For Erdős–Rényi random graphs with average degree γ, and uniformly random γ-regular
graph on n vertices, we prove that with high probability the size of both the Max-Cut and …

This note explores the applicability of unsupervised machine learning techniques towards
hard optimization problems on random inputs. In particular we consider Graph Neural …

The microscopic and macroscopic dynamics of random networks is investigated in the
strong-dilution limit (ie, for sparse networks). By simulating chaotic maps, Stuart-Landau …

Recent work has established that large informatics graphs such as social and information
networks have non-trivial tree-like structure when viewed at moderate size scales. Here, we …

The asymptotic properties of random regular graphs are objects of extensive study in
mathematics and physics. In this paper we argue, using the theory of spin glasses in …

The ferromagnetic Ising model is a model of a magnetic material and a central topic in
statistical physics. It also plays a starring role in the algorithmic study of approximate …

We study the belief-propagation algorithm for the graph bi-partitioning problem, ie the
ground state of the ferromagnetic Ising model at a fixed magnetization. Application of a …

The scaling of fluctuations in the distribution of ground state energies or costs with the
system size N for Ising spin glasses is considered using an extensive set of simulations with …

The average ground state energies for spin glasses on Bethe lattices of connectivities r=
3,..., 15 are studied numerically for a Gaussian bond distribution. The Extremal Optimization …

We study worst-case fairness in resource allocation and cooperative games with
transferable utility, the stable division most dissimilar to a normative standard of fairness …