Matchings, Random Walks, and Sampling

  • Sanjeev Khanna
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8370)


The maximum matching problem is among the most well-studied problems in combinatorial optimization with many applications. The matching problem is well-known to be efficiently solvable, that is, there are algorithms that solve the matching problem using polynomial space and time. However, as large data sets become more prevalent, there is a growing interest in sublinear algorithms — these are algorithms whose resource requirements are substantially smaller than the size of the input that they operate on. In this talk, we will describe some results that illustrate surprising effectiveness of randomization in solving exact and approximate matching problems in sublinear space or time.


Perfect Match Match Problem Input Graph Polynomial Space Stochastic Matrice 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Birkhoff, G.: Tres observaciones sobre el algebra lineal. Univ. Nac. Tucumán Rev. Ser. A 5, 147–151 (1946)zbMATHMathSciNetGoogle Scholar
  2. 2.
    Cole, R., Ost, K., Schirra, S.: Edge-coloring bipartite multigraphs in O(E logD) time. Combinatorica 21(1), 5–12 (2001)CrossRefzbMATHMathSciNetGoogle Scholar
  3. 3.
    Goel, A., Kapralov, M., Khanna, S.: Perfect matchings via uniform sampling in regular bipartite graphs. ACM Transactions on Algorithms 6(2) (2010)Google Scholar
  4. 4.
    Goel, A., Kapralov, M., Khanna, S.: Perfect matchings in O(n logn) time in regular bipartite graphs. SIAM J. Comput. 42(3), 1392–1404 (2013)CrossRefzbMATHGoogle Scholar
  5. 5.
    Goel, A., Kapralov, M., Khanna, S.: Perfect matchings in \(\tilde{O}(n^{\mbox{1.5}})\) time in regular bipartite graphs. To appear in Combinatorica (2013)Google Scholar
  6. 6.
    Hopcroft, J., Karp, R.: An \(n^{\frac{5}{2}}\) algorithm for maximum matchings in bipartite graphs. SIAM J. Comput. 2(4), 225–231 (1973)CrossRefzbMATHMathSciNetGoogle Scholar
  7. 7.
    Kapralov, M., Khanna, S., Sudan, M.: On the communication and streaming complexity of maximum bipartite matching. In: Proceedings of the Twenty-Fifth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA (2014)Google Scholar
  8. 8.
    König, D.: Über graphen und ihre anwendung auf determinententheorie und mengenlehre. Math. Annalen 77, 453–465 (1916)CrossRefzbMATHGoogle Scholar
  9. 9.
    von Neumann, J.: A certain zero-sum two-person game equivalent to the optimal assignment problem. Contributions to the Optimal Assignment Problem to the Theory of Games 2, 5–12 (1953)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Sanjeev Khanna
    • 1
  1. 1.Dept. of Computer & Information ScienceUniversity of PennsylvaniaPhiladelphiaUSA

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