Data structures and network algorithms
Data structures and network algorithms
A fast perfect-matching algorithm in random graphs
SIAM Journal on Discrete Mathematics
LEDA: a platform for combinatorial and geometric computing
Communications of the ACM
Analysis of a simple greedy matching algorithm on random cubic graphs
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
An Efficient Implementation of Edmonds' Algorithm for Maximum Matching on Graphs
Journal of the ACM (JACM)
A linear-time algorithm for a special case of disjoint set union
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
A Theory of Alternating Paths and Blossoms for Proving Correctness of the $O(\'sqrt{VE})$ General Graph Matching Algorithm
Multicast Routing and Design of Sparse Connectors
Algorithmics of Large and Complex Networks
Heuristic initialization for bipartite matching problems
Journal of Experimental Algorithmics (JEA)
Linear time local improvements for weighted matchings in graphs
WEA'03 Proceedings of the 2nd international conference on Experimental and efficient algorithms
Design, implementation, and analysis of maximum transversal algorithms
ACM Transactions on Mathematical Software (TOMS)
A more reliable greedy heuristic for maximum matchings in sparse random graphs
SEA'12 Proceedings of the 11th international conference on Experimental Algorithms
Push-relabel based algorithms for the maximum transversal problem
Computers and Operations Research
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We conduct an experimental study of several greedy algorithms for finding large matchings in graphs. Further we propose a new graph reduction, called k-Block Reduction, and present two novel algorithms using extra heuristics in the matching step and k-Block Reduction for k = 3. Greedy matching algorithms can be used for finding a good approximation of the maximum matching in a graph G if no exact solution is required, or as a fast preprocessing step to some other matching algorithm. The studied greedy algorithms run in O(m). They are easy to implement and their correctness and their running time are simple to prove. Our experiments show that a good greedy algorithm looses on average at most one edge on random graphs from Gn,p with up to 10,000 vertices. Furthermore the experiments show for which edge densities in random graphs the maximum matching problem is difficult to solve.