The students in this course were required to take turns scribing lecture notes. They were provided with detailed instructions and a template. The process of scribing lecture notes provides students with valuable experience preparing mathematical documents, and also generates a useful set of lecture notes for the class.
| 1 |
Introduction |
No notes for Lecture 1 |
| 2 |
LINEAR PROGRAMMING (LP): basic notions, simplex method
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(PDF) (Courtesy of Alice Oh. Used with permission.) |
| 3 |
LP: Farkas Lemma, duality |
(PDF) (Courtesy of Abhinav Kumar and Nodari Sitchinava. Used with permission.) |
| 4 |
LP: complexity issues, ellipsoid method |
(PDF) (Courtesy of Reina Riemann. Used with permission.) |
| 5 |
LP: ellipsoid method |
(PDF) (Courtesy of Dennis Quan. Used with permission.) |
| 6 |
LP: optimization vs. separation, interior-point algorithm |
(PDF) (Courtesy of Bin Song and Hanson Zhou. Used with permission.) |
| 7 |
LP: optimality conditions, interior-point algorithm (analysis |
(PDF) (Courtesy of Nick Hanssens and Nicholas Matsakis. Used with permission.) |
| 8 |
LP: interior-point algorithm wrap up
NETWORK FLOWS (NF)
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(PDF) (Courtesy of Jelena Spasojevic. Used with permission.) |
| 9 |
NF: Min-cost circulation problem (MCCP) |
(PDF) (Courtesy of Jasper Lin. Used with permission.) |
| 10 |
NF: Cycle cancelling algs for MCCP |
(PDF) (Courtesy of Ashish Koul. Used with permission.) |
| 11 |
NF: Goldberg-Tarjan alg for MCCP and analysis |
(PDF) (Courtesy of Mohammad Hajiaghayi and Vahab Mirrokni. Used with permission.) |
| 12 |
NF: Cancel-and-tighten
DATA STRUCTURES (DS): Binary search trees
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(PDF) (Courtesy of David Woodruff and Xiaowen Xin. Used with permission.) |
| 13 |
DS: Splay trees, amortized analysis, dynamic tree |
(PDF) (Courtesy of Naveen Sunkavally. Used with permission.) |
| 14 |
DS: dynamic tree operations |
(PDF) (Courtesy of Sanmay Das. Used with permission.) |
| 15 |
DS: analysis of dynamic trees
NF: use of dynamic trees for cancel-and-tighten
|
(PDF) (Courtesy of Timothy Danford. Used with permission.) |
| 16 |
APPROXIMATION ALGORITHMS (AA): hardness, inapproximability, analysis of approximation algorithms |
(PDF) (Courtesy of Nicole Immorlica and Mana Taghdiri. Used with permission.) |
| 17 |
AA: Vertex cover (rounding, primal-dual), generalized Steiner tree |
(PDF) (Courtesy of Matt Peters and Steven Richman. Used with permission.) |
| 18 |
AA: Primal-dual alg for generalized Steiner tree |
(PDF) (Courtesy of Johnny Chen and Ahmed Ismail. Used with permission.) |
| 19 |
AA: Derandomization |
(PDF) (Courtesy of Shalini Agarwal and Shane Swenson. Used with permission.) |
| 20 |
AA: MAXCUT, SDP-based 0.878-approximation algorithm |
(PDF) (Courtesy of William Theis and David Liben-Nowell. Used with permission.) |
| 21 |
AA: Polynomial approximation schemes, scheduling problem: P||Cmax |
(PDF) |
| 22 |
AA: Approximation Scheme for Euclidean TSP |
(PDF)* (Courtesy of Salil Vadhan (Thomas D. Cabot Associate Professor of Computer Science). Used with permission.) |
| 23 |
AA: Multicommodity flows and cuts and embeddings of metrics |
(PDF)** |
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* There were no scribe notes for this lecture for the Fall 2001 term. The notes from a previous term cover the same topic and are linked here.
* There were no scribe notes for this lecture for the Fall 2001 term. Section 8 of the notes from a previous term cover the same topic and are linked here.