Shay Kels, Nira Dyn and Evgeny Lipovetsky
Article: Computation of the Metric Average of 2D Sets with Piecewise Linear Boundaries
Algorithms 2010, 3(3), 265-275; doi:10.3390/a3030265 - published online 26 July 2010
Show/Hide AbstractAbstract: 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 piecewise linear boundaries.

Paul M.B. Vitanyi
Obituary: Ray Solomonoff, Founding Father of Algorithmic Information Theory
Algorithms 2010, 3(3), 260-264; doi:10.3390/a3030260 - published online 20 July 2010
Show/Hide AbstractAbstract: 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 length of objects and is commonly designated by the term “Kolmogorov complexity.” In the 1950s Solomonoff was one of the first researchers to treat probabilistic grammars and the associated languages. He treated probabilistic Artificial Intelligence (AI) when “probabilistic” was unfashionable, and treated questions of machine learning early on. But his greatest contribution is the creation of Algorithmic Information Theory. [...]

Grace Solomonoff
Obituary: Ray Solomonoff (1926-2009)
Algorithms 2010, 3(3), 255-259; doi:10.3390/a30302555 - published online 20 July 2010
Show/Hide AbstractAbstract: 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 ran very fast. Helped by a friend, he built a year round house in N.H. He put in thick insulation, enabling him to heat the house with two rows of light bulbs along the ceiling. I met Ray shortly after he finished this house, in 1969. I knew about foraging, so I showed him edible plants like Indian Cucumber Root. He was so happy: it was as if we found a fountain of champagne. [...]

Zhivko Nedev
Article: An O(n)-Round Strategy for the Magnus-Derek Game
Algorithms 2010, 3(3), 244-254; doi:10.3390/a3030244 - published online 15 July 2010
Show/Hide AbstractAbstract: 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 number of rounds. The other player, Derek, attempts to minimize the number of visited positions. We present a new strategy for Magnus that succeeds in visiting the maximal number of positions in 3(n – 1) rounds, which is the optimal number of rounds up to a constant factor.

Sanjay Mehrotra and Zhifeng Li
Article: Segment LLL Reduction of Lattice Bases Using Modular Arithmetic
Algorithms 2010, 3(3), 224-243; doi:10.3390/a3030224 - published online 12 July 2010
Show/Hide AbstractAbstract: 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 a segment-LLL basis reduction algorithm that generates lattice basis satisfying a weaker condition than the LLL reduced basis with O(n) improvement than the LLL algorithm. In this paper we combine Storjohann’s modular arithmetic approach with the segment-LLL approach to further improve the worst case complexity of the segment-LLL algorithms by a factor of n^_0.5.

Henri Schurz
Article: Algorithmic Solution of Stochastic Differential Equations
Algorithms 2010, 3(3), 216-223; doi:10.3390/a3030216 - published online 1 July 2010
Show/Hide AbstractAbstract: 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 systems of SDEs driven by standard Wiener processes and with adapted initial data. Several examