Results 1  10
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20
On graph problems in a semistreaming model
 In 31st International Colloquium on Automata, Languages and Programming
, 2004
"... Abstract. We formalize a potentially rich new streaming model, the semistreaming model, that we believe is necessary for the fruitful study of efficient algorithms for solving problems on massive graphs whose edge sets cannot be stored in memory. In this model, the input graph, G = (V, E), is prese ..."
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Cited by 60 (12 self)
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Abstract. We formalize a potentially rich new streaming model, the semistreaming model, that we believe is necessary for the fruitful study of efficient algorithms for solving problems on massive graphs whose edge sets cannot be stored in memory. In this model, the input graph, G = (V, E), is presented as a stream of edges (in adversarial order), and the storage space of an algorithm is bounded by O(n · polylog n), where n = V . We are particularly interested in algorithms that use only one pass over the input, but, for problems where this is provably insufficient, we also look at algorithms using constant or, in some cases, logarithmically many passes. In the course of this general study, we give semistreaming constant approximation algorithms for the unweighted and weighted matching problems, along with a further algorithm improvement for the bipartite case. We also exhibit log n / log log n semistreaming approximations to the diameter and the problem of computing the distance between specified vertices in a weighted graph. These are complemented by Ω(log (1−ɛ) n) lower bounds. 1
Linear Time 1/2Approximation Algorithm for Maximum Weighted Matching in General Graphs
 IN GENERAL GRAPHS, SYMPOSIUM ON THEORETICAL ASPECTS OF COMPUTER SCIENCE, STACS 99
, 1998
"... A new approximation algorithm for maximum weighted matching in general edgeweighted graphs is presented. It calculates a matching with an edge weight of at least 1/2 of the edge weight of a maximum weighted matching. Its time complexity is O(E), with E being the number of edges in the graph. T ..."
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Cited by 37 (0 self)
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A new approximation algorithm for maximum weighted matching in general edgeweighted graphs is presented. It calculates a matching with an edge weight of at least 1/2 of the edge weight of a maximum weighted matching. Its time complexity is O(E), with E being the number of edges in the graph. This improves over the previously known 1/2approximation algorithms for maximum weighted matching which require O(E log(V)) steps, where V is the number of vertices.
Quality Matching and Local Improvement for Multilevel GraphPartitioning
, 1999
"... Multilevel strategies have proven to be very powerful approaches in order to partition graphs efficiently. Their efficiency is dominated by two parts; the coarsening and the local improvement strategies. Several methods have been developed to solve these problems, but their efficiency has only been ..."
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Cited by 28 (9 self)
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Multilevel strategies have proven to be very powerful approaches in order to partition graphs efficiently. Their efficiency is dominated by two parts; the coarsening and the local improvement strategies. Several methods have been developed to solve these problems, but their efficiency has only been proven on an experimental basis. In this paper we present new and efficient methods for both problems, while satisfying certain quality measurements. For the coarsening part we develop a new approximation algorithm for maximum weighted matching in general edgeweighted graphs. It calculates a matching with an edge weight of at least 1 2 of the edge weight of a maximum weighted matching. Its time complexity is O(jEj), with jEj being the number of edges in the graph. Furthermore, we use the HelpfulSet strategy for the local improvement of partitions. For partitioning graphs with a regular degree of 2k into 2 parts, it guarantees an upper bound of k\Gamma1 2 jV j + 1 on the cut size of th...
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 28 (3 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].
Parallel Approximation Algorithms for Maximum Weighted Matching in General Graphs
 Information Processing Letters
, 2000
"... . The problem of computing a matching of maximum weight in a given edgeweighted graph is not known to be Phard or in RNC. This paper presents four parallel approximation algorithms for this problem. The first is an RNCapproximation scheme, i.e., an RNC algorithm that computes a matching of weight ..."
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Cited by 15 (0 self)
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. The problem of computing a matching of maximum weight in a given edgeweighted graph is not known to be Phard or in RNC. This paper presents four parallel approximation algorithms for this problem. The first is an RNCapproximation scheme, i.e., an RNC algorithm that computes a matching of weight at least 10 ffl times the maximum for any given constant ffl ? 0. The second one is an NC approximation algorithm achieving an approximation ratio of 1 2+ffl for any fixed ffl ? 0. The third and fourth algorithms only need to know the total order of weights, so they are useful when the edge weights require a large amount of memories to represent. The third one is an NC approximation algorithm that finds a matching of weight at least 2 31+2 times the maximum, where 1 is the maximum degree of the graph. The fourth one is an RNC algorithm that finds a matching of weight at least 1 21+4 times the maximum on average, and runs in O(log 1) time, not depending on the size of the graph. Key word...
