The problem of controllability of the dynamical state of a network is central in network theory
and has wide applications ranging from network medicine to financial markets. The driver …

The minimum dominating set (MDS) problem has wide applications in network science and
related fields. It aims at constructing a node set of smallest size such that any node of the …

The ability to learn new tasks and generalize to others is a remarkable characteristic of both
human brains and recent artificial intelligence systems. The ability to perform multiple tasks …

Previously, the controllability problem of a linear time-invariant dynamical system was
mapped to the maximum matching (MM) problem on the bipartite representation of the …

The minimum vertex-cover problems on random α-uniform hypergraphs are studied using
two different approaches, a replica method in statistical mechanics of random systems and a …

The ability to learn new tasks and generalize performance to others is one of the most
remarkable characteristics of the human brain and of recent AI systems. The ability to …

The greedy leaf removal (GLR) procedure on a graph is an iterative removal of any vertex
with degree one (leaf) along with its nearest neighbor (root). Its result has two faces: a …

Typical performance of approximation algorithms is studied for randomized minimum vertex
cover problems. A wide class of random graph ensembles characterized by an arbitrary …

This study investigated the typical performance of approximation algorithms known as belief
propagation, the greedy algorithm, and linear-programming relaxation for maximum …

Typical behavior of the linear programming (LP) problem is studied as a relaxation of the
minimum vertex cover (min-VC), a type of integer programming (IP) problem. A lattice-gas …