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 18.1, Problem 1E
Program Plan Intro
To explain the reason of not allowing a minimum degree of
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You are organizing a conference that has received n submitted papers. Your goal is to get people to review as many
of them as possible. To do this, you have enlisted the help of k reviewers. Each reviewer i has a cost sij for writing a
review for paper j. The strategy of each reviewer i is to select a subset of papers to write a review for. They can select
any subset S; C {1,2, ..., n}, as long as the total cost to write all reviews is less than T (the time before the deadline):
2 Sij 1.
(b) Show that for B = 2 this fraction is close to 1/3. [Hint: You can consider an instance with 3n + 1 papers and
only n will be reviewed.]
If A={8,12,16,20} and B={12,16,20,24,28}, what is the value of P (A and B)?
TM M = (Q, E, I, 6, 90, 9a, qr), where Q = {90, 91, 92, 9a, 9r}, Σ = {0, 1}, r = {0, 1, L}, and 8 is:
8(qo, U)
=
(qr, U, R)
8(90, 0) =
8(go, 1)
(91, 0, R)
(qo, 1, R)
=
8(g1, L) = (ga, U, R)
8(91,0) = (91, 0, R)
8(91, 1) =
(92, 1, R)
=
(92, U, R)
8(92, U)
8(92, 0) =
(90, 0, R)
8(92, 1) = (92, 1, R)
i. Prove that M is NOT a decider.
ii. Mathematically describe the language A that M recognises. Prove that A ≤ L(M).
iii. Prove A = L(M).
iv. Is A Turing-decidable? [Give clear reasons for your answer. No need for a formal proof.]
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