Lecture 10 Matroid. Independent System Consider a finite set S and a collection C of subsets of S....
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Transcript of Lecture 10 Matroid. Independent System Consider a finite set S and a collection C of subsets of S....
Independent System
• Consider a finite set S and a collection C of subsets of S. (S,C) is called an independent system if
CACBBA ,
i.e., it is hereditary.
Each subset in C is called an independent set.
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About Matriod
Theorem An independent system (S,C) is a matroid iff for any cost function c( ), the greedy algorithm MAX gives a maximum solution.
Proof. (=>)
solution. optimal gives MAX Therefore,
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What we learnt in this lecture?
• What is matroid?.
• matric matroid and graphic matroid.
• Relationship between matroid and greedy algorithm.