Theory Seminar - Algorithms and Hardness for Linear Algebra on Geometric Graphs, Aaron Schild

Explore algorithms and hardness results for linear algebra on geometric graphs in this theory seminar. Delve into efficient spectral graph theory for k-graphs, examining problems like matrix-vector multiplication, spectral sparsification, and Laplacian system solving. Investigate the relationship between function parameters and algorithmic efficiency, considering SETH-based hardness results. Learn about the limitations of the fast multipole method and its dimensional dependence. Gain insights into well-separated pairs decomposition, approximate nearest neighbors, and open problems in the field of geometric graph algorithms.

Intro
The n-body problem (gravitation)
body as adjacency matrix-vector multiplication
Fast multipole method (FMM) (GR87)
Remainder of the Talk
Outline of FMM (GR87)
Background: Well-separated pairs decomposition (WSPD)
Callahan-Kosaraju construction of 2-WSPD on X
h= f and A, B are arbitrary
Can FMM be improved?
Background strong exponential time hypothesis (SETH)
Background: approximate nearest neighbors
Hardness part 1
Hardness Summary
Open problem 1: when does FMM apply?
Other problems we studied
Open problem 2: graph problems we didn't study
Conclusion