The analysis of algorithms
Data structures and network algorithms
Data structures and network algorithms
An O(EV log V) algorithm for finding a maximal weighted matching in general graphs
SIAM Journal on Computing
Efficient implementation of graph algorithms using contraction
Journal of the ACM (JACM)
Faster scaling algorithms for general graph matching problems
Journal of the ACM (JACM)
A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs
SIAM Journal on Scientific Computing
Data structures for weighted matching and nearest common ancestors with linking
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
An Efficient Implementation of Edmonds' Algorithm for Maximum Matching on Graphs
Journal of the ACM (JACM)
Quality matching and local improvement for multilevel graph-partitioning
Parallel Computing - Special issue on graph partioning and parallel computing
A simple approximation algorithm for the weighted matching problem
Information Processing Letters
Computing Minimum-Weight Perfect Matchings
INFORMS Journal on Computing
A simpler linear time 2/3 - ε approximation for maximum weight matching
Information Processing Letters
Linear time local improvements for weighted matchings in graphs
WEA'03 Proceedings of the 2nd international conference on Experimental and efficient algorithms
Linear time 1/2 -approximation algorithm for maximum weighted matching in general graphs
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
ACM SIGCOMM Computer Communication Review
Approximating weighted matchings in parallel
Information Processing Letters
Approximating the Metric TSP in Linear Time
Graph-Theoretic Concepts in Computer Science
Enhanced Approximation Algorithms for Maximum Weight Matchings of Graphs
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Information Processing Letters
Engineering algorithms for approximate weighted matching
WEA'07 Proceedings of the 6th international conference on Experimental algorithms
A self-stabilizing weighted matching algorithm
SSS'07 Proceedings of the 9h international conference on Stabilization, safety, and security of distributed systems
A parallel approximation algorithm for the weighted maximum matching problem
PPAM'07 Proceedings of the 7th international conference on Parallel processing and applied mathematics
A simple parallel approximation algorithm for maximum weight matching
Proceedings of the Third Conference on Partitioned Global Address Space Programing Models
Linear programming in the semi-streaming model with application to the maximum matching problem
ICALP'11 Proceedings of the 38th international conference on Automata, languages and programming - Volume Part II
Linear programming in the semi-streaming model with application to the maximum matching problem
Information and Computation
Linear-Time Approximation for Maximum Weight Matching
Journal of the ACM (JACM)
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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+n2log 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. This improves the previously best performance ratio of 1/2. 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.