Lecture 8: Matroids [fa'10]

Lecture 8: Matroids [fa'13]

Many problems that can be correctly solved by greedy algorithms can be described in terms of an abstract combinatorial object called a matroid. Matroids were first described in 1935 by the mathematician Hassler Whitney as a combinatorial generalization of linear independence of vectors—‘matroid’ means ‘something sort of like a matrix’. A matroid M is a finite collection of finite sets that sati...

Lecture 8: Matroids [fa'13] Released under a Creative Commons Attribution-noncommercial-sharealike 3.0 License

Many problems that can be correctly solved by greedy algorithms can be described in terms of an abstract combinatorial object called a matroid. Matroids were first described in 1935 by the mathematician Hassler Whitney as a combinatorial generalization of linear independence of vectors—‘matroid’ means ‘something sort of like a matrix’. A matroid M is a finite collection of finite sets that sati...

Lecture : Matroids [fa'''] Matroids .. Definitions

Many problems that can be correctly solved by greedy algorithms can be described in terms of an abstract combinatorial object called a matroid. Matroids were first described in 1935 by the mathematician Hassler Whitney as a combinatorial generalization of linear independence of vectors—‘matroid’ means ‘something sort of like a matrix’. A matroid M is a finite collection of finite sets that sati...

Lecture Notes on Oriented Matroids and Geometric Computation

CME 305: Discrete Mathematics and Algorithms

There are two main topics we cover in this lecture. First, we introduce and study matroids a generalization of spanning trees and the notion of independence that embody the greedy algorithm we saw last class. Second, we start a new problem, the maximum ow problem. In some sense, todays lecture is about one of the easiest and hardest problems in combinatorial optimization for which we have reaso...