Algorithms (F2008)

We looked at the problem of computing a maximum matching in a bipartite graph, and showed that a simple max flow formulation yields the optimal matching. As an aside, I asked you to consider the following strategy:

Take any edge that doesn’t intersect the set of edges chosen thus far.

How badly might this do ?

We also saw that Hall’s theorem, a structural way of characterizing the existence of a perfect matching in a bipartite graph, can be proved using flow principles.

Finally, we examined some variants of the max flow problem that can all be reduced to the standard formulation. These were:

• circulations: having multiple sources and sinks, each with their own specified demands
• Lower bounds on edge capacities (like lower limits on speeds on a highway)
• Vertex capacities: limiting the amount of flow through a vertex (for example, this can arise when you have a warehouse that’s storing shipments, but can only store a limited amount of material)

The first two sections are taken from Section 7.5 of the text, and the last part is taken from Section 7.7.

This entry was posted on Sunday, October 5th, 2008 at 1:44 am and is filed under lectures, news.