Maximum matchings in general graphs through randomization
Journal of Algorithms
Computing a maximum cardinality matching in a bipartite graph in time On1.5m/logn
Information Processing Letters
Randomized $\tilde{O}(M(|V|))$ Algorithms for Problems in Matching Theory
SIAM Journal on Computing
Generalizing data to provide anonymity when disclosing information (abstract)
PODS '98 Proceedings of the seventeenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Algorithms for Enumerating All Perfect, Maximum and Maximal Matchings in Bipartite Graphs
ISAAC '97 Proceedings of the 8th International Symposium on Algorithms and Computation
On the complexity of optimal K-anonymity
PODS '04 Proceedings of the twenty-third ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
An O(VE) algorithm for ear decompositions of matching-covered graphs
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Checking for k-anonymity violation by views
VLDB '05 Proceedings of the 31st international conference on Very large data bases
k-Anonymization with Minimal Loss of Information
IEEE Transactions on Knowledge and Data Engineering
ICDE '08 Proceedings of the 2008 IEEE 24th International Conference on Data Engineering
A Fast Algorithm for Enumerating Bipartite Perfect Matchings
ISAAC '01 Proceedings of the 12th International Symposium on Algorithms and Computation
Perfect matchings in o(n log n) time in regular bipartite graphs
Proceedings of the forty-second ACM symposium on Theory of computing
ICDT'05 Proceedings of the 10th international conference on Database Theory
Persistency in maximum cardinality bipartite matchings
Operations Research Letters
| Hi-index | 5.23 |
We consider the problem of finding all maximally-matchable edges in a bipartite graph G=(V,E), i.e., all edges that are included in some maximum matching. We show that given any maximum matching in the graph, it is possible to perform this computation in linear time O(n+m) (where n=|V| and m=|E|). Hence, the time complexity of finding all maximally-matchable edges reduces to that of finding a single maximum matching, which is O(n^1^/^2m) (Hopcroft and Karp [12]), or O((n/logn)^1^/^2m) for dense graphs with m=@Q(n^2) (Alt et al. [2]). This time complexity improves upon that of the best known algorithms for the problem, which is O(nm) (Costa [5] for bipartite graphs, and Carvalho and Cheriyan [6] for general graphs). Other algorithms for solving that problem are randomized algorithms due to Rabin and Vazirani [15] and Cheriyan [3], the runtime of which is O@?(n^2^.^3^7^6). Our algorithm, apart from being deterministic, improves upon that time complexity for bipartite graphs when m=O(n^r) and r