A competitive (dual) simplex method for the assignment problem
Mathematical Programming: Series A and B
Direct methods for sparse matrices
Direct methods for sparse matrices
Remarks on implementation of O(n1/2τ) assignment algorithms
ACM Transactions on Mathematical Software (TOMS)
Algorithms for two bottleneck optimization problems
Journal of Algorithms
A new approach to the maximum-flow problem
Journal of the ACM (JACM)
Computing the block triangular form of a sparse matrix
ACM Transactions on Mathematical Software (TOMS)
Computing a maximum cardinality matching in a bipartite graph in time On1.5m/logn
Information Processing Letters
Average-case analysis of algorithms for matchings and related problems
Journal of the ACM (JACM)
Clique partitions, graph compression and speeding-up algorithms
Journal of Computer and System Sciences
A Competitive Strong Spanning Tree Algorithm for the Maximum Bipartite Matching Problem
SIAM Journal on Discrete Mathematics
Maximum matchings in sparse random graphs: Karp-Sipser revisited
Random Structures & Algorithms
Greeding matching algorithms, an experimental study
Journal of Experimental Algorithmics (JEA)
Augment or push: a computational study of bipartite matching and unit-capacity flow algorithms
Journal of Experimental Algorithmics (JEA)
LEDA: a platform for combinatorial and geometric computing
LEDA: a platform for combinatorial and geometric computing
On Algorithms for Obtaining a Maximum Transversal
ACM Transactions on Mathematical Software (TOMS)
Maximum Matchings via Gaussian Elimination
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Matching Theory (North-Holland mathematics studies)
Matching Theory (North-Holland mathematics studies)
Direct Methods for Sparse Linear Systems (Fundamentals of Algorithms 2)
Direct Methods for Sparse Linear Systems (Fundamentals of Algorithms 2)
Maximum matching in sparse random graphs
SFCS '81 Proceedings of the 22nd Annual Symposium on Foundations of Computer Science
Heuristic initialization for bipartite matching problems
Journal of Experimental Algorithmics (JEA)
Finding a maximum matching in a sparse random graph in O(n) expected time
Journal of the ACM (JACM)
Computing maximum matching in parallel on bipartite graphs: worth the effort?
Proceedings of the first workshop on Irregular applications: architectures and algorithm
Push-relabel based algorithms for the maximum transversal problem
Computers and Operations Research
GPU accelerated maximum cardinality matching algorithms for bipartite graphs
Euro-Par'13 Proceedings of the 19th international conference on Parallel Processing
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We report on careful implementations of seven algorithms for solving the problem of finding a maximum transversal of a sparse matrix. We analyze the algorithms and discuss the design choices. To the best of our knowledge, this is the most comprehensive comparison of maximum transversal algorithms based on augmenting paths. Previous papers with the same objective either do not have all the algorithms discussed in this article or they used nonuniform implementations from different researchers. We use a common base to implement all of the algorithms and compare their relative performance on a wide range of graphs and matrices. We systematize, develop, and use several ideas for enhancing performance. One of these ideas improves the performance of one of the existing algorithms in most cases, sometimes significantly. So much so that we use this as the eighth algorithm in comparisons.