Introduction: Graphs Considered: Planar, Bounded-Genus, Apex-Minor
By Erik Demaine - MIT
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Lecture Description
Introduction: Graphs considered: planar, bounded-genus, apex-minor-free, H-minor-free. Problems considered and survey of results.
This lecture is an introduction to the whole class, in particular an overview of the different types of graphs that we'll be talking about (the mysterious "Beyond" in the title). We also survey many different problems where we can do a lot better on planar graphs than we can on general graphs, to give you a flavor of what we will learn in the class. Algorithms for Planar Graphs and Beyond- MIT Video lectures.
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.
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