Related papers: Complexity of 2D bootstrap percolation difficulty:…
An important objective of research in counting complexity is to understand which counting problems are approximable. In this quest, the complexity class TotP, a hard subclass of #P, is of key importance, as it contains self-reducible…
It is natural to expect that there are only three possible types of scaling limits for the collection of all percolation interfaces in the plane: (1) a trivial one, consisting of no curves at all, (2) a critical one, in which all points of…
In this paper we study monotone cellular automata in $d$ dimensions. We develop a general method for bounding the growth of the infected set when the initial configuration is chosen randomly, and then use this method to prove a lower bound…
Bootstrap percolation is a type of cellular automaton which has been used to model various physical phenomena, such as ferromagnetism. For each natural number $r$, the $r$-neighbour bootstrap process is an update rule for vertices of a…
Theoretical complexity is a vital subfield of computer science that enables us to mathematically investigate computation and answer many interesting queries about the nature of computational problems. It provides theoretical tools to assess…
Determining the universality class of a system exhibiting critical phenomena is one of the central problems in physics. There are several methods to determine this universality class from data. As methods performing collapse plots onto…
In our companion paper \cite{Stojnicclupint19} we introduced a powerful mechanism that we referred to as the Controlled Loosening-up (CLuP) for handling MIMO ML-detection problems. It turned out that the algorithm has many remarkable…
We propose very efficient algorithms for the bootstrap percolation and the diffusion percolation models by extending the Newman-Ziff algorithm of the classical percolation [M. E. J. Newman and R. M. Ziff, Phys. Rev. Lett. 85 (2000) 4104].…
We discuss a characterization of complexity based on successive approximations of the probability density describing a system by means of maximum entropy methods, thereby quantifying the respective role played by different orders of…
Bootstrap percolation on an arbitrary graph has a random initial configuration, where each vertex is occupied with probability p, independently of each other, and a deterministic spreading rule with a fixed parameter k: if a vacant site has…
Many practical problems in almost all scientific and technological disciplines have been classified as computationally hard (NP-hard or even NP-complete). In life sciences, combinatorial optimization problems frequently arise in molecular…
In this paper we study in complete generality the family of two-state, deterministic, monotone, local, homogeneous cellular automata in $\mathbb{Z}^d$ with random initial configurations. Formally, we are given a set…
The Hamming torus of dimension $d$ is the graph with vertices $\{1,\dots,n\}^d$ and an edge between any two vertices that differ in a single coordinate. Bootstrap percolation with threshold $\theta$ starts with a random set of open…
Rigidity Percolation is a crucial framework for describing rigidity transitions in amorphous systems. We present a new, efficient algorithm to study central-force Rigidity Percolation in two dimensions. This algorithm combines the Pebble…
A promising approach to achieve computational supremacy over the classical von Neumann architecture explores classical and quantum hardware as Ising machines. The minimisation of the Ising Hamiltonian is known to be NP-hard problem for…
In majority bootstrap percolation on a graph G, an infection spreads according to the following deterministic rule: if at least half of the neighbours of a vertex v are already infected, then v is also infected, and infected vertices remain…
We introduce a new class of two-dimensional cellular automata with a bootstrap percolation-like dynamics. Each site can be either empty or occupied by a single particle and the dynamics follows a deterministic updating rule at discrete…
We analyze the question of deciding whether a quadratic or a hyperbolic 0-1 programming instance has a unique optimal solution. Both uniqueness questions are known to be NP-hard, but are unlikely to be contained in the class NP. We…
Clustering is a central primitive in unsupervised learning, yet practice is dominated by heuristics whose outputs can be unstable and highly sensitive to representations, hyperparameters, and initialisation. Existing theoretical results are…
We survey recent developments in the study of probabilistic complexity classes. While the evidence seems to support the conjecture that probabilism can be deterministically simulated with relatively low overhead, i.e., that $P=BPP$, it also…