Related papers: Complexity of 2D bootstrap percolation difficulty:…
The culling process in Bootstrap Percolation is Abelian since the final stable configuration does not depend on the details of the updating procedure. An efficient algorithm is devised using this idea for the determination of the bootstrap…
Given a satisfiable instance of 1-in-3 SAT, it is NP-hard to find a satisfying assignment for it, but it may be possible to efficiently find a solution subject to a weaker (not necessarily Boolean) predicate than `1-in-3'. There is a…
This paper deals with the computational complexity of conditions which guarantee that the NP-hard problem of finding the sparsest solution to an underdetermined linear system can be solved by efficient algorithms. In the literature, several…
The first quantum technologies to solve computational problems that are beyond the capabilities of classical computers are likely to be devices that exploit characteristics inherent to a particular physical system, to tackle a bespoke…
We give new evidence that quantum computers -- moreover, rudimentary quantum computers built entirely out of linear-optical elements -- cannot be efficiently simulated by classical computers. In particular, we define a model of computation…
Consider a $p$-random subset $A$ of initially infected vertices in the discrete cube $[L]^3$, and assume that the neighbourhood of each vertex consists of the $a_i$ nearest neighbours in the $\pm e_i$-directions for each $i \in \{1,2,3\}$,…
Measuring software complexity plays an important role to meet the demands of complex software. The cyclomatic complexity is one of most used and renowned metric among the other three proposed and researched metrics that are namely: Line of…
Consider a $p$-random subset $A$ of initially infected vertices in the discrete cube $[L]^d$, and assume that the neighbourhood of each vertex consists of the $a_i$ nearest neighbours in the $\pm e_i$-directions for each $i \in \{1,2,\dots,…
Block Sorting is a well studied problem, motivated by its applications in Optical Character Recognition (OCR), and Computational Biology. Block Sorting has been shown to be NP-Hard, and two separate polynomial time 2-approximation…
This chapter delves into the realm of computational complexity, exploring the world of challenging combinatorial problems and their ties with statistical physics. Our exploration starts by delving deep into the foundations of combinatorial…
We study directed rigidity percolation (equivalent to directed bootstrap percolation) on three different lattices: square, triangular, and augmented triangular. The first two of these display a first-order transition at p=1, while the…
We consider a family of percolation models in which geometry and connectivity are defined by two independent random processes. Such models merge characteristics of discrete and continuous percolation. We develop an algorithm allowing…
The polynomial hierarchy plays a central role in classical complexity theory. Here, we define a quantum generalization of the polynomial hierarchy, and initiate its study. We show that not only are there natural complete problems for the…
Jigsaw percolation is a nonlocal process that iteratively merges connected clusters in a deterministic "puzzle graph" by using connectivity properties of a random "people graph" on the same set of vertices. We presume the Erdos--Renyi…
Percolation, a paradigmatic geometric system in various branches of physical sciences, is known to possess logarithmic factors in its correlators. Starting from its definition, as the $Q\rightarrow1$ limit of the $Q$-state Potts model with…
State minimization of combinatorial filters is a fundamental problem that arises, for example, in building cheap, resource-efficient robots. But exact minimization is known to be NP-hard. This paper conducts a more nuanced analysis of this…
Bootstrap percolation models have been extensively studied during the two past decades. In this article, we study the following "anisotropic" bootstrap percolation model: the neighborhood of a point (m,n) is the set…
Bootstrap percolation on the random graph $G_{n,p}$ is a process of spread of "activation" on a given realization of the graph with a given number of initially active nodes. At each step those vertices which have not been active but have at…
A standard type of uncertainty set in robust optimization is budgeted uncertainty, where an interval of possible values for each parameter is given and the total deviation from their lower bounds is bounded. In the two-stage setting,…
Automata networks are a versatile model of finite discrete dynamical systems composed of interacting entities (the automata), able to embed any directed graph as a dynamics on its space of configurations (the set of vertices, representing…