Highlights of this Course
Introduction to new trends of discrete algorithms such as online algorithms, approximation algorithms, interactive algorithms, communication complexities, parameterized complexities, and so on.

Course Description
Traditional lectures on algorithms are based on the idea that algorithms must be correct and efficient. However, this basic concept has been changed a lot in the last two to three decades. Namely, we have to be satisfied with algorithms that would not always give us correct answers. For instance, an algorithm for stock trading needs to decide the current action without knowing the future inputs (future prices of stocks) so that its profit will be as much as possible compared to the “god” that does know the future input completely. As another example, the amount of communication is more important than the amount of computation time and/or memory space, which requires us to design algorithms being efficient in the amount of bits exchanged between two or more parties. In this case, it is also often important to consider leak of information in the course of communication. We also have to give up exact solutions for NP-complete problems and the notion of approximation comes in naturally. The goal of this course is to give basic ideas of these “new” algorithms, studying several techniques for their design and analysis.