# 263-4507-00L Advances in Distributed Graph Algorithms

Semester | Spring Semester 2020 |

Lecturers | M. Ghaffari |

Periodicity | yearly recurring course |

Course | Does not take place this semester. |

Language of instruction | English |

Abstract | How can a network of computers solve the graph problems needed for running that network? |

Objective | This course will familiarize the students with the algorithmic tools and techniques in local distributed graph algorithms, and overview the recent highlights in the field. This will also prepare the students for independent research at the frontier of this area. This is a special‐topics course in algorithm design. It should be accessible to any student with sufficient theoretical/algorithmic background. In particular, it assumes no familiarity with distributed computing. We only expect that the students are comfortable with the basics of algorithm design and analysis, as well as probability theory. It is possible to take this course simultaneously with the course “Principles of Distributed Computing”. If you are not sure whether you are ready for this class or not, please consult the instructor. |

Content | How can a network of computers solve the graph problems needed for running that network? Answering this and similar questions is the underlying motivation of the area of Distributed Graph Algorithms. The area focuses on the foundational algorithmic aspects in these questions and provides methods for various distributed systems --- e.g., the Internet, a wireless network, a multi-processor computer, etc --- to solve computational problems that can be abstracted as graph problems. For instance, think about shortest path computation in routing, or about coloring and independent set computation in contention resolution. Over the past decade, we have witnessed a renaissance in the area of Distributed Graph Algorithms, with tremendous progress in many directions and solutions for a number of decades-old central problems. This course overviews the highlights of these results. The course will mainly focus on one half of the field, which revolves around locality and local problems. The other half, which relates to the issue of congestion and dealing with limited bandwidth in global problems, will not be addressed in this offering of the course. The course will cover a sampling of the recent developments (and open questions) at the frontier of research of distributed graph algorithms. The material will be based on a compilation of recent papers in this area, which will be provided throughout the semester. The tentative list of topics includes: - The shattering technique for local graph problems and its necessity - Lovasz Local Lemma algorithms, their distributed variants, and distributed applications - Distributed Derandomization - Distributed Lower bounds - Graph Coloring - Complexity Hierarchy and Gaps - Primal-Dual Techniques |

Prerequisites / Notice | The class assumes no knowledge in distributed algorithms/computing. Our only prerequisite is the undergraduate class Algorithms, Probability, and Computing (APC) or any other course that can be seen as the equivalent. In particular, much of what we will discuss uses randomized algorithms and therefore, we will assume that the students are familiar with the tools and techniques in randomized algorithms and analysis (to the extent covered in the APC class). |