To argue that if heuristic H does not know the access sequence in advance then the worse-case cost of H on an access sequence σ is C H ( σ ) = Ω ( m n ) .

Question

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Answer 1

Question

Chapter 17, Problem 5P

(a)

Program Plan Intro

To argue that if heuristic H does not know the access sequence in advance then the worse-case cost of H on an access sequence σ is CH(σ)=Ω(mn) .

(b)

Program Plan Intro

To show that if σi accesses element x in list L using the move-to-front heuristic the ci=2.rankL(x)−1.

(c)

Program Plan Intro

To explain that equation ci=rankLi−1(x)+ti.

(d)

Program Plan Intro

To argue the transposition either increases the potential by 2 or decrease the potential by 2.

(e)

Program Plan Intro

To argue that rankLi−1(x)=|A|+|B|+1 and rankL*i−1(x)=|A|+|C|+1 .

(f)

Program Plan Intro

To show that access σi causes a change in potential of Φ(Li)=Φ(Li−1)≤2(|A|−|B|+ti) .

(g)

Program Plan Intro

To show that the amortized cost of access is bound by 4ci .

(h)

Program Plan Intro

To show the cost CMTF(σ) of access σ sequence with move-to-front is at most 4 times the cost CH(σ) of σ with any other heuristic H .

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Answer 2

Question

Chapter 17, Problem 5P

(a)

Program Plan Intro

To argue that if heuristic H does not know the access sequence in advance then the worse-case cost of H on an access sequence σ is CH(σ)=Ω(mn) .

(b)

Program Plan Intro

To show that if σi accesses element x in list L using the move-to-front heuristic the ci=2.rankL(x)−1.

(c)

Program Plan Intro

To explain that equation ci=rankLi−1(x)+ti.

(d)

Program Plan Intro

To argue the transposition either increases the potential by 2 or decrease the potential by 2.

(e)

Program Plan Intro

To argue that rankLi−1(x)=|A|+|B|+1 and rankL*i−1(x)=|A|+|C|+1 .

(f)

Program Plan Intro

To show that access σi causes a change in potential of Φ(Li)=Φ(Li−1)≤2(|A|−|B|+ti) .

(g)

Program Plan Intro

To show that the amortized cost of access is bound by 4ci .

(h)

Program Plan Intro

To show the cost CMTF(σ) of access σ sequence with move-to-front is at most 4 times the cost CH(σ) of σ with any other heuristic H .

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Answer 3

Question

Chapter 17, Problem 5P

(a)

Program Plan Intro

To argue that if heuristic H does not know the access sequence in advance then the worse-case cost of H on an access sequence σ is CH(σ)=Ω(mn) .

(b)

Program Plan Intro

To show that if σi accesses element x in list L using the move-to-front heuristic the ci=2.rankL(x)−1.

(c)

Program Plan Intro

To explain that equation ci=rankLi−1(x)+ti.

(d)

Program Plan Intro

To argue the transposition either increases the potential by 2 or decrease the potential by 2.

(e)

Program Plan Intro

To argue that rankLi−1(x)=|A|+|B|+1 and rankL*i−1(x)=|A|+|C|+1 .

(f)

Program Plan Intro

To show that access σi causes a change in potential of Φ(Li)=Φ(Li−1)≤2(|A|−|B|+ti) .

(g)

Program Plan Intro

To show that the amortized cost of access is bound by 4ci .

(h)

Program Plan Intro

To show the cost CMTF(σ) of access σ sequence with move-to-front is at most 4 times the cost CH(σ) of σ with any other heuristic H .

Expert Solution & Answer

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Answer 4

Question

Chapter 17, Problem 5P

(a)

Program Plan Intro

To argue that if heuristic H does not know the access sequence in advance then the worse-case cost of H on an access sequence σ is CH(σ)=Ω(mn) .

(b)

Program Plan Intro

To show that if σi accesses element x in list L using the move-to-front heuristic the ci=2.rankL(x)−1.

(c)

Program Plan Intro

To explain that equation ci=rankLi−1(x)+ti.

(d)

Program Plan Intro

To argue the transposition either increases the potential by 2 or decrease the potential by 2.

(e)

Program Plan Intro

To argue that rankLi−1(x)=|A|+|B|+1 and rankL*i−1(x)=|A|+|C|+1 .

(f)

Program Plan Intro

To show that access σi causes a change in potential of Φ(Li)=Φ(Li−1)≤2(|A|−|B|+ti) .

(g)

Program Plan Intro

To show that the amortized cost of access is bound by 4ci .

(h)

Program Plan Intro

To show the cost CMTF(σ) of access σ sequence with move-to-front is at most 4 times the cost CH(σ) of σ with any other heuristic H .

Expert Solution & Answer

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Answer 5

Chapter 17, Problem 5P

(a)

Program Plan Intro

To argue that if heuristic H does not know the access sequence in advance then the worse-case cost of H on an access sequence σ is CH(σ)=Ω(mn) .

