Related papers: On the power of choice for Boolean functions

There is still much to discover about the mechanisms and nature of discontinuous percolation transitions. Much of the past work considers graph evolution algorithms known as Achlioptas processes in which a single edge is added to the graph…

We introduce a model of graph-constrained dynamic choice with reinforcement modeled by positively $\alpha$-homogeneous rewards. We show that its empirical process, which can be written as a stochastic approximation recursion with Markov…

Achlioptas processes are a class of dynamically grown random graphs where on each step several edges are chosen at random but only one is added. The sum rule, product rule, and bounded size rules have been extensively studied. Here we…

We propose an adaptive version of the total variation algorithm proposed in [3] for computing the balanced cut of a graph. The algorithm from [3] used a sequence of inner total variation minimizations to guarantee descent of the balanced…

For a Boolean function $\Phi\colon\{0,1\}^d\to\{0,1\}$ and an assignment to its variables $\mathbf{x}=(x_1, x_2, \dots, x_d)$ we consider the problem of finding the subsets of the variables that are sufficient to determine the function…

We examine the number T of queries that a quantum network requires to compute several Boolean functions on {0,1}^N in the black-box model. We show that, in the black-box model, the exponential quantum speed-up obtained for partial functions…

We associate to each Boolean function a polynomial whose evaluations represents the distances from all possible Boolean affine functions. Both determining the coefficients of this polynomial from the truth table of the Boolean function and…

The approximate degree of a Boolean function $f \colon \{-1, 1\}^n \rightarrow \{-1, 1\}$ is the least degree of a real polynomial that approximates $f$ pointwise to error at most $1/3$. We introduce a generic method for increasing the…

Despite their apparent simplicity, random Boolean networks display a rich variety of dynamical behaviors. Much work has been focused on the properties and abundance of attractors. The topologies of random Boolean networks with one input per…

We develop a new algorithmic technique that allows to transfer some constant time approximation algorithms for general graphs into random order streaming algorithms. We illustrate our technique by proving that in random order streams with…

We study a variant of the parallel Moser-Tardos Algorithm. We prove that if we restrict attention to a class of problems whose dependency graphs have subexponential growth, then the expected total number of random bits used by the algorithm…

The graphical balls-into-bins process is a generalization of the classical 2-choice balls-into-bins process, where the bins correspond to vertices of an arbitrary underlying graph $G$. At each time step an edge of $G$ is chosen uniformly at…

In the restricted shortest paths problem, we are given a graph $G$ whose edges are assigned two non-negative weights: lengths and delays, a source $s$, and a delay threshold $D$. The goal is to find, for each target $t$, the length of the…

We consider Boolean functions f:{-1,1}^n->{-1,1} that are close to a sum of independent functions on mutually exclusive subsets of the variables. We prove that any such function is close to just a single function on a single subset. We also…

We consider here on-line algorithms for Achlioptas processes. Given a initially empty graph $G$ on $n$ vertices, a random process that at each step selects independently and uniformly at random two edges from the set of non-edges is…

In this paper, we present two main results. First, by only one conjecture (Conjecture 2.9) for recognizing a vertex symmetric graph, which is the hardest task for our problem, we construct an algorithm for finding an isomorphism between two…

The theorem states that: Every Boolean function can be $\epsilon -approximated$ by a Disjunctive Normal Form (DNF) of size $O_{\epsilon}(2^{n}/\log{n})$. This paper will demonstrate this theorem in detail by showing how this theorem is…

For genetic algorithms using a bit-string representation of length~$n$, the general recommendation is to take $1/n$ as mutation rate. In this work, we discuss whether this is really justified for multimodal functions. Taking jump functions…

The evolution of the largest component has been studied intensely in a variety of random graph processes, starting in 1960 with the Erd\"os-R\'enyi process. It is well known that this process undergoes a phase transition at n/2 edges when,…

The semi-random graph process is a single player game in which the player is initially presented an empty graph on $n$ vertices. In each round, a vertex $u$ is presented to the player independently and uniformly at random. The player then…