Flow In Planar Graphs III
By Shay Mozes - MIT
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244
- Report An Inaccuracy In Lecture Information:
Lecture Description
We present an O(n log3n) time algorithm for maximum flow with multiple sources and sinks in directed planar graphs. The reduction from multiple sources and sinks to single sources and sinks violates planarity. The algorithm is radically different from the algorithm for maximum st-flows of lecture 19, and uses almost all the technique for exact algorithms in planar graphs that we covered in class so far.
Course Description
Graphs in the real world tend to have a lot of special structure. In particular, graphs arising on this planet are often planar (or nearly so), meaning that they can be drawn in the plane or a sphere without any (or with few) edge crossings. This class is about efficient algorithms that exploit the structure of planar graphs and related graph classes, specifically graphs embeddable on a surface of low genus and graphs excluding a minor. We will focus on recent results in this exciting area (which all of the instructors actively do research in).
We will organize an optional problem-solving session, during which we can jointly try to solve open problems. In the past, these sessions have led to important new results and published papers, as well as class projects.
Class projects more generally can take the form of formulations of clean, new open problems; implementations of existing algorithms; or well-written descriptions of one or more papers in the area. Projects can be purely mathematical and/or theoretical computer science (algorithmic/complexity theoretic), or purely practical.
