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Questions tagged [matroids]

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1answer
110 views

Activity Selection and Matroid Theory

Many people on different articles suggests that if an optimization problem has a greedy solution, the underlying structure must have matroid property. I was trying to understand this. So far, I was ...
1
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1answer
90 views

Can LP for matroid polytopes be solved using the greedy algorithm?

For general linear programming (LP), i.e. optimization of a linear objective over a general polyhedron, to the best of my knowledge/recollection one can use the simplex algorithm (or hypothetically, ...
1
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1answer
37 views

A $log(k)$ algorithm for the matroid secretary problem

I'm reading the following article that presents a $log(k)$ algorithm for your secretary problem. I'm in the analysis section at the left part of page 5 there is the following claim: $B^*$ is a ...
6
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0answers
142 views

When does greediness guarantee optimality?

I was wondering if there is any theoretical results characterizing under what condition does greedy algorithm actually finds the optimal solution. Here is a motivating example. Suppose you are trying ...
3
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0answers
84 views

Is the intersection of $k \geq 3$ graphic matroids in P? [closed]

It is known that intersection of three general matroids is NP-hard (wiki), which is done via reduction from Hamiltonian cycle. The reduction uses one graphic matroid and two connectivity matroids. A ...
4
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1answer
312 views

Finding a maximum-weight base of a a matroid, in reverse

Given a weighted matroid with positive weights, we can find a independent set with a maximum weight with a greedy algorithm: Start with an empty set (by definition of matroid, it is independent). Add ...
2
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1answer
92 views

What is a good resource to learn about oriented matroids in the context of digraphs and optimization?

I am interested in oriented matroids in the context of directed graphs and optimization. Unfortunately, I know very little of the topic. Is there a book, article or a resource that serves as a good ...
7
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1answer
865 views

Greedy choice and matroids (greedoids)

As I was going through the material about the greedy approach, I came to know that a knowledge on matroids (greedoids) will help me approaching the problem properly. After reading about matroids I ...
22
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1answer
1k views

How fundamental are matroids and greedoids in algorithm design?

Initially, matroids were introduced to generalize the notions of linear independence of a collection of subsets $E$ over some ground set $I$. Certain problems that contain this structure permit greedy ...