Advanced Algorithms Lecture Notes
نویسنده
چکیده
Preface This is a set of lecture notes for the 3rd year course " Advanced Algorithms " which I gave in Tsinghua University for Yao-class students in the Spring and Fall terms in 2011. This set of notes is partially based on the notes scribed by students taking the course the first time it was given. Many thanks to Xiahong Hao and Nathan Hobbs for their hard work in critically revising, editing, and adding figures to last year's material. I'd also like to give credit to the students who already took the course and scribed notes. These lecture notes, together with students' names can be found in the Spring 2011 course website. This version of the course has a few topics different than its predecessor. In particular, I removed the material on algorithmic applications of Finite Metric Embeddings and SDP relaxations and its likes, and I added elements of Fourier Analysis on the boolean cube with applications to property testing. I also added a couple of lectures on algorithmic applications of Szemerédi's Regularity Lemma. Except from property testing and the regularity lemma the remaining topics are: a brief revision of the greedy, dynamic programming and network-flows paradigms; a rather in-depth introduction to geometry of polytopes, Linear Programming, applications of duality theory, algorithms for solving linear programs; standard topics on approximation algorithms; and an introduction to Streaming Algorithms. I would be most grateful if you bring to my attention any typos, or send me your recommendations , corrections, and suggestions to [email protected].
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