References
N. Alon, P. Frankl, H. Huang, V. Rödl, A. Ruciński and B. Sudakov: Large matchings in uniform hypergraphs and the conjectures of Erdős and Samuels, Journal of Combinatorial Theory, Series A 119 (2012), 1200–1215.
A. Asadpour, U. Feige and A. Saberi: Santa claus meets hypergraph matchings, ACM Transactions on Algorithms (TALG) 8 (2012), 24.
C. Annamalai, C. Kalaitzis and O. Svensson: Combinatorial algorithm for re-stricted max-min fair allocation, in: Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms, 1357–1372, 2015.
N. Bansal and M. Sviridenko: The santa claus problem, in: Proceedings of the Thirty-Eighth Annual ACM Symposium on Theory of Computing, 31–40. ACM, 2006.
M. Conforti, G. Cornuéjols, A. Kapoor and K. Vuőkovič: Perfect matchings in balanced hypergraphs, Combinatorica 16 (1996), 325–329.
M. Cygan, F. Grandoni and M. Mastrolilli: How to sell hyperedges: The hypermatching assignment problem, in: Proceedings of the Twenty-Fourth Annual ACMSIAM Symposium on Discrete Algorithms, 342–351. SIAM, 2013.
Y. H. Chan and L. C. Lau: On linear and semidefinite programming relaxations for hypergraph matching, Mathematical Programming 135 (2012), 123–148.
M. Cygan: Improved approximation for 3-dimensional matching via bounded pathwidth local search, in: Proceedings of the Fifty-Fourth Annual Symposium on Foundations of Computer Science, 509–518. IEEE, 2013.
G. A. Dirac: Some theorems on abstract graphs, Proceedings of the London Mathematical Society 3 (1952), 69–81.
U. Feige: On allocations that maximize fairness, in: Proceedings of the Nineteenth Annual ACM-SIAM Symposium on Discrete Algorithms, 287–293. Society for Industrial and Applied Mathematics, 2008.
M. Fürer and H. Yu: Approximating the k-set packing problem by local improvements, in: Combinatorial Optimization, 408–420. Springer, 2014.
P. Hall: On representatives of subsets, J. London Math. Soc 10 (1935), 26–30.
M. M. Halldórsson: Approximating discrete collections via local improvements, in: Proceedings of the Sixth Annual ACM-SIAM Symposium on Discrete Algorithms, volume 95, 160–169. SIAM, 1995.
P. E. Haxell: A condition for matchability in hypergraphs, Graphs and Combinatorics 11 (1995), 245–248.
J. E. Hopcroft and R. M. Karp: An n5=2 algorithm for maximum matchings in bipartite graphs, SIAM Journal on Computing 2 (1973), 225–231.
G. H. Hardy and S. Ramanujan: Asymptotic formula in combinatory analysis, Proceedings of the London Mathematical Society, s2 17 (1918), 75.
C. A. J. Hurkens and A. Schrijver: On the size of systems of sets every t of which have an SDR, with an application to the worst-case ratio of heuristics for packing problems, SIAM Journal on Discrete Mathematics 2 (1989), 68–72.
B. Haeupler, B. Saha and A. Srinivasan: New constructive aspects of the lovasz local lemma, Journal of the ACM (JACM) 58 (2011), 28.
R. M. Karp: Reducibility among combinatorial problems, Springer, 1972.
A. V. Karzanov: O nakhozhdenii maksimal’nogo potoka v setyakh spetsial’nogo vida i nekotorykh prilozheniyakh, Matematicheskie Voprosy Upravleniya Proizvodstvom 5 (1973), 81.
L. Lovász: On determinants, matchings, and random algorithms, in: FCT, volume 79, 565–574, 1979.
A. Madry: Navigating central path with electrical flows: From ows to matchings, and back, in: Proceedings of the Fifty-Fourth Annual Symposium on Foundations of Computer Science, 253–262. IEEE, 2013.
M. Mucha and P. Sankowski: Maximum matchings via gaussian elimination, in: Proceedings of the Forty-Fifth Annual Symposium on Foundations of Computer Science, 248–255. IEEE, 2004.
L. Polacek and O. Svensson: Quasi-polynomial local search for restricted maxmin fair allocation, in: Automata, Languages, and Programming, 726–737. Springer, 2012.
M. Singh and K. Talwar: Improving integrality gaps via Chvátal-Gomory rounding, in: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, 366–379. Springer, 2010.
O. Svensson: Santa Claus schedules jobs on unrelated machines, SIAM Journal on Computing 41 (2012), 1318–1341.
M. Sviridenko and J. Ward: Large neighborhood local search for the maximum set packing problem, in: Automata, Languages, and sProgramming, 792–803. Springer, 2013.
D. B. West: Introduction to graph theory, volume 2, Prentice hall Upper Saddle River, 2001.
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Annamalai, C. Finding Perfect Matchings in Bipartite Hypergraphs. Combinatorica 38, 1285–1307 (2018). https://doi.org/10.1007/s00493-017-3567-2
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DOI: https://doi.org/10.1007/s00493-017-3567-2