Nonnegative Matrix Factorization for Combinatorial Optimization: Spectral Clustering, Graph Matching, and Clique Finding
 EIGHTH IEEE INTERNATIONAL CONFERENCE ON DATA MINING
, 2008
"... Nonnegative matrix factorization (NMF) is a versatile model for data clustering. In this paper, we propose several NMF inspired algorithms to solve different data mining problems. They include (1) multiway normalized cut spectral clustering, (2) graph matching of both undirected and directed graphs ..."
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Cited by 10 (0 self)
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Nonnegative matrix factorization (NMF) is a versatile model for data clustering. In this paper, we propose several NMF inspired algorithms to solve different data mining problems. They include (1) multiway normalized cut spectral clustering, (2) graph matching of both undirected and directed graphs, and (3) maximal clique finding on both graphs and bipartite graphs. Key features of these algorithms are (a) they are extremely simple to implement; and (b) they are provably convergent. We conduct experiments to demonstrate the effectiveness of these new algorithms. We also derive a new spectral bound for the size of maximal edge bicliques as a byproduct of our approach.
A new NCalgorithm for finding a perfect matching in bipartite planar and small genus graphs (Extended Abstract)
, 2000
"... It has been known for a long time now that the problem of counting the number of perfect matchings in a planar graph is in NC. This result is based on the notion of a pfaffian orientation of a graph. (Recently, Galluccio and Loebl [7] gave a Ptime algorithm for the case of graphs of small genus.) H ..."
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Cited by 8 (2 self)
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It has been known for a long time now that the problem of counting the number of perfect matchings in a planar graph is in NC. This result is based on the notion of a pfaffian orientation of a graph. (Recently, Galluccio and Loebl [7] gave a Ptime algorithm for the case of graphs of small genus.) However, it is not known if the corresponding search problem, that of finding one perfect matching in a planar graph, is in NC. This situation is intriguing as it seems to contradict our intuition that search should be easier than counting. For the case of planar bipartite graphs, Miller and Naor [22] showed that a perfect matching can indeed be found using an NC algorithm. We present a very different NCalgorithm for this problem. Unlike the Miller...
Approximating weighted matchings in parallel
"... revised Version Abstract. We present an NC approximation 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. ( 1 2 ..."
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Cited by 6 (1 self)
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revised Version Abstract. We present an NC approximation 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. ( 1 2
Accurate Recognition of Large Number of Hand Gestures
 K.N. Toosi University of Technology
, 2003
"... A hierarchical gesture recognition algorithm is introduced to recognise a large number of gestures. Three stages of the proposed algorithm are based on a new hand tracking technique to recognise the actual beginning of a gesture using a Kalman filtering process, hidden Markov models and graph ma ..."
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Cited by 5 (0 self)
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A hierarchical gesture recognition algorithm is introduced to recognise a large number of gestures. Three stages of the proposed algorithm are based on a new hand tracking technique to recognise the actual beginning of a gesture using a Kalman filtering process, hidden Markov models and graph matching. Processing time is important in working with large databases. Therefore, special cares are taken to deal with the large number of gestures, which are partially similar.
Simultaneous Matchings
 Proceedings of the 16th Annual International Symposium on Algorithms and Computation (ISAAC 2005), volume 3827 of LNCS
, 2005
"... Given a bipartite graph G = (X D, E D), an X perfect matching is a matching in G that saturates every node in X. In this paper we study the following generalisation of the Xperfect matching problem, which has applications in constraint programming: Given a bipartite graph as above and a ..."
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Cited by 4 (1 self)
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Given a bipartite graph G = (X D, E D), an X perfect matching is a matching in G that saturates every node in X. In this paper we study the following generalisation of the Xperfect matching problem, which has applications in constraint programming: Given a bipartite graph as above and a collection of k subsets of X, find a subset M E of the edges such that for each C , the edge set M D) is a Cperfect matching in G (or report that no such set exists). We show that the decision problem is NPcomplete and that the corresponding optimisation problem is in APX when k = O(1) and even APXcomplete already for k = 2. On the positive side, we show that a 2/(k + 1)approximation can be found in O(2 poly(k, X # D)) time.