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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 19 (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 Heuristic for Dijkstra's Algorithm with Many Targets and its Use in Weighted Matching Algorithms
 LECTURE NOTES IN COMPUTER SCIENCE
, 2003
"... We consider the singlesource manytargets shortestpath (SSMTSP) problem in directed graphs with nonnegative edge weights. A source node s and a target set T is specified and the goal is to compute a shortest path from s to a node in T . Our interest in the shortest path problem with many targ ..."
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Cited by 9 (2 self)
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We consider the singlesource manytargets shortestpath (SSMTSP) problem in directed graphs with nonnegative edge weights. A source node s and a target set T is specified and the goal is to compute a shortest path from s to a node in T . Our interest in the shortest path problem with many targets stems from its use in weighted bipartite matching algorithms. A weighted bipartite matching in a graph with n nodes on each side reduces to n SSMTSP problems, where the number of targets varies between n and 1. The SSMTSP problem can be solved by Dijkstra's algorithm. We describe a heuristic that leads to a significant improvement in running time for the weighted matching problem; in our experiments a speedup by up to a factor of 10 was achieved. We also present a partial analysis that gives some theoretical support for our experimental findings.
A Scene Learning and Recognition Framework
, 2005
"... ii As multiagent systems grow in complexity and diversity, they become increasingly difficult to design. Agents are described in terms of their behaviour, typically trained by an expert who prepares knowledge representations or training data for supervised machine learning. To reduce development ti ..."
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ii As multiagent systems grow in complexity and diversity, they become increasingly difficult to design. Agents are described in terms of their behaviour, typically trained by an expert who prepares knowledge representations or training data for supervised machine learning. To reduce development time, agents could learn by observing the behaviour of other agents. This thesis describes an effort to train a RoboCup soccer agent by capturing data from existing players, generating a knowledge representation, and using a realtime scene recognition system. The trained agent later exhibits behaviour traits similar to the observed agent and can appear to completely imitate the behaviour of the original; the process requires little human intervention. Experiments are performed using three agents of varying complexity. The “scene” knowledge description format, and simple scene matching algorithm, are limited to imitation of stateless and deterministic agent behaviours. Future work includes improving
DOI 10.1007/s1253200900028 FULL LENGTH PAPER
"... Abstract We describe a new implementation of the Edmonds’s algorithm for computing a perfect matching of minimum cost, to which we refer as Blossom V. A key feature of our implementation is a combination of two ideas that were shown to be effective for this problem: the “variable dual updates ” appr ..."
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Abstract We describe a new implementation of the Edmonds’s algorithm for computing a perfect matching of minimum cost, to which we refer as Blossom V. A key feature of our implementation is a combination of two ideas that were shown to be effective for this problem: the “variable dual updates ” approach of Cook and Rohe (INFORMS J Comput 11(2):138–148, 1999) and the use of priority queues. We achieve this by maintaining an auxiliary graph whose nodes correspond to alternating trees in the Edmonds’s algorithm. While our use of priority queues does not improve the worstcase complexity, it appears to lead to an efficient technique. In the majority of our tests Blossom V outperformed previous implementations of Cook and Rohe (INFORMS J Comput 11(2):138–148, 1999) and Mehlhorn and Schäfer (J Algorithmics Exp (JEA) 7:4, 2002), sometimes by an order of magnitude. We also show that for large VLSI instances it is beneficial to update duals by solving a linear program, contrary to a conjecture by Cook and Rohe.
4. TITLE AND SUBTITLE: Applications of Assignment Algorithms to Nonparametric Tests for Homogeneity
, 2009
"... Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instruction, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments ..."
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Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instruction, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington headquarters Services, Directorate for Information
Maximum Matching in General Graphs Without Explicit Consideration of Blossoms Revisited
"... We reduce the problem of finding an augmenting path in a general graph to a reachability problem in a directed bipartite graph. A slight modification of depthfirst search leads to an algorithm for finding such paths. Although this setting is equivalent to the traditional terminology of blossoms due ..."
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We reduce the problem of finding an augmenting path in a general graph to a reachability problem in a directed bipartite graph. A slight modification of depthfirst search leads to an algorithm for finding such paths. Although this setting is equivalent to the traditional terminology of blossoms due to Edmonds, there are some advantages. Mainly, this point of view enables the description of algorithms for the solution of matching problems without explicit analysis of blossoms, nested blossoms, and so on. Exemplary, we describe an efficient realization of the HopcroftKarp approach for the computation of a maximum cardinality matching in general graphs and a variant of Edmonds ’ primaldual algorithm for the maximum weighted matching problem. 1. Introduction and