Introduction to Combinatorial Optimization in Matroids
نویسنده
چکیده
1. Matroids and Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1 2. Greedy Algorithm and Matroids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .13 3. Duality, Minors and Constructions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 4. Matroid Intersection and Partition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 5. Matroid Connectivity and Decompositions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 6. Flows in Matroids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 7. The Parity Problem
منابع مشابه
What is a matroid? Theory and Applications, from the ground up
Gian-Carlo Rota said that “Anyone who has worked with matroids has come away with the conviction that matroids are one of the richest and most useful ideas of our day.” [20] Hassler Whitney introduced the theory of matroids in 1935 and developed a striking number of their basic properties as well as different ways to formulate the notion of a matroid. As more and more connections between matroi...
متن کاملRough matroids based on coverings
The introduction of covering-based rough sets has made a substantial contribution to the classical rough sets. However, many vital problems in rough sets, including attribution reduction, are NP-hard and therefore the algorithms for solving them are usually greedy. Matroid, as a generalization of linear independence in vector spaces, it has a variety of applications in many fields such as algor...
متن کاملConsidering Stochastic and Combinatorial Optimization
Here, issues connected with characteristic stochastic practices are considered. In the first part, the plausibility of covering the arrangements of an improvement issue on subjective subgraphs is studied. The impulse for this strategy is a state where an advancement issue must be settled as often as possible for discretionary illustrations. Then, a preprocessing stage is considered that would q...
متن کاملCs 598csc: Combinatorial Optimization
One of several major contributions of Edmonds to combinatorial optimization is algorithms and polyhedral theorems for matroid intersection, and more generally polymatroid intersection. From an optimization point of view, the matroid intersection problem is the following: Let M1 = (S, I1) and M2 = (S, I2) be two matroids on the same ground set S. Then I1 ∩ I2 is the collection of all sets that a...
متن کاملA unified interpretation of several combinatorial dualities
Several combinatorial structures exhibit a duality relation that yields interesting theorems, and, sometimes, useful explanations or interpretations of results that do not concern duality explicitly. We present a common characterization of the duality relations associated with matroids, clutters (Sperner families), oriented matroids, and weakly oriented matroids. The same conditions characteriz...
متن کامل