Advanced Topics in Algorithm Design

K. Subramani LDCSEE, West Virginia University, Morgantown, WV {ksmani@csee.wvu.edu}

1 General Information

(a) Instructor: K. Subramani.

(b) Meeting Times: M 4 : 00 pm - 5 : 15 pm.

Location: 749 ESB.

(c) Contact Information: 749 ESB, ksmani@csee.wvu.edu.

(d) Office Hours: Tu, Th - 10 : 00 am - 11 : 00 am.

(e) Textbook - There will not be an official text for the course. However, I will make copies of [CLRS09], [MR95] and [BEY98] available for reference.

(f) Assessment:

(a) Presentations (2) - You will be required to present allotted material. The presentation will be graded on the basis of clarity, comprehensiveness and effectiveness. The presentations will be worth 40% of your grade.

(b) Homework Assignments - You will be handed several homework assignments. These assignments constitute 60% of your grade.

A maximum of 5 bonus points will be awarded for class performance.

(g) Grade Boundaries (a) A: 80 and up

(b) B: 65 − 79

(c) C: 50 − 64

(d) D: 45 − 49

(e) F: 0 − 44

(h) Grading policy - If you have any questions about the grading, you must contact the instructor within two days of your paper being returned.

(i) Makeup Policy - If for some reason, you are unable to attend a test or an exam, please meet me at the earliest and I will set an alternate date.

(j) Course Objectives - The objectives of this course are as follows:

(a) To reintroduce students to concepts from probability.

(b) To introduce students to the design and analysis of randomized algorithms.

(c) To introduce students to the notion of NP-completeness.

(d) To introduce students to the design and analysis of approximation algorithms.

(e) To provide a brief introduction to the notion of online algorithms.

(k) Learning Outcomes - Upon successful completion of this course, students will be able to:

(i) Attack problems in probability theory.

(ii) Design approximation algorithms for NP-hard problems satisfying certain structural properties.

(iii) Develop randomized strategies against deterministic adversaries.

(iv) Develop strategies for problems in an online setting.

1.1 Counting, Probability and Probabilistic Analysis

Counting, Probability, Discrete random variables, The geometric and binomial distributions, Tail bounds, Application of tail bounds to the analysis of randomized algorithms.

1.2 NP-completeness

Polynomial time, Polynomial-time verification, NP-completeness and reducibility, NP-completeness proofs, NP-complete problems.

1.3 Approximation Algorithms

The vertex-cover problem, The traveling salesman problem, The set-covering problem, Randomization and linear programming, The subset-sum problem.

1.4 Online Algorithms

Introduction to Competitive Analysis and its Applications, Self-Organizing Data Structures, Unsorted Linear Lists and Binary Search Trees, Online Paging, Deterministic and Randomized Algorithms, Variations on Competetive Analysis, Variations on the Paging Problem.

I would like to reiterate that this is a sketch of the topics that we will be covering. For various reasons, I may choose to drop a mentioned topic or cover a new topic. In such cases, advance notice will be given.

2 Academic Integrity Statement

The integrity of the classes offered by any academic institution solidifies the foundation of its mission and cannot be sacrificed to expediency, ignorance, or blatant fraud. Therefore, I will enforce rigorous standards of academic integrity in all aspects and assignments of this course. For the detailed policy of West Virginia University regarding the definitions of acts considered to fall under academic dishonesty and possible ensuing sanctions, please see the Student Conduct Code

at http://www.arc.wvu.edu/admissions/integrity.html  . Should you have any questions about possibly

improper research citations or references, or any other activity that may be interpreted as an attempt at academic dishonesty, please see me before the assignment is due to discuss the matter.

3 Social Justice Statement

West Virginia University is committed to social justice. I concur with that commitment and expect to foster a nurturing learning environment, based upon open communication, mutual respect and non-discrimination. Our University does not discriminate on the basis of race, sex, age, disability, veteran status, religion, sexual orientation, color or national origin. Any suggestions to further such a positive and open environment in this class will be appreciated and given serious consideration. If you are a person with a disability and anticipate needing any type accommodation, in order to participate in this class, please advise me of the same and make appropriate arrangements with Disability Services (293 − 6700).

If you feel that you are being treated inappropriately or unfairly in any way, please feel free to bring your concerns to my attention; rest assured that doing so will not prejudice the grading process. In return, I expect you to behave professionally and ethically.

References

[BEY98] Allan Borodin and Ran El-Yaniv. Online Computation and Competitive Analysis. Cambridge University Press, Cambridge, 1998.

[CLRS09] T. H. Cormen, C. E. Leiserson, R. L. Rivest, and C. Stein. Introduction to Algorithms. MIT Press, 3^{rd} edition, 2009.

[MR95] Rajeev Motwani and Prabhakar Raghavan. Randomized Algorithms. Cambridge University Press, Cambridge, England, June 1995.