CSE 712: Advanced Topics in Algorithm Design (Fall 2015)

Important Announcements

Logistics

      Course credits    :    1, 2 or 3
      Time                   :    2:00pm - 4:30pm, Wed
      Location             :    Davis 310

Instructor

     Shi Li
     328 Davis Hall,
     Buffalo, NY 14260,
     USA

     Email                :       shil*buffalo*edu    (first * to @, second * to .)
     Office Hours     :       2:00pm - 3:00pm, Tue, Davis 328

Overview

This graduate-level seminar course will cover algorithmic concepts and techniques in the research frontier in algorithm design. There are three main themes for the course:

1. Approximation and randomized algorithms;
2. Streaming algorithms;
3. Online algorithms.

The main goal of course is not to give an in-depth coverage of tools and techniques for any of these themes, but rather, to let students have a taste of these different models for algorithm design and some of the basic ideas used to tackle problems in these models. Some topics of the course are:

• Linear and semi-definite programming relaxation for combinatorial optimization problems.
• Rounding and primal-dual approach to design approximation algorithms.
• Sampling and hash-function methods for computing simple functions of a streaming data set.
• Online algorithms for secretary and matching problems.

The course is based on student and instructor presentations of research papers and book chapters/sections. Each student needs to give a presentation once (unless he/she registered the course only for 2 credits). Students can always volunteer to give more presentations. The instructor will give the presentations when a lecture is not assigned to any student.

Prerequisites

• CSE531: Analysis of Algorithms (Required)
• CSE632: Analysis of Algorithms II (Highly Recommended)

Students should have mastery of basic mathematical tools such as mathematical induction, probability theory and matrix multiplication, and should be comfortable with mathematical proofs. The course is intended for graduate students who are already or are interested in pursuing research in theoretical computer science. Exceptional undergraduate students who have strong interest in research in algorithms and have taken CSE331 can ask the instructor for permission to register the course.

Grading

The grading contains 3 parts:

1. Class attendance and participation. Maximum score: 20.
2. Presentation. Maximum score: 40.
3. Project. Maximum score: 40.

The final score for the course will be S/U (S means satisfactory; U means unsatisfactory). You may choose to register the course for 1 credit, 2 credits or 3 credits. To get an "S" with 3 credits, you need to get at least 75 total score. If you registered the course for 2 credits, you can choose between part B and part C. To get an "S" with 2 credits, your score for part A plus the maximum of your score for part B and for part C must be at least 45. To get an "S" for 1 credit, your score for part A must be at least 15.

Participation

Participation of class is required and graded. Each lecture (except for the first and last lectures) is worth 10 points:

• 6 points: be present in the lecture.
• 2 points: participation in the discussion.
• 2 points: solve the problem given by the presenter. (The solution will be submitted at the beginning of the next lecture, so you have one week to solve the problem.)

The score will be scaled so the maximum possible score for this part is 20.

Presentation

The score for a presentation is based on how well the presentation is organized and how clear the presenter delivers the ideas and techniques. If you give more than one presentations, your score for this part will be the best score of all presentations. The presenter for a lecture should also design a homework problem for the rest of the class.

It is recommended that the presenter meets and discusses the papers/sections he/she will present with the instructor on Tuesday, the day before the presentation day. The discussion does not affect the score of the presentation on Wednesday; so the presenter is encouraged to ask as many questions as possible.

Final Project

The final project can be one of the following forms:

1. A report on a papper you read.
2. An implementation of a known algorithm.

Academic Integrity

Please refer to the university Academic Integrity Policy regarding academic dishonesty:

• Undergraduate Academic Integrity Policy
• Graduate Academic Integrity Policy

Schedule

Lec#	Date	Content	Reading Material	Presenter
1	Sep 3	Introduction		Shi Li
2	Sep 9	TSP and k-center	Section 1.1, 2.2, 2.4 of WS book	Shi Li
3	Sep 16	LP rounding for set cover	Section 1.2, 1.3, 1.7 of WS book	Rohit Dubey
4	Sep 23	Greedy and primal-dual for set cover	Section 1.4, 1.5, 1.6 of WS book	Sai Vikneshwar
5	Sep 30	FPTAS for knapsack problem	Chapter 8 of Vaz book	Erika Santos
6	Oct 7	LP rounding for multi-cut	Section 8.3 of WS book	Poonam Kumari
7	Oct 14	SDP rounding for max-cut	Section 6.1, 6.2 of WS book	Chaowen Guan
8	Oct 21	Online paging problem	Chapter 1,2, 3.1 of BRICS minicourse	Shiva Mariswamy Subramnir
9	Oct 28	Move-to-front algorithm for list-accessing	ST paper	Sathish Kumar Deivasigamani
10	Nov 4	KVV online algorithm for bipartite matching	KVV paper	Dhinesh Nakkeerar
11	Nov 11	Streaming algorithm for estimating L_0 norm	Lecture Notes by Tim Roughgarden Section 1,2,3,5	Sahajdeep Singh Bedi
12	Nov 18	Streaming algorithm for estimating L_2 norms	Lecture Notes by Tim Roughgarden Section 4	Subramanian Madhanagopal Sivasankaran
13	Dec 2	Lower bound via communication complexity	Lecture Notes by Tim Roughgarden Section 6,7,8,9
14	Dec 9	Summary

Homework Problems

• Lecture 2: Design a constant approximation algorithm for the k-center problem with the restriction that some points can not be selected as centers. More specifically, we are given a metric (V, d), an integer k and a set U ⊆ V. The goal of the problem is to find k points v₁, v₂, ..., v_k ∈ U so as to minimize max_{v ∈ V} min_{i ∈ [k]} d(v, v_i).
• Lecture 3
• Lecture 3: Write down the integer programming and the linear programming relaxation for the variant of the set cover problem where we are only required to cover p fraction of the elements.
• Lecture 4: Give the primal and the dual LPs for the edge cover problem.
• Lecture 5: Show that a strongly NP-hard problem can not have a pseudo-polynomial time algorithm unless P = NP.
• Lecture 6: In the algorithm for the multi-cut problem, we defined f(r) (i.e., the "volume" of the ball of radius r around s_i) to be LP/k plus the total contribution of all edges. Why do we choose the additive term to be LP/k? In particular, why can not we make it much bigger or much smaller?
• Lecture 7: Give the dual of the semidefinite programming for MAX-CUT problem.
• Lecture 8: The ski rental problem - we do not know how many days we are going to ski in this winter. Buying rate is 300$. Renting rate is 20$/day. The optimal algorithm knows how many days you are going to ski and thus decides whether to buy or rent depending on which will be minimum. Design an online solution that is as much as close to optimal offline algorithm as possible; analyze the competitive ratio.
• Lecture 9: Prove that MTF is 2-competitive if the cost of the MTF operation for the item accessed is free.
• Lecture 10: Prove that the greedy algorithm for bipartite matching gives the same matching if the roles of U and V are switched.
• Lecture 11: Give an algorithm to calculate the majority element using constant number of words.

Papers for the Final Project (Topics for the Approximation Algorithms part)

You can choose one of the following topics. For the topic you selected, read one paper from the list. You can either write a 5-10 page report, or implement the algorithm in the paper. The report should be self-contained and should contain formal proofs. If you choose to implement the algorithm, you need to provide some necessary comments in your source files and some sample inputs and ouputs. If you have any questions, do not hestitate to ask the instructor.

You can find the list of topics and papers here.