Related papers: Abstract Geometrical Computation 8: Small Machines…
Computing properties of the set of precursors of a given configuration is a common problem underlying many important questions about cellular automata. Unfortunately, such computations quickly become intractable in dimension greater than…
We generalize the ordinary aggregation process to allow for choice. In ordinary aggregation, two random clusters merge and form a larger aggregate. In our implementation of choice, a target cluster and two candidate clusters are randomly…
We survey an area of recent development, relating dynamics to theoretical computer science. We discuss the theoretical limits of simulation and computation of interesting quantities in dynamical systems. We will focus on central objects of…
We study the problem of aggregating polygons by covering them with disjoint representative regions, thereby inducing a clustering of the polygons. Our objective is to minimize a weighted sum of the total area and the total perimeter of the…
Packing problems, even of objects with regular geometries, are in general non-trivial. For few special shapes, the features of crystalline as well as random, irregular two-dimensional (2D) packings are known. The packing of 2D crosses does…
In this work, we present a variant of the multilayer random sequential adsorption (RSA) process that is inspired by orthogonal resource sharing in wireless communication networks. In the one-dimensional (1D) version of this variant, the…
Emerging reconfigurable optical communication technologies allow to enhance datacenter topologies with demand-aware links optimized towards traffic patterns. This paper studies the algorithmic problem of jointly optimizing topology and…
Debugging accumulation of floating-point errors is hard; ideally, computer should track it automatically. Here we consider twofold approximation of an exact real with value + error pair of floating-point numbers. Normally, value + error sum…
In this article we are interested in the geometric and analytic mixing scales of solutions to passive scalar problems. Here, we show that both notions are comparable after possibly removing large scale projections. In order to discuss our…
Accelerated gradient descent iterations are widely used in optimization. It is known that, in the continuous-time limit, these iterations converge to a second-order differential equation which we refer to as the accelerated gradient flow.…
Owing to recent advances in artificial intelligence and internet of things (IoT) technologies, collected big data facilitates high computational performance, while its computational resources and energy cost are large. Moreover, data are…
We study a kinetic mean-field equation for a system of particles with different sizes, in which particles are allowed to coagulate only if their sizes sum up to a prescribed time-dependent value. We prove well-posedness of this model, study…
Congestion on the Internet is an old problem but still a subject of intensive research. The TCP protocol with its AIMD (Additive Increase and Multiplicative Decrease) behavior hides very challenging problems; one of them is to understand…
Given a weighted graph, we introduce a partition of its vertex set such that the distance between any two clusters is bounded from below by a power of the minimum weight of both clusters. This partition is obtained by recursively merging…
We study a random aggregation process involving rectangular clusters. In each aggregation event, two rectangles are chosen at random and if they have a compatible side, either vertical or horizontal, they merge along that side to form a…
In parallel computing, a valid graph coloring yields a lock-free processing of the colored tasks, data points, etc., without expensive synchronization mechanisms. However, coloring is not free and the overhead can be significant. In…
Log-normal continuous random cascades form a class of multifractal processes that has already been successfully used in various fields. Several statistical issues related to this model are studied. We first make a quick but extensive review…
We propose a new type of approximate counting algorithms for the problems of enumerating the number of independent sets and proper colorings in low degree graphs with large girth. Our algorithms are not based on a commonly used Markov chain…
Existing asynchronous distributed optimization algorithms often use diminishing step-sizes that cause slow practical convergence, or fixed step-sizes that depend on an assumed upper bound of delays. Not only is such a delay bound hard to…
We study the problem of approximately counting the number of list packings of a graph. The analogous problem for usual vertex coloring and list coloring has attracted a lot of attention. For list packing the setup is similar but we seek a…