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Seminars in Combinatorics and Optimization
Tutte colloquium-Xiao Hu
Title:What is New in Join-Aggregate Query Processing?
Speaker: | Xiao Hu |
Affiliation: | University of Waterloo |
Location: | MC 5501 |
Abstract: Join-aggregate queries defined over commutative semirings subsume a wide variety of common algorithmic problems, such as graph pattern matching, graph colorability, matrix multiplication, and constraint satisfaction problems. Developing efficient algorithms for computing join-aggregate queries in the conventional RAM model has been a holy grail in database theory. One of the most celebrated results in this area is the Yannakakis algorithm dating back to 1981. Despite its prominence as a textbook solution, no improvements in its complexity have been made over the past 40 years. In this talk, I will present the first algorithm that improves upon Yannakakis for computing acyclic join-aggregate queries. Moreover, this algorithm is proven to be output-optimal among all combinatorial algorithms. One application is an output-optimal algorithm for chain matrix multiplication over sparse matrices. Beyond combinatorial algorithms, I will also show how fast matrix multiplication can further speed up the processing of conjunctive queries, a critical subclass of join-aggregate queries. Finally, I will highlight a few interesting open problems in this area.
Algebraic Graph Theory-Theo McKenzie
Title: : Precise Eigenvalue Location for Random Regular Graphs
Speaker: | Theo McKenzie |
Affiliation: | Stanford University |
Location: | Please contact Sabrina Lato for Zoom link. |
Abstract:The spectral theory of regular graphs has broad applications in theoretical computer science, statistical physics, and other areas of mathematics. Graphs with optimally large spectral gap are known as Ramanujan graphs. Previous constructions of Ramanujan graphs are based on number theory and have specific constraints on the degree and number of vertices. In this talk, we show that, in fact, most regular graphs are Ramanujan; specifically, a randomly selected regular graph has a probability of 69% of being Ramanujan. We establish this through a rigorous analysis of the Green’s function of the adjacency operator, focusing on its behavior under random edge switches.
Tutte colloquium-Peter Nelson
Title:Two-coloured lines in finite geometry
Speaker: | Peter Nelson |
Affiliation: | University of Waterloo |
Location: | MC 5501 |
Abstract: Given a colouring of the points of a projective plane, when is it true that every line contains at most two colours? I will discuss recent generalizations of classical results in this area, and a surprising link with a famous question in graph theory.