PPT-Randomized / Hashing Algorithms

Shannon Quinn with thanks to William Cohen of Carnegie Mellon University and J Leskovec A Rajaraman and J Ullman of Stanford University First Upcoming deadlines TONIGHT 115959pm Assignment 3. The analysis uses only very basic and intuitively understandable concepts of probability theory and is meant to be accessible even for undergraduates taking their 64257rst algorithms course 1 Introduction dictionary is a data structure for storing a Up to this point the greatest drawback of cuckoo hashing appears to be that there is a polynomially small but practically signicant probability that a failure occurs during the insertion of an item requiring an expensive rehashing of all items in th CS648. . Lecture 3. Two fundamental problems. Balls into bins. Randomized Quick Sort. Random Variable and Expected . value. 1. Balls into BINS. Calculating probability of some interesting events. 2. CS648. . Lecture 15. Randomized Incremental Construction . (building the background). 1. Partition Theorem. A set of events . ,…,. . defined over a probability space (. ,. P. ) is said to induce a partition of . CS648. . Lecture 6. Reviewing the last 3 lectures. Application of Fingerprinting Techniques. 1-dimensional Pattern matching. . Preparation for the next lecture.. . 1. Randomized Algorithms . discussed till now. CS648. . Lecture 17. Miscellaneous applications of . Backward analysis. 1. Minimum spanning tree. 2. Minimum spanning tree. . 3. b. a. c. d. h. x. y. u. v. 18. 7. 1. 19. 22. 10. 3. 12. 3. 15. 11. 5. CS648. . Lecture . 25. Derandomization. using conditional expectation. A probability gem. 1. Derandomization. using . conditional expectation. 2. Problem 1. : Large cut in a graph. Problem:. Let . CS648. . Lecture 4. Linearity of Expectation with applications. (Most important tool for analyzing randomized algorithms). 1. RECAP from the last lecture. 2. Random variable. Definition. :. . A random variable defined over a probability space (. Lecture Note #15. Hashing. For efficient look-up in a table. Objectives. 2. [CS1020 Lecture 15: Hashing]. References. 3. [CS1020 Lecture 15: Hashing]. Outline. Direct Addressing Table. Hash Table. Hash Functions. Plan. I spent the last decade advising on numerous cases where hash tables/functions were used. A few observations on . What data structures I’ve seen implemented and where. What do developers think, were they need help. In static hashing, function . h. maps search-key values to a fixed set of . B. . buckets, that contain a number of (K,V) entries.. . . Problem: d. atabases . grow . (or shrink) . with time. . If initial number of buckets is too small, and file grows, performance will degrade due to too much overflows.. Outline. Randomized methods. : today. SGD with the hash trick (recap). Bloom filters. Later:. count-min sketches. l. ocality sensitive hashing. THE Hash Trick: A Review. Hash Trick - Insights. Save memory: don’t store hash keys. 3. William Cohen. 1. Outline. Randomized methods - so far. SGD with the hash trick. Bloom filters. count-min sketches. Today:. Review and discussion. More on count-min. Morris counters. locality sensitive hashing. these trees, grafted components; a combinatorid structures, seen already, (exponential) generating letters or (see e.g., e.g., )offers the possibility of translating directly specifications of the typ