Probabilistic aspects of minimum spanning trees
Give the edges of the complete graph Kn independent uniformly distributed edge weights, and let Mn be the resulting minimum spanning tree. What can be said about the structure of Mn? A classic result of Alan Frieze is that the total weight of Mn converges to zeta(3) as n–infinity. We rather focus on the metric space structure of Mn, bounding its diameter and discussing its graph-theoretic distributional properties. In particular, we will outline a proof that Mn typically has diameter of order the cube root of n; this in particular distinguishes Mn from a uniformly random spanning tree of Kn, which has typical diameter of order the square root of n.
Speaker Details
Louigi Addario-Berry is an assistant professor at McGill University. Previously, he held an assistant professorship at Université de Montreal and a Marie Curie research fellowship at the University of Oxford. http://www.math.mcgill.ca/louigi/
- Series:
- Microsoft Research Talks
- Date:
- Speakers:
- Louigi Addario-Berry
- Affiliation:
- McGill University
-
-
Jeff Running
-
Series: Microsoft Research Talks
-
-
-
-
Galea: The Bridge Between Mixed Reality and Neurotechnology
Speakers:- Eva Esteban,
- Conor Russomanno
-
Current and Future Application of BCIs
Speakers:- Christoph Guger
-
Challenges in Evolving a Successful Database Product (SQL Server) to a Cloud Service (SQL Azure)
Speakers:- Hanuma Kodavalla,
- Phil Bernstein
-
Improving text prediction accuracy using neurophysiology
Speakers:- Sophia Mehdizadeh
-
-
DIABLo: a Deep Individual-Agnostic Binaural Localizer
Speakers:- Shoken Kaneko
-
-
Recent Efforts Towards Efficient And Scalable Neural Waveform Coding
Speakers:- Kai Zhen
-
-
Audio-based Toxic Language Detection
Speakers:- Midia Yousefi
-
-
From SqueezeNet to SqueezeBERT: Developing Efficient Deep Neural Networks
Speakers:- Sujeeth Bharadwaj
-
Hope Speech and Help Speech: Surfacing Positivity Amidst Hate
Speakers:- Monojit Choudhury
-
-
-
-
-
'F' to 'A' on the N.Y. Regents Science Exams: An Overview of the Aristo Project
Speakers:- Peter Clark
-
Checkpointing the Un-checkpointable: the Split-Process Approach for MPI and Formal Verification
Speakers:- Gene Cooperman
-
Learning Structured Models for Safe Robot Control
Speakers:- Ashish Kapoor
-
-