Data structures and network algorithms
Data structures and network algorithms
Matrix multiplication via arithmetic progressions
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Flow in Planar Graphs with Multiple Sources and Sinks
SIAM Journal on Computing
Bipartite Edge Coloring in $O(\Delta m)$ Time
SIAM Journal on Computing
Efficient algorithms for Petersen's matching theorem
Journal of Algorithms
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)
Planar graphs, negative weight edges, shortest paths, and near linear time
Journal of Computer and System Sciences - Special issue on FOCS 2001
Maximum matching in graphs with an excluded minor
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Computing large matchings fast
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
An O(v|v| c |E|) algoithm for finding maximum matching in general graphs
SFCS '80 Proceedings of the 21st Annual Symposium on Foundations of Computer Science
Worst-case ration for planar graphs and the method of induction on faces
SFCS '81 Proceedings of the 22nd Annual Symposium on Foundations of Computer Science
Computing large matchings fast
ACM Transactions on Algorithms (TALG)
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In this paper we present algorithms that compute large matchings in planar graphs with fixed minimum degree. The algorithms give a guarantee on the size of the computed matching and run in linear time. Thus they are faster than the best known algorithm for computing maximum matchings in general graphs and in planar graphs, which run in $O(\sqrt{n}m)$ and O(n 1.188) time, respectively. For the class of planar graphs with minimum degree 3 the bounds we achieve are known to be best possible. Further, we discuss how minimum degree 5 can be used to obtain stronger bounds on the matching size.