stylistic:style_transfer, information:extraction, information:filtering
Advanced algorithms

An improvement to this algorithm is given by the more elaborate Hopcroft–Karp algorithm, which searches for multiple augmenting paths simultaneously. This algorithm runs in O (V E) {\displaystyle O({\sqrt {V}}E)} time.

The algorithm of Chandran and Hochbaum for bipartite graphs runs in time that depends on the size of the maximum matching k, which for | X | < | Y | is

Using boolean operations on words of size λ {\displaystyle \lambda } the complexity is further improved to

More efficient algorithms exist for special kinds of bipartite graphs: