Algorithms, Volume 3, Issue 3

We compare univariate L1 interpolating splines calculated on 5-point windows, on 7-point windows and on global data sets using four different spline functionals, namely, ones based on the second derivative, the first derivative, the function value an...

We present a car traffic simulation prototype for complex networks, that is formed by a collection of roads and junctions. Traffic load evolution is described by a model based on fluid dynamic conservation laws, deduced from conservation of the numbe...

We analytically investigate univariate C1 continuous cubic L1 interpolating splines calculated by minimizing an L1 spline functional based on the second derivative on 5-point windows. Specifically, we link geometric properties of the data points in t...

The metric average is a binary operation between sets in Rn which is used in the approximation of set-valued functions. We introduce an algorithm that applies tools of computational geometry to the computation of the metric average of 2D sets with pi...

Ray Solomonoff was always inventive. As a child, he had a lab in his parent's cellar in Cleveland and a secret air hole to vent the smoke from his experiments. He gave his friend Marvin Minsky a so-called "Hurry" clock — a clock labeled "HURRY" that...

Ray J. Solomonoff died on December 7, 2009, in Cambridge, Massachusetts, of complications of a stroke caused by an aneurism in his head. Ray was the first inventor of Algorithmic Information Theory which deals with the shortest effective description...

We analyze further the Magnus-Derek game, a two-player game played on a round table with n positions. The players jointly control the movement of a token. One player, Magnus, aims to maximize the number of positions visited while minimizing the numbe...

The algorithm of Lenstra, Lenstra, and Lovász (LLL) transforms a given integer lattice basis into a reduced basis. Storjohann improved the worst case complexity of LLL algorithms by a factor of O(n) using modular arithmetic. Koy and Schnorr developed...

This brief note presents an algorithm to solve ordinary stochastic differential equations (SDEs). The algorithm is based on the joint solution of a system of two partial differential equations and provides strong solutions for finite-dimensional syst...