CSC Topics in Algorithms: Combinatorial Optimization and Approximation Algorithms Lecture 1: Jan 10

Basic Information  Course homepage:  Blog:  Instructor: Lau, Lap Chi ( 劉立志 )  Office hour: by appointment  Lectures: H6 (ERB 703), F2-3 (ERB 703)  Tutor: Le Jilin, Jerry  Tutorial: H5

Course Material  No textbook.  See course information page. Extra lecture H5 (ERB 803).

Outcome  Distinguish polynomial time solvable problems and NP-complete problems.  Learn the basic of linear programming (e.g. duality), and integer programming.  Learn different techniques to design heuristics that are provably “good”.  Use LP and SDP to design approximation algorithms.

Course Requirement  3 Homework, 37.5%  Notes taking, 12.5%  Project, 50%

Homework  See last year homeworks.  3 out of 8.  Encourage discussion, can use references, but write your own solutions. Bonus questions!

Notes Taking  Each student takes notes for one lecture.  Use latex to typeset it. See examples.  Due next Monday.  Discussion after class, provide references.

Project  For your research, algorithmic topic relevant to your area.  See course project page.  1-2 students a group.

Project Requirement  Read 3 papers, write a report, and a 15-mins presentation.  Meet 3 times during the semester to discuss the progress.  Choose a topic (Feb 14-15), discussion (Feb 18-22)  Outline (Mar 13-14), discussion (Mar 17-20)  Presentation (Apr 24-25), discussion (Apr 28-30)  Report (early May)

Project Ideas  Belief propagation and its applications  Graph minor theory and its applications  Computational limitations on unsupervised learning  Graph partitioning problems and automatic news story segmentation  Pricing selfish users in multicommodity networks  PC-tree and its applications  Relevant ranking on multi-class data  Spectral graph theory and its applications  Graph labeling and image processing  Spectral clustering and semi-supervised learning  Optimizing in non-cooperative environment via duality of LP  Approximation algorithms for facility location problems  Nearest neighbour search

Project Ideas  Surface simplification in computer graphics  Network coding  Fixed parameter algorithms and approximation algorithms  Pattern matching algorithms  Delaunay triangulation and its application  Approximate string matching  Approximating max-k-cut using semidefinite programming  Semidefinite programming and machine learning  Winner determination problem in combinatorial auctions  Decentralized search algorithms in small world graphs  Searching techniques in peer-to-peer networks  Sparsest cut and its applications  The Multiplicative Weights Update Method and Its Applications

Course Requirement  3 Homework, 37.5%  Notes taking, 12.5%  Project, 50% workload, grades…

Blog  Discuss lectures  Discuss homework  Discuss course notes