the problem, such as computing (1 − ɛ)approximate MWMs or finding maximum cardinality matchings, are not known to be much easier (on sparse graphs). The best algorithms for these problems also run in Õ(m √ n) time. In this paper we present the first nearlinear time algorithm for computing (1 − ɛ)approximate MWMs. Specifically, given an arbitrary realweighted graph and ɛ> 0, our algorithm computes such a matching in O(mɛ −2 log 3 n) time. The previous best approximate MWM algorithm with comparable running time could only guarantee a (2/3 − ɛ)approximate solution. In addition, we present a faster algorithm, running in O(m log n log ɛ −1) time, that computes a (3/4−ɛ)approximate MWM.
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 Israel ..."
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Cited by 10 (2 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
Simple distributed weighted matchings
 In eprint cs.DC/0410047
, 2004
"... Wattenhofer et al. [WW04] derive a complicated distributed algorithm to compute a weighted matching of an arbitrary weighted graph, that is at most a factor 5 away from the maximum weighted matching of that graph. We show that a variant of the obvious sequential greedy algorithm [Pre99], that comput ..."
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Cited by 9 (1 self)
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Wattenhofer et al. [WW04] derive a complicated distributed algorithm to compute a weighted matching of an arbitrary weighted graph, that is at most a factor 5 away from the maximum weighted matching of that graph. We show that a variant of the obvious sequential greedy algorithm [Pre99], that computes a weighted matching at most a factor 2 away from the maximum, is easily distributed. This yields the best known distributed approximation algorithm for this problem so far. 1
A parallel approximation algorithm for the weighted maximum matching problem
 In Proc. Seventh Int. Conf. on Parallel Processing and Applied Mathematics (PPAM
, 2007
"... Abstract. We consider the problem of computing a weighted edge matching in a large graph using a parallel algorithm. This problem has application in several areas of combinatorial scientific computing. Since an exact algorithm for the weighted matching problem is both fairly expensive to compute and ..."
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Cited by 9 (2 self)
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Abstract. We consider the problem of computing a weighted edge matching in a large graph using a parallel algorithm. This problem has application in several areas of combinatorial scientific computing. Since an exact algorithm for the weighted matching problem is both fairly expensive to compute and hard to parallelise we instead consider fast approximation algorithms. We analyse a distributed algorithm due to Hoepman [8] and show how this can be turned into a parallel algorithm. Through experiments using both complete as well as sparse graphs we show that our new parallel algorithm scales well using up to 32 processors. 1
Linear Time Local Improvements for Weighted Matchings in Graphs
 IN INTERNATIONAL WORKSHOP ON EXPERIMENTAL AND ECIENT ALGORITHMS (WEA), LNCS 2647
, 2003
"... Recently two different linear time approximation algorithms for the weighted matching problem in graphs have been suggested [5][17]. Both these ..."
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Cited by 7 (1 self)
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Recently two different linear time approximation algorithms for the weighted matching problem in graphs have been suggested [5][17]. Both these
Lowcomplexity distributed fair scheduling for wireless multihop networks
"... Abstract — Maxmin fair bandwidth allocation is a meaningful objective whenever the level of user satisfaction cannot be clearly expressed as a function of the allocated bandwidth. In this work, we address the issue of approximating maxmin fairness in a wireless network without the requirement for ..."
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Cited by 4 (0 self)
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Abstract — Maxmin fair bandwidth allocation is a meaningful objective whenever the level of user satisfaction cannot be clearly expressed as a function of the allocated bandwidth. In this work, we address the issue of approximating maxmin fairness in a wireless network without the requirement for networkwide node coordination and we present a lowoverhead greedy distributed algorithm for reaching this goal. The algorithm is based on distributed computation of a maximum weighted matching based on appropriately defined flow weights and subsequent scheduling of link flows in an effort to provide maxmin rates to them. An inherent feature of our approach is its immunity to topology changes as well as to flow traffic variations. Our method is shown to outperform significantly the centralized (yet, conservative) algorithm of maxmin fair rate computation in general topologies in terms of total resulting throughput, minimum shares and node resource utilization. I.