Media Summary: Distinct elements, k-wise independence, geometric subsampling of streams. Logistics, course topics, basic tail bounds (Markov, Chebyshev, Chernoff, Bernstein), Morris' Fusion trees, word-level parallelism, most significant set bit in constant time.
Algorithms For Big Data Compsci 229r Lecture 2 - Detailed Analysis & Overview
Distinct elements, k-wise independence, geometric subsampling of streams. Logistics, course topics, basic tail bounds (Markov, Chebyshev, Chernoff, Bernstein), Morris' Fusion trees, word-level parallelism, most significant set bit in constant time. External memory model: linked list, matrix multiplication, B-tree, buffered repository tree, sorting. Approximate matrix multiplication with Frobenius error via sampling / JL, matrix median trick, subspace embeddings. Necessity of randomized/approximate guarantees, linear sketching, AMS sketch, p-stable sketch for p less than
Low-rank approximation, column-based matrix reconstruction, k-means, compressed sensing. MapReduce: TeraSort, minimum spanning tree, triangle counting. P-stable sketch analysis, Nisan's PRG, ℓp estimation for p Amnesic dynamic programming (approximate distance to monotonicity).
