**Sunday, 30.06.2024 23:59**.

## News

## Typo on exercise sheet
Dear students, We uploaded a new version of the exercise sheet, correcting a typo in the last exercise. |

## Lecture starts at 16:00
Dear students, As decided in the lecture yesterday, from now on the lecture will always start at 16:00 sharp. |

## Fine-Grained Complexity Theory

Complexity theory traditionally distinguishes whether a problem can be solved in polynomial time (by providing an efficient algorithm) or the problem is NP-hard (by providing a reduction). However, for practical purposes the label "polynomial-time" is too coarse: It can make a huge difference whether an algorithm runs in say linear, quadratic, or cubic time. In this course we explore an emerging subfield at the intersection of complexity theory and algorithm design which aims at a more fine-grained view of the complexity of polynomial-time problems. We present a mix of algorithms and conditional lower bounds for fundamental problems, often by drawing interesting connections between seemingly unrelated problems. A prototypical result presented in this course is the following: If there is a substantially faster algorithm for computing all-pairs shortest paths in a weighted graph, then there also is a substantially faster algorithm for checking whether the graph has a negative triangle (and vice versa). The techniques for proving such statements have been developed relatively recently and the majority of the results taught in this course are less than ten years old.

### Time & Date & Format

This course consists of one lecture per week (Tuesday 16:00-17:30) and a tutorial every other week (Friday 10:15-12:00).

The first lecture is on April 16. The first tutorial is held on April 26, then starting from May 03 a tutorial is held in every second week. Lectures and tutorials are held physically in room 024 building E1 4.

### Prerequisites

We assume basic knowledge in algorithms and theoretical computer science, as taught in the basic courses "Grundzüge von Algorithmen und Datenstrukturen"/"Fundamentals of Algorithms and Data Structures" and "Grundzüge der Theoretischen Informatik"/"Introduction to Theoretical Computer Science". The core lecture "Algorithms and Data Structures" is useful, but no formal prerequisite.

### Registration

You need to register on this webpage to get access to exercise sheets and other course material.

### Exercises

An important part of the course are the exercises, where you will design conditional lower bounds essentially on your own. There will be 6 exercise sheets and you need to collect at least 50% of all points on exercise sheets to be admitted to the exam. You are allowed to collaborate on the exercise sheets, but you have to write down a solution on your own, using your own words. Please indicate the names of your collaborators for each exercise you solve. Further, cite all external sources that you use (books, websites, research papers, etc.).

### Exam

To be admitted to the exam, you need to achieve 50% of the points on the exercise sheets. There will be a written or oral exam.

### Schedule

This is a tentative list of topics.

Lecture | Tutorial | Topic |
---|---|---|

Apr 16 | Introduction | |

Apr 23 | SAT Algorithms | |

Apr 26 | Q&A and presence exercises | |

Apr 30 | Lower Bounds from P!=NP and ETH | |

May 3 | ||

May 07 | Lower Bounds from SETH and OVH | |

May 14 | Subset Sum lower bound from SETH | |

May 17 | ||

May 21 | Subset Sum algorithms | |

May 28 | Subcubic Equivalences of APSP | |

May 31 | ||

Jun 04 | Subcubic Equivalences of APSP continued | |

Jun 11 | Matrix Multiplication and special cases of APSP | |

Jun 14 | ||

Jun 18 | Lower bounds from 3SUM | |

Jun 25 | More lower bounds from 3SUM | |

Jun 28 | ||

Jul 02 | Lower Bounds for Dynamic Problems | |

Jul 09 | Hardness of Approximation in P | |

Jul 12 | ||

Jul 16 | ? | |

Jul 23 | Outlook (recap, further hypotheses, multivariate lower bounds) | |

Jul 26 |

### Literature

We do not follow a particular book. You can find slides and partial lecture notes from previous iterations of this course on the following webpages. We closely follow the course from 2021.

Winter 2021: Fine-Grained Complexity Theory

Summer 2019: Fine-Grained Complexity Theory

Summer 2018: Selected Topics in Fine-Grained Complexity Theory