The Problem Solved by BF: Approximate Set Membership ☐ Given a set S={x.),construct data structure to answer queries of the form"Is y in S?" Data structure should be: Fast(Faster than searching through S). ■ Small(Smaller than explicit representation) To obtain speed and size improvements,allow some probability of error. ■ False positives:y gs but we reportyeS ■False negatives:y∈S but we reporty &S4 The Problem Solved by BF: Approximate Set Membership  Given a set S = { x 1,x 2,…,x n }, construct data structure to answer queries of the form “Is y in S?”  Data structure should be:  Fast (Faster than searching through S).  Small (Smaller than explicit representation).  To obtain speed and size improvements, allow some probability of error.  False positives: y  S but we report y  S  False negatives: y  S but we report y  S