Algorithms for Similarity Search and Pseudorandomness

We study the problem of approximate near neighbor (ANN) search
and show the following results:
• An improved framework for solving the ANN problem using
locality-sensitive hashing, reducing the number of evaluations
of locality-sensitive hash functions and the word-RAM complexity compared to the standard framework.
• A framework for solving the ANN problem with space-time
tradeoffs as well as tight upper and lower bounds for the spacetime tradeoff of framework solutions to the ANN problem
under cosine similarity.
• A novel approach to solving the ANN problem on sets along
with a matching lower bound, improving the state of the
art. A self-tuning version of the algorithm is shown through
experiments to outperform existing similarity join algorithms.
• Tight lower bounds for asymmetric locality-sensitive hashing
which has applications to the approximate furthest neighbor
problem, orthogonal vector search, and annulus queries.
• A proof of the optimality of a well-known Boolean localitysensitive hashing scheme.
We study the problem of efficient algorithms for producing highquality pseudorandom numbers and obtain the following results:
• A deterministic algorithm for generating pseudorandom numbers of arbitrarily high quality in constant time using nearoptimal space.
• A randomized construction of a family of hash functions that
outputs pseudorandom numbers of arbitrarily high quality
with space usage and running time nearly matching known
cell-probe lower bounds.