Graphical structure is ubiquitous in robotics, computer vision, and machine learning applications, including, for example, probabilistic inference, multi-agent estimation and control, and distributed learning. Consequently, understanding what specific features of graphs influence the properties of problems defined over them (and how), provides a powerful unifying lens for studying a wide range of practically-important problems, as well as devising new algorithmic approaches to solve them. In particular, recent work in robotics and computer vision has shown algebraic graph theory to be especially useful.  In brief, this field of mathematics studies properties of graphs by means of algebraic objects (e.g., matrices and their spectra, linear spaces, and/or groups) constructed from them, thus bringing to bear the powerful tools of algebra. These techniques have recently enabled sharp novel insights into the intrinsic difficulty of several fundamental problems in estimation and control, as well as novel state-of-the-art algorithms.

The goal of this workshop is to introduce and promote this powerful suite of tools to a broader robotics audience.  In particular, the technical program will be structured around the following three themes:

• Mathematical fundamentals:  What is algebraic graph theory, and what is it good for?

• Current research:  How are researchers currently using these techniques to devise state-of-the-art algorithms in robotics, computer vision, and machine learning?

• Future directions:  What kinds of emerging applications and new research frontiers might these techniques enable in the future?

EXPECTED OUTCOMES

• Foundations:  What is algebraic graph theory, and what is it good for?

• Applications:  What are the latest results and emerging applications for algebraic/spectral graph theory in robotics? What open challenges are there toward improving the application of these techniques?

• Frontiers: What are emerging capabilities that people have not yet exploited for these kinds of problems?

13:30 - 15:00 Session 1:

• 13:30 - 14:00 Welcome and Introduction

• 14:00 - 14:30 Luana Ruiz, Large-scale graph machine learning: tradeoffs, guarantees and dynamics

• 14:30 - 15:00 Federica Arrigoni, Synchronization Problems in Computer Vision

15:00 - 15:30 Coffee break

15:30 - 17:30 Session 2:

• 15:30 - 15:55  Kevin Doherty, MAC: Maximizing Algebraic Connectivity for Graph Sparsification

• 15:55 - 16:20  Yulun Tian, Rotation Averaging via Fast Laplacian Solvers

• 16:20 - 16:45  Julio Placed, Exploiting the Graph Spectrum to Make Optimal Decisions in Active SLAM

• 16:45 - 17:10  Yongbo Chen, Spectral Graph-Theoretic Methods for SLAM

We welcome extended abstracts (up to 1 page) on new applications of algebraic and/or spectral graph theory (broadly construed) in robotics, computer vision, control engineering, and machine learning. Submissions will be reviewed by the organizers and a program committee and those accepted will be featured in lightning talks and posters.

Abstract Submission: https://forms.gle/7vUSAvmCuJYcmoKq9

Submission Deadline: Friday, June 23, 2023 - 11:59 PM AoE