Community detection and stochastic block models: recent developments
E Abbe - Journal of Machine Learning Research, 2018 - jmlr.org
The stochastic block model (SBM) is a random graph model with planted clusters. It is widely
employed as a canonical model to study clustering and community detection, and provides …
employed as a canonical model to study clustering and community detection, and provides …
[图书][B] Analysis of boolean functions
R O'Donnell - 2014 - books.google.com
Boolean functions are perhaps the most basic objects of study in theoretical computer
science. They also arise in other areas of mathematics, including combinatorics, statistical …
science. They also arise in other areas of mathematics, including combinatorics, statistical …
[图书][B] Handbook of approximation algorithms and metaheuristics
TF Gonzalez - 2007 - taylorfrancis.com
Delineating the tremendous growth in this area, the Handbook of Approximation Algorithms
and Metaheuristics covers fundamental, theoretical topics as well as advanced, practical …
and Metaheuristics covers fundamental, theoretical topics as well as advanced, practical …
Algorithmic barriers from phase transitions
D Achlioptas, A Coja-Oghlan - 2008 49th Annual IEEE …, 2008 - ieeexplore.ieee.org
For many random constraint satisfaction problems, by now there exist asymptotically tight
estimates of the largest constraint density for which solutions exist. At the same time, for …
estimates of the largest constraint density for which solutions exist. At the same time, for …
Optimality and sub-optimality of PCA I: Spiked random matrix models
A central problem of random matrix theory is to understand the eigenvalues of spiked
random matrix models, introduced by Johnstone, in which a prominent eigenvector (or …
random matrix models, introduced by Johnstone, in which a prominent eigenvector (or …
The computer science and physics of community detection: Landscapes, phase transitions, and hardness
C Moore - arXiv preprint arXiv:1702.00467, 2017 - arxiv.org
Community detection in graphs is the problem of finding groups of vertices which are more
densely connected than they are to the rest of the graph. This problem has a long history, but …
densely connected than they are to the rest of the graph. This problem has a long history, but …
Information-theoretic thresholds from the cavity method
Vindicating a sophisticated but non-rigorous physics approach called the cavity method, we
establish a formula for the mutual information in statistical inference problems induced by …
establish a formula for the mutual information in statistical inference problems induced by …
A supernodal formulation of vertex colouring with applications in course timetabling
For many problems in scheduling and timetabling, the choice of a mathematical
programming formulation is determined by the formulation of the graph colouring …
programming formulation is determined by the formulation of the graph colouring …
Rigorous location of phase transitions in hard optimization problems
D Achlioptas, A Naor, Y Peres - Nature, 2005 - nature.com
It is widely believed that for many optimization problems, no algorithm is substantially more
efficient than exhaustive search. This means that finding optimal solutions for many practical …
efficient than exhaustive search. This means that finding optimal solutions for many practical …
Concentration of the adjacency matrix and of the Laplacian in random graphs with independent edges
RI Oliveira - arXiv preprint arXiv:0911.0600, 2009 - arxiv.org
Consider any random graph model where potential edges appear independently, with
possibly different probabilities, and assume that the minimum expected degree is omega (ln …
possibly different probabilities, and assume that the minimum expected degree is omega (ln …