Comments on: Teaching Matroids http://blogs.oregonstate.edu/glencora/2011/10/19/teaching-matroids/ Assistant Professor, School of Electrical Engineering and Computer Science, Oregon State University Mon, 06 May 2013 04:32:43 +0000 hourly 1 http://wordpress.org/?v=3.5.1 By: Stasys http://blogs.oregonstate.edu/glencora/2011/10/19/teaching-matroids/#comment-248 Stasys Thu, 20 Oct 2011 17:40:19 +0000 http://www.glencora.org/?p=746#comment-248 … sorry, doesn’t seem to work here. The link is:

http://www.thi.informatik.uni-frankfurt.de/~jukna/EC_Book/matroids.pdf

]]> By: Stasys http://blogs.oregonstate.edu/glencora/2011/10/19/teaching-matroids/#comment-247 Stasys Thu, 20 Oct 2011 17:36:34 +0000 http://www.glencora.org/?p=746#comment-247 Perhaps this short excerpt from 2nd edition of my “Extremal Combinatorics” book could be interesting in matroids class. It deals with the question: when greedy algorithms can *approximate* the problem?

]]> By: Glencora http://blogs.oregonstate.edu/glencora/2011/10/19/teaching-matroids/#comment-246 Glencora Thu, 20 Oct 2011 14:33:28 +0000 http://www.glencora.org/?p=746#comment-246 Do you find it interesting enough to get to the definition of matroids using … definitions?

My motivation by getting there through example was to have the students see what it is about forests and trees that allows the greedy algorithm to work. Since they are very comfortable with MSTs, they have some interesting ideas for this. But I don’t think students would arrive at the very abstract notion of a matroid without the motivation to characterize a structure that can be found greedily.

]]> By: Glencora http://blogs.oregonstate.edu/glencora/2011/10/19/teaching-matroids/#comment-245 Glencora Thu, 20 Oct 2011 14:29:02 +0000 http://www.glencora.org/?p=746#comment-245 Yes, I agree! If I could have gotten there within 2 lecture hours, I would have done it. Sadly, spending more than one of ten weeks on matroids isn’t an option in this “core” grad class.

]]> By: Chandra http://blogs.oregonstate.edu/glencora/2011/10/19/teaching-matroids/#comment-244 Chandra Wed, 19 Oct 2011 19:51:06 +0000 http://www.glencora.org/?p=746#comment-244 The result of Geelen, Gerards and Whittle for binary matroids is not so new in that they have been speaking about it for the last few years.

]]> By: D. Eppstein http://blogs.oregonstate.edu/glencora/2011/10/19/teaching-matroids/#comment-243 D. Eppstein Wed, 19 Oct 2011 18:42:58 +0000 http://www.glencora.org/?p=746#comment-243 Some exciting news about matroids: http://cameroncounts.wordpress.com/2011/10/19/the-aitken-lectures/

]]> By: Stefan http://blogs.oregonstate.edu/glencora/2011/10/19/teaching-matroids/#comment-242 Stefan Wed, 19 Oct 2011 16:29:10 +0000 http://www.glencora.org/?p=746#comment-242 From an algorithmic point of view, matroid intersection is the big star. Furthermore, Seymour’s Decomposition Theorem is of interest for integer programming. I like to think (though I never tried) that one can pretty quickly teach matroids to the point that the statement of the theorem can be understood.

]]> By: Chandra http://blogs.oregonstate.edu/glencora/2011/10/19/teaching-matroids/#comment-241 Chandra Wed, 19 Oct 2011 16:12:52 +0000 http://www.glencora.org/?p=746#comment-241 I am teaching graduate algorithms this semester and taught matroids. I introduce matroids via vectors and abstract notion of independence systems which is how Whitney defined them. And then show that graphs are also captured. I feel that discussing history and the original motivation is often useful for students to see. I don’t personally like motivating matroids via the greedy algorithm for MST because it is dry and seems some what of an artificial jump and is histortically not accurate.

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