please solve a and b

We will design a few (very useful) LSH families for li and 12 spaces. a) For li, consider the following hashing function h: Rd Zd. Fix weights wi.... ...wd by picking each W; = 100. Also, choose bi.... bd randomly uniformly from [0,1]. Then define W2 wd h(x) = ([: +62 L2 + b2 al) Note that this corresponds to partitioning the space by imposing a randomly-shifted grid with side-lengths defined by w1.... Wd. Deduce a lower bound on probability Pi and an upper bound on probability P2, for r = 1 (you may want to compute the probability of collision of two points r, y as a function of the distance || 1 y||1 = -1 |2; yil). Prove that p 5 1.1/c. Hint: you can use the following useful bound: Pi. We will design a few (very useful) LSH families for li and 12 spaces. a) For li, consider the following hashing function h: Rd Zd. Fix weights wi.... ...wd by picking each W; = 100. Also, choose bi.... bd randomly uniformly from [0,1]. Then define W2 wd h(x) = ([: +62 L2 + b2 al) Note that this corresponds to partitioning the space by imposing a randomly-shifted grid with side-lengths defined by w1.... Wd. Deduce a lower bound on probability Pi and an upper bound on probability P2, for r = 1 (you may want to compute the probability of collision of two points r, y as a function of the distance || 1 y||1 = -1 |2; yil). Prove that p 5 1.1/c. Hint: you can use the following useful bound: Pi