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Consider a bitwise Bloom filter A1 and a counting Bloom filter A2, both of size m = 17. The hash functions used are h₁(k) = (k·13) mod m and h₂(k) = (k·19) mod m. The set S₁ = {49, 35, 83, 58, 34, 76, 63} is to be inserted into these filters. 1. Fill the bitwise Bloom filter A1 with the elements of S₁ and write the resulting filter. Then, do the same for the counting Bloom filter A2. 2. If you want to delete the number 34, can this be done in A₁? Justify your answer. Can this be done in A2? If yes, explain the process and justify its correctness. 3. Now, consider another set S₂ = {4, 76, 5, 7, 49, 97}, which has been inserted into a bitwise Bloom filter B₁ = [0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1] and a counting Bloom filter B2 = [0, 1, 1, 1, 0, 0, 1, 1, 2, 0, 1, 0, 0, 1, 2, 0, 1]. How can you compute the bitwise Bloom filter C1 and counting Bloom filter C2 for the union S = S₁ U S2 using A1, B1, A2, and B2? Justify your answers.

Consider a bitwise Bloom filter A1 and a counting Bloom filter A2, both of size m = 17. The hash functions used are h₁(k) = (k·13) mod m and h₂(k) = (k·19) mod m. The set S₁ = {49, 35, 83, 58, 34, 76, 63} is to be inserted into these filters. 1. Fill the bitwise Bloom filter A1 with the elements of S₁ and write the resulting filter. Then, do the same for the counting Bloom filter A2. 2. If you want to delete the number 34, can this be done in A₁? Justify your answer. Can this be done in A2? If yes, explain the process and justify its correctness. 3. Now, consider another set S₂ = {4, 76, 5, 7, 49, 97}, which has been inserted into a bitwise Bloom filter B₁ = [0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1] and a counting Bloom filter B2 = [0, 1, 1, 1, 0, 0, 1, 1, 2, 0, 1, 0, 0, 1, 2, 0, 1]. How can you compute the bitwise Bloom filter C1 and counting Bloom filter C2 for the union S = S₁ U S2 using A1, B1, A2, and B2? Justify your answers.

C++ Programming: From Problem Analysis to Program Design
C++ Programming: From Problem Analysis to Program Design
8th Edition
ISBN:9781337102087
Author:D. S. Malik
Publisher:D. S. Malik
Chapter5: Control Structures Ii (repetition)
Section: Chapter Questions
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Consider a bitwise Bloom filter A1 and a counting Bloom filter A2, both of size m = 17. The hash functions used are h₁(k) = (k·13) mod m and h₂(k) = (k·19) mod m. The set S₁ = {49, 35, 83, 58, 34, 76, 63} is to be inserted into these filters. 1. Fill the bitwise Bloom filter A1 with the elements of S₁ and write the resulting filter. Then, do the same for the counting Bloom filter A2. 2. If you want to delete the number 34, can this be done in A₁? Justify your answer. Can this be done in A2? If yes, explain the process and justify its correctness. 3. Now, consider another set S₂ = {4, 76, 5, 7, 49, 97}, which has been inserted into a bitwise Bloom filter B₁ = [0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1] and a counting Bloom filter B2 = [0, 1, 1, 1, 0, 0, 1, 1, 2, 0, 1, 0, 0, 1, 2, 0, 1]. How can you compute the bitwise Bloom filter C1 and counting Bloom filter C2 for the union S = S₁ U S2 using A1, B1, A2, and B2? Justify your answers.
Transcribed Image Text:Consider a bitwise Bloom filter A1 and a counting Bloom filter A2, both of size m = 17. The hash functions used are h₁(k) = (k·13) mod m and h₂(k) = (k·19) mod m. The set S₁ = {49, 35, 83, 58, 34, 76, 63} is to be inserted into these filters. 1. Fill the bitwise Bloom filter A1 with the elements of S₁ and write the resulting filter. Then, do the same for the counting Bloom filter A2. 2. If you want to delete the number 34, can this be done in A₁? Justify your answer. Can this be done in A2? If yes, explain the process and justify its correctness. 3. Now, consider another set S₂ = {4, 76, 5, 7, 49, 97}, which has been inserted into a bitwise Bloom filter B₁ = [0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1] and a counting Bloom filter B2 = [0, 1, 1, 1, 0, 0, 1, 1, 2, 0, 1, 0, 0, 1, 2, 0, 1]. How can you compute the bitwise Bloom filter C1 and counting Bloom filter C2 for the union S = S₁ U S2 using A1, B1, A2, and B2? Justify your answers.
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