A separator theorem for graphs of bounded genus
Journal of Algorithms
A linear algorithm for embedding planar graphs using PQ-trees
Journal of Computer and System Sciences
The analysis of a nested dissection algorithm
Numerische Mathematik
NC algorithms for computing the number of perfect matchings in K3,3-free graph and related problems
Information and Computation
Matrix multiplication via arithmetic progressions
Journal of Symbolic Computation - Special issue on computational algebraic complexity
Graph minors. VIII. A Kuratowski theorem for general surfaces
Journal of Combinatorial Theory Series B
Faster scaling algorithms for general graph matching problems
Journal of the ACM (JACM)
A Linear Time Algorithm for Embedding Graphs in an Arbitrary Surface
SIAM Journal on Discrete Mathematics
Determinant algorithms for random planar structures
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Journal of the ACM (JACM)
A New Approach to Maximum Matching in General Graphs
ICALP '90 Proceedings of the 17th International Colloquium on Automata, Languages and Programming
Maximum Matchings via Gaussian Elimination
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Graph Minors. XX. Wagner's conjecture
Journal of Combinatorial Theory Series B - Special issue dedicated to professor W. T. Tutte
APPROX '07/RANDOM '07 Proceedings of the 10th International Workshop on Approximation and the 11th International Workshop on Randomization, and Combinatorial Optimization. Algorithms and Techniques
A linear-time algorithm to find a separator in a graph excluding a minor
ACM Transactions on Algorithms (TALG)
Computing Large Matchings in Planar Graphs with Fixed Minimum Degree
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Single source shortest paths in H-minor free graphs
Theoretical Computer Science
Computing large matchings fast
ACM Transactions on Algorithms (TALG)
Computing large matchings in planar graphs with fixed minimum degree
Theoretical Computer Science
A simple reduction from maximum weight matching to maximum cardinality matching
Information Processing Letters
Matrix sparsification and nested dissection over arbitrary fields
Journal of the ACM (JACM)
Cliques in odd-minor-free graphs
CATS '12 Proceedings of the Eighteenth Computing: The Australasian Theory Symposium - Volume 128
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We present a new randomized algorithm for finding a maximum matching in H-minor free graphs. For every fixed H, our algorithm runs in O(n3ω/(ω+3)) O(n1.326) time, where n is the number of vertices of the input graph and ω O(n1.5) time bound obtained by applying the O(mn1/2)-time algorithm of Micali and Vazirani on this important class of graphs. For graphs with bounded genus, which are special cases of H-minor free graphs, we present a randomized algorithm for finding a maximum matching in O(nω/2) O(n1.19) time. This extends a previous randomized algorithm of Mucha and Sankowski, having the same running time, that finds a maximum matching in a planar graphs. We also present a deterministic algorithm with a running time of O(n1+ω/2) O(n2.19) for counting the number of perfect matchings in graphs with bounded genus. This algorithm combines the techniques used by the algorithms above with the counting technique of Kasteleyn. Using this algorithm we can also count, within the same running time, the number of T-joins in planar graphs. As special cases, we get algorithms for counting Eulerian subgraphs (T = &phis;) and odd subgraphs (T = V) of planar graphs.