, Volume 38, Issue 6, pp 1285–1307 | Cite as

Finding Perfect Matchings in Bipartite Hypergraphs

  • Chidambaram AnnamalaiEmail author
Original paper

Mathematics Subject Classification (2000)

05C65 05C70 05C85 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    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.zbMATHGoogle Scholar
  2. [2]
    A. Asadpour, U. Feige and A. Saberi: Santa claus meets hypergraph matchings, ACM Transactions on Algorithms (TALG) 8 (2012), 24.MathSciNetzbMATHGoogle Scholar
  3. [3]
    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.CrossRefGoogle Scholar
  4. [4]
    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.Google Scholar
  5. [5]
    M. Conforti, G. Cornuéjols, A. Kapoor and K. Vuőkovič: Perfect matchings in balanced hypergraphs, Combinatorica 16 (1996), 325–329.MathSciNetCrossRefzbMATHGoogle Scholar
  6. [6]
    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.CrossRefGoogle Scholar
  7. [7]
    Y. H. Chan and L. C. Lau: On linear and semidefinite programming relaxations for hypergraph matching, Mathematical Programming 135 (2012), 123–148.MathSciNetCrossRefzbMATHGoogle Scholar
  8. [8]
    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.Google Scholar
  9. [9]
    G. A. Dirac: Some theorems on abstract graphs, Proceedings of the London Mathematical Society 3 (1952), 69–81.MathSciNetCrossRefzbMATHGoogle Scholar
  10. [10]
    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.Google Scholar
  11. [11]
    M. Fürer and H. Yu: Approximating the k-set packing problem by local improvements, in: Combinatorial Optimization, 408–420. Springer, 2014.Google Scholar
  12. [12]
    P. Hall: On representatives of subsets, J. London Math. Soc 10 (1935), 26–30.CrossRefzbMATHGoogle Scholar
  13. [13]
    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.Google Scholar
  14. [14]
    P. E. Haxell: A condition for matchability in hypergraphs, Graphs and Combinatorics 11 (1995), 245–248.MathSciNetCrossRefzbMATHGoogle Scholar
  15. [15]
    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.MathSciNetCrossRefzbMATHGoogle Scholar
  16. [16]
    G. H. Hardy and S. Ramanujan: Asymptotic formula in combinatory analysis, Proceedings of the London Mathematical Society, s2 17 (1918), 75.zbMATHGoogle Scholar
  17. [17]
    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.MathSciNetCrossRefzbMATHGoogle Scholar
  18. [18]
    B. Haeupler, B. Saha and A. Srinivasan: New constructive aspects of the lovasz local lemma, Journal of the ACM (JACM) 58 (2011), 28.MathSciNetCrossRefzbMATHGoogle Scholar
  19. [19]
    R. M. Karp: Reducibility among combinatorial problems, Springer, 1972.CrossRefzbMATHGoogle Scholar
  20. [20]
    A. V. Karzanov: O nakhozhdenii maksimal’nogo potoka v setyakh spetsial’nogo vida i nekotorykh prilozheniyakh, Matematicheskie Voprosy Upravleniya Proizvodstvom 5 (1973), 81.Google Scholar
  21. [21]
    L. Lovász: On determinants, matchings, and random algorithms, in: FCT, volume 79, 565–574, 1979.zbMATHGoogle Scholar
  22. [22]
    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.Google Scholar
  23. [23]
    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.CrossRefGoogle Scholar
  24. [24]
    L. Polacek and O. Svensson: Quasi-polynomial local search for restricted maxmin fair allocation, in: Automata, Languages, and Programming, 726–737. Springer, 2012.CrossRefGoogle Scholar
  25. [25]
    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.CrossRefGoogle Scholar
  26. [26]
    O. Svensson: Santa Claus schedules jobs on unrelated machines, SIAM Journal on Computing 41 (2012), 1318–1341.MathSciNetCrossRefzbMATHGoogle Scholar
  27. [27]
    M. Sviridenko and J. Ward: Large neighborhood local search for the maximum set packing problem, in: Automata, Languages, and sProgramming, 792–803. Springer, 2013.CrossRefGoogle Scholar
  28. [28]
    D. B. West: Introduction to graph theory, volume 2, Prentice hall Upper Saddle River, 2001.Google Scholar

Copyright information

© János Bolyai Mathematical Society and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Computer ScienceETH ZurichZürichSwitzerland

Personalised recommendations