bipartite matching using ford fulkerson algorithm

1. BIPARTITE
MATCHING PROBLEM
Prepared by
GEETHU RANGAN
MTECH TECHNOLOGY MANAGEMENT
DEPT OF FUTURE STUDIES
UNIVERSITY OF KERALA

2. Bipartite Matching
• A matching in a Bipartite Graph is a set of the
edges chosen in such a way that no two edges
share an endpoint.
• A maximum matching is a matching of maximum
size (maximum number of edges).
• In other words, a matching is maximum if any
edge is added to it, it is no longer a matching.
There can be more than one maximum
matchings for a given Bipartite Graph.

3. Example
• There are M job applicants
and N jobs.
• Each applicant has a subset
of jobs that he/she is
interested in.
• Each job opening can only
accept one applicant and a
job applicant can be
appointed for only one job.
• Find an assignment of jobs to
applicants in such that as
many applicants as possible
get jobs.

4. Bipartite Matching
• A Bipartite Graph G = (V,E) is a
graph in which the vertex set V
can be divided into two disjoint
subsets X and Y such that every
edge e ६ E has one end point in
X and the other end point in Y .
• A matching M is a subset of
edges such that each node in V
appears in at most one edge in
M.

7. EXAMPLE

12. THANK YOU