http://www.cs.princeton.edu/~rs/AlgsDS07/
Overview
Union-Find Algorithms
Stacks and Queues
Sorting Algorithms
Advanced Topics in Sorting
Priority Queues
Symbol Tables
Binary Search Trees
Balanced Trees
Hashing
Undirected Graphs
Directed Graphs
Minimum Spanning Trees
Shortest Paths
Geometric Algorithms
Search and Intersection
Radix Sorts
Tries
Data Compression
Pattern Matching
Linear Programming
Reductions
Combinatorial Search
http://www.cs.cmu.edu/afs/cs/academic/class/15854-f05/www/scribe/lec9.pdf
http://www.sciencedirect.com/science/article/pii/S0022000008000500
Matching problems are often concerned with bipartite graphs. Finding a maximum bipartite matching[3] (often called a maximum cardinality bipartite matching) in a bipartite graph
is perhaps the simplest problem.
The Augmenting path algorithm finds it by finding an augmenting path from each x ∈ X to 
and adding it to the matching if it exists. As each path can be found in 
time, the running time is 
. This solution is equivalent to adding a super source 
with edges to all vertices in 
, and a super sink 
with edges from all vertices in , and finding amaximal flow from 
to . All edges with flow from to then constitute a maximum matching.
An improvement over this is the Hopcroft–Karp algorithm, which runs in 
time. Another approach is based on the fast matrix multiplication algorithm and gives 
complexity,[4] which is better in theory for sufficiently dense graphs, but in practice the algorithm is slower.[5]
