CS 614 | Jan-Apr 2022

Advanced Algorithms
(A part of the IITM Online Undergraduate Program.)

June — August 2023

About the Course

This course will explores the tradeoffs involved in coping with NP-completeness.

When we think about designing algorithms, we are usually very demanding in how we go about it: we require our algorithms to be fast and accurate on all conceivable inputs. This is asking for quite a bit, and perhaps it is not surprising that we cannot afford this luxury all the time. The good news is that most of the time we can make meaningful progress by relaxing just one of these demands:

1. Give up on accuracy, but not completely: look for solutions that are good enough (approximation) and/or work with algorithms that report the right solution most of the time (Las-Vegas style randomization).

2. Give up on coverage, a little bit: let your algorithms work well on structured inputs. Hopefully the structure is such that it is not too limiting and is interesting enough for some application scenario, and is also enough to give you algorithmic leverage, i.e, there’s enough that you can exploit to make fast and accurate algorithms.

3. Give up on speed, to some extent: going beyond the traditional allowance of polynomial time, which is the holy grail of what is considered efficient, takes you places. You could either allow for your algorithms have super-polynomial running times, and optimize as much as possible while being accurate on all inputs (exact algorithms), or allow for bad running times on a bounded subset of instances (Monte-Carlo style randomization).

This course is an introduction to techniques in achieving specific trade-offs, and understanding the theoretical foundations of frameworks that help us establish when certain tradeoffs are simply not feasible.

Fig. Exploring tradeoffs between the demands of accuracy, speed, and coverage.

Target Audience

Anyone who is biting their nails from the NP-completeness cliffhanger at the end of their introduction to algorithms will probably enjoy this course.

Prerequisites

This is a theoretical course that will require mathematical maturity (in particular, the ability to understand and write formal mathematical proofs), and some background in the design and analysis of algorithms. Programming experience is tangentially useful but not necessary.

References

1. The Design of Approximation Algorithms • David P. Williamson and David B. Shmoys
2. Parameterized Algorithms • Marek Cygan, Fedor V. Fomin, Lukasz Kowalik, Daniel Lokshtanov, Daniel Marx, Marcin Pilipczuk, Michal Pilipczuk, and Saket Saurabh
3. Randomized Algorithms • Motwani and Raghavan
4. Beyond the Worst-Case Analysis of Algorithms • Tim Roughgarden
5. Algorithms • Jeff Erickson

Timings and Venue

Online

Register

This course is meant for students of the IITM online BS program. If you are not enrolled in this program, but are interested in following along, please feel free to do so by going through the materials here. Send me an email if you would like to have access to the assignment problems.

Lectures

Weekly Practice

Exams