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URL:/combinatorics-and-optimization/events/tutte-colloq
 uium-sanjeev-khanna
SUMMARY:Tutte Colloquium - Sanjeev Khanna
CLASS:PUBLIC
DESCRIPTION:Summary \n\nTITLE: A Faster Combinatorial Algorithm for Maximum
  Bipartite\nMatching           \n\nSPEAKER:\n Sanjeev Khanna\n\n
 AFFILIATION:\n University of Pennsylvania\n\nLOCATION:\n MC 5501\n\nABSTRA
 CT: The maximum bipartite matching problem is among the most\nfundamental 
 and well-studied problems in combinatorial optimization. A\nbeautiful and 
 celebrated combinatorial algorithm of Hopcroft and Karp\n(1973) shows that
  maximum bipartite matching can be solved in $O(m\n\\sqrt{n})$ time on a g
 raph with $n$ vertices and $m$ edges. For the\ncase of very dense graphs\,
  a fast matrix multiplication based approach\ngives a running time of $O(n
 ^{2.371})$. These results represented the\nfastest known algorithms for th
 e problem until 2013\, when Madry\nintroduced a new approach based on cont
 inuous techniques achieving\nmuch faster runtime in sparse graphs. \n 
DTSTAMP:20250706T090827Z
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