(b)

Program Plan Intro

To show that if σi accesses element x in list L using the move-to-front heuristic the ci=2.rankL(x)−1.

(c)

Program Plan Intro

To explain that equation ci=rankLi−1(x)+ti.

(d)

Program Plan Intro

To argue the transposition either increases the potential by 2 or decrease the potential by 2.

(e)

Program Plan Intro

To argue that rankLi−1(x)=|A|+|B|+1 and rankL*i−1(x)=|A|+|C|+1 .

(f)

Program Plan Intro

To show that access σi causes a change in potential of Φ(Li)=Φ(Li−1)≤2(|A|−|B|+ti) .

(g)

Program Plan Intro

To show that the amortized cost of access is bound by 4ci .

(h)

Program Plan Intro

To show the cost CMTF(σ) of access σ sequence with move-to-front is at most 4 times the cost CH(σ) of σ with any other heuristic H .

Answer 6

Chapter 17, Problem 5P

(a)

Program Plan Intro

To argue that if heuristic H does not know the access sequence in advance then the worse-case cost of H on an access sequence σ is CH(σ)=Ω(mn) .

Answer 7

Chapter 17, Problem 5P

(a)

Program Plan Intro

To argue that if heuristic H does not know the access sequence in advance then the worse-case cost of H on an access sequence σ is CH(σ)=Ω(mn) .

Answer 8

(b)

Program Plan Intro

To show that if σi accesses element x in list L using the move-to-front heuristic the ci=2.rankL(x)−1.

Answer 9

(b)

Program Plan Intro

To show that if σi accesses element x in list L using the move-to-front heuristic the ci=2.rankL(x)−1.

Answer 10

(c)

Program Plan Intro

To explain that equation ci=rankLi−1(x)+ti.

Answer 11

(c)

Program Plan Intro

To explain that equation ci=rankLi−1(x)+ti.

Answer 12

(d)

Program Plan Intro

To argue the transposition either increases the potential by 2 or decrease the potential by 2.

Answer 13

(d)

Program Plan Intro

To argue the transposition either increases the potential by 2 or decrease the potential by 2.

Answer 14

(e)

Program Plan Intro

To argue that rankLi−1(x)=|A|+|B|+1 and rankL*i−1(x)=|A|+|C|+1 .

Answer 15

(e)

Program Plan Intro

To argue that rankLi−1(x)=|A|+|B|+1 and rankL*i−1(x)=|A|+|C|+1 .

Answer 16

(f)

Program Plan Intro

To show that access σi causes a change in potential of Φ(Li)=Φ(Li−1)≤2(|A|−|B|+ti) .

Answer 17

(f)

Program Plan Intro

To show that access σi causes a change in potential of Φ(Li)=Φ(Li−1)≤2(|A|−|B|+ti) .

Answer 18

(g)

Program Plan Intro

To show that the amortized cost of access is bound by 4ci .

Answer 19

(g)

Program Plan Intro

To show that the amortized cost of access is bound by 4ci .

Answer 20

(h)

Program Plan Intro

To show the cost CMTF(σ) of access σ sequence with move-to-front is at most 4 times the cost CH(σ) of σ with any other heuristic H .

Answer 21

(h)

Program Plan Intro

To show the cost CMTF(σ) of access σ sequence with move-to-front is at most 4 times the cost CH(σ) of σ with any other heuristic H .

Answer 22

Expert Solution & Answer

Answer 23

Expert Solution & Answer

Answer 24

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Answer 25

Ch. 17.1 - Prob. 1E Ch. 17.1 - Prob. 2E Ch. 17.1 - Prob. 3E Ch. 17.2 - Prob. 1E Ch. 17.2 - Prob. 2E Ch. 17.2 - Prob. 3E Ch. 17.3 - Prob. 1E Ch. 17.3 - Prob. 2E Ch. 17.3 - Prob. 3E Ch. 17.3 - Prob. 4E

To argue that if heuristic H does not know the access sequence in advance then the worse-case cost of H on an access sequence σ is C H ( σ ) = Ω ( m n ) .

Solution Summary: The author argues that if heuristic H does not know the access sequence in advance, the worse-case cost of H is CH(sigma )=Omega (mn).

Concept explainers

To argue that if heuristic H does not know the access sequence in advance then the worse-case cost of H on an access sequence σ is CH(σ)=Ω(mn) .

To show that if σi accesses element x in list L using the move-to-front heuristic the ci=2.rankL(x)−1.

To explain that equation ci=rankLi−1(x)+ti.

To argue the transposition either increases the potential by 2 or decrease the potential by 2.

To argue that rankLi−1(x)=|A|+|B|+1 and rankL*i−1(x)=|A|+|C|+1 .

To show that access σi causes a change in potential of Φ(Li)=Φ(Li−1)≤2(|A|−|B|+ti) .

To show that the amortized cost of access is bound by 4ci .

To show the cost CMTF(σ) of access σ sequence with move-to-front is at most 4 times the cost CH(σ) of σ with any other heuristic H .

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Chapter 17 Solutions