Computer Science 284/484

Advanced Algorithms

Spring 2020

Instructor: Daniel Stefankovic
Class: Tuesday, Thursday 12:30pm-13:45pm, Wilmot 116.
Instructor office hours (Wegmans 2315): Tuesday, Thursday 2pm - 3pm.

TA: Ben Reber.


Textbooks: there is no required textbook; see each section for the recommended reading (mostly online; I will also supply handouts).

Other resources/recommended reading:

• [CLRS09] Introduction to Algorithms (3rd edition), T. Cormen, C. Leiserson, R. Rivest, and C. Stein, 2009.
• [K91] The Design and Analysis of Algorithms, D. Kozen, 1991.
• [KT05] Algorithm Design, J. Kleinberg and E. Tardos, 2005.
• [AHU74] The Design and Analysis of Computer Algorithms, A. Aho, J. Hopcroft, J. Ulman, 1974.


• [MU05] Probability and Computing: Randomized Algorithms and Probabilistic Analysis, M. Mitzenmacher, E. Upfal, 2005.
• [MR95] Randomized Algorithms, R. Motwani, P. Raghavan, 1995.
• [H02] Finite Markov chains and algorithmic applications, O. Haggstrom, 2002.
• [G97] Counting, sampling and integrating: algorithms and complexity, M. Jerrum, 2003.


• [WS11] The Design of Approximation Algorithms, D.Williamson, D. Shmoys, 2011
• [V04] Approximation Algorithms, V. Vazirani, 2004.


• [BE98] Online Computation and Competitive Analysis, A. Borodin, R. El-Yaniv, 1998.
• [M05] Data Streams: Algorithms and Applications, S. Muthukrishnan, 2005.


• [BCKO08] Computational Geometry: Algorithms and Applications, M. de Berg, O. Cheong, M. van Kreveld, M. Overmars, 2008.
• [PS85] Computational Geometry: An Introduction, F. Preparata, M. Shamos, 1985.
• [M93] Computational Geometry: An Introduction Through Randomized Algorithms, K. Mulmuley, 1993.
• [G97] Algorithms on Strings, Trees and Sequences: Computer Science and Computational Biology, D. Gusfield, 1997.

Prerequisites: CSC282.

Schedule

TOPIC 1: Max-Flow

Jan. 16 Th - Max Flow I (basics, Ford-Fulkerson, min-cut max-flow)

Jan. 21 Tu - Max Flow II (Edmonds Karp)
Jan. 23 Th - Max Flow III (Push Relabel)

homework 1 (max flow) - due Feb. 6

TOPIC 2: Linear Programming/Semidefinite programming

Jan. 28 Tu - Linear Programming I (Basics, duality)
Jan. 30 Th - Linear Programming II (Simplex algorithm I)

Feb. 4 Tu - Linear Programming III (Simplex algorithm II)
Feb. 6 Th - Linear Programming IV (applications)

homework 2 (linear programming) - due Feb. 20

Feb. 11 Tu - Semidefinite programming I (basics, semidefiniteness, Cholesky decomposition)
Feb. 13 Th - Semidefinite programming II (Max-Cut)

Feb. 18 Tu - Semidefinite programming III (metric embeddings)

homework 3 (semidefinite programming) - due Mar. 5



TOPIC 3: Computational Geometry

Feb. 20 Th - Computational Geometry I (sweep technique)

Feb. 25 Tu - Computational Geometry II (convex hulls)
Feb. 27 Th - Computational Geometry III (closest pair of points)

Mar. 3 Tu - Computational Geometry IV (Voronoi diagrams)

homework 4 (computational geometry) - due Mar. 19



TOPIC 4: String Algorithms

Mar. 5 Th - String Algorithms I (Suffix Trees)

Mar. 10 Tu - SPRING BREAK
Mar. 12 Th - SPRING BREAK

Mar. 17 Tu - String Algorithms II (Suffix Trees)
Mar. 19 Th - String Algorithms III (Suffix Arrays)

Mar. 24 Tu - String Algorithms IV (Suffix Arrays)

homework 5 (string algorithms) - due Apr. 2

TOPIC 5: Streaming Algorithms

reading:
Finite Probability Spaces (Babai).
Streaming Algorithms (Chakrabarti), chapters 1-5.


Mar. 26 Th - Probability I

Mar. 31 Tu - Probability II
Apr. 2 Th - Streaming Algorithms I (distinct elements)

Apr. 7 Tu - Streaming Algorithms II (sketching)
Apr. 9 Th - Streaming Algorithms III (frequency moments)

Apr. 14 Tu - Streaming Algorithms IV

homework 6 (streaming algorithms) - due Apr. 23

TOPIC 6: Something Fun

Apr. 16 Th - TBD
Apr. 21 Tu - TBD

Apr. 23 Th - TBD
Apr. 28 Tu - TBD

Grading

The grade for the course is based on the homework (theoretical and applied; there will be 6 problem sets); there are no exams.

Homework Rules

• Theoretical homework should be typeset (LaTeX preferred) and emailed to the instructor by the deadline (specific for each assignment). You may work with other people on the theoretical homework, but you must each write up your solutions separately (without any written aid). If you work with other people, indicate who you worked with on your solution.
  
  
• No late homework will be accepted without instructor's permission (a permission must be requested at least 24 hours before the due date).

This course follows The University Policy on Academic Honesty .