# Seminar: Exact Exponential Algorithms

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Algorithms and machine learning
Year Semester Date Period Language In charge
2011 autumn 06.09-29.11. 1-2 English Mikko Koivisto

## Lectures

Time Room Lecturer Date
Tue 14-16 B119 Mikko Koivisto 06.09.2011-11.10.2011
Tue 14-16 B119 Mikko Koivisto 01.11.2011-29.11.2011

## Information for international students

The language of the seminar is English if there is one or more participant who do not speak Finnish.

## General

The seminar is intended to students that know at least the basics of algorithms design and analysis.

The topic of the seminar is well described in the back cover of the course book, "Exact Exponential Algorithms" by Dieter Kratsch and Fedor Fomin (Springer 2010):

"Today most computer scientists believe that NP-hard problems cannot be solved by polynomial-time algorithms. From the polynomial-time perspective, all NP-complete problems are equivalent but their exponential-time properties vary widely. Why do some NP-hard problems appear to be easier than others? Are there algorithmic techniques for solving hard problems that are significantly faster than the exhaustive, brute-force methods? The algorithms that address these questions are known as exact exponential algorithms.

The history of exact exponential algorithms for NP-hard problems dates back to the 1960s. The two classical examples are Bellman, Held and Karp’s dynamic programming algorithm for the traveling salesman problem and Ryser’s inclusion–exclusion formula for the permanent of a matrix. The design and analysis of exact algorithms leads to a better understanding of hard problems and initiates interesting new combinatorial and algorithmic challenges. The last decade has witnessed a rapid development of the area, with many new algorithmic techniques discovered. This has transformed  exact algorithms into a very active research field. This book provides an introduction to the area and explains the most common algorithmic techniques, and the text is supported throughout with exercises and detailed notes for further reading.

The book is intended for advanced students and researchers in computer science, operations research, optimization and combinatorics."

The purpose of the seminar is to go through selected chapters and sections of the book, solve many of the exercises and formulate new ones. Related topics not covered by the book may be considered as well.

## Completing the course

Passing the seminar and getting the credit units requires active participation in the seminar sessions (every Tuesday). In addition, each student (1) writes a seminar paper and (2) gives a presentation on a selected topic, and (3) acts as an opponent of another presenter. The exact requirements for passing and the grounds for grading will be announced later.

The first session will give an introduction to the course; the following 3-4 sessions are reserved for individual guidance on preparing the material; the remaining sessions are for presentations and discussion.

NOTE: the first seminar session (after the introduction session on September 6) will be on October 11.