Consider the universe B = {0,1}d of length d bits strings. Define the Index Distance as...
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Consider the universe B = {0,1}d of length d bits strings. Define the Index Distance as d₂(x,y)= Σ i for all x, y = B. xi‡Yi For example, the 5-bit strings x = 01111 and y= = 10101 differ in bits 1, 2, and 4, so dƒ(x, y) = 1+2+4=7. Give a hash function which is locality sensitive with regards to the Index Distance. Remember to prove that it is locality sensitive. Give explicit values for both p₁ and på (these should only depend on r, c and d). Consider the universe B = {0,1}d of length d bits strings. Define the Index Distance as d₂(x,y)= Σ i for all x, y = B. xi‡Yi For example, the 5-bit strings x = 01111 and y= = 10101 differ in bits 1, 2, and 4, so dƒ(x, y) = 1+2+4=7. Give a hash function which is locality sensitive with regards to the Index Distance. Remember to prove that it is locality sensitive. Give explicit values for both p₁ and på (these should only depend on r, c and d).
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Solutions Step 1 To create a hash function that is localitysensitive to the Index Distance for binary strings This means that if two binary strings ar... View the full answer
Related Book For
Introduction to Algorithms
ISBN: 978-0262033848
3rd edition
Authors: Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest
Posted Date:
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