Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
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Chapter 16.4, Problem 3E
Program Plan Intro
To show that if ( S , I ) is matriod then ( S , I’ ) is also matriod.
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Students have asked these similar questions
· Tonsider a set S of 4 elements. Prove that we can choose any two subsets
óf S of size 3, say A and B, and construct a matroid M = (S, 1) such that A and B are
the only maximum independent sets in M.
If A and B are sets and f: A→ B, then for any subset S of A we define
f(S) = {be B: b= f(a) for some a € S}.
Similarly, for any subset T of B we define the pre-image of T as
f(T) = {ae A: f(a) e T}.
Note that f-¹(T) is well defined even if f does not have an inverse!
For each of the following state whether it is True or False. If True then give a proof. If False
then give a counterexample:
(a) f(S₁US₂) = f(S₁) u f(S₂)
(b) f(Sin S₂) = f(S₁) nf (S₂)
(c) f¹(T₁UT₂) = f¹(T₁)uf-¹(T₂) (d) f-¹(T₁T₂) = f-¹(T₁) nf-¹(T₂)
Computer Science
Suppose (S, I) is a matroid, and suppose I' = { A' | S – A' contains some maximal A∈I }. Show that I' satisfies the heredity property with respect to the set S as well.
Chapter 16. Introduction to algorithms, Cormen
Chapter 16 Solutions
Introduction to Algorithms
Ch. 16.1 - Prob. 1ECh. 16.1 - Prob. 2ECh. 16.1 - Prob. 3ECh. 16.1 - Prob. 4ECh. 16.1 - Prob. 5ECh. 16.2 - Prob. 1ECh. 16.2 - Prob. 2ECh. 16.2 - Prob. 3ECh. 16.2 - Prob. 4ECh. 16.2 - Prob. 5E
Ch. 16.2 - Prob. 6ECh. 16.2 - Prob. 7ECh. 16.3 - Prob. 1ECh. 16.3 - Prob. 2ECh. 16.3 - Prob. 3ECh. 16.3 - Prob. 4ECh. 16.3 - Prob. 5ECh. 16.3 - Prob. 6ECh. 16.3 - Prob. 7ECh. 16.3 - Prob. 8ECh. 16.3 - Prob. 9ECh. 16.4 - Prob. 1ECh. 16.4 - Prob. 2ECh. 16.4 - Prob. 3ECh. 16.4 - Prob. 4ECh. 16.4 - Prob. 5ECh. 16.5 - Prob. 1ECh. 16.5 - Prob. 2ECh. 16 - Prob. 1PCh. 16 - Prob. 2PCh. 16 - Prob. 3PCh. 16 - Prob. 4PCh. 16 - Prob. 5P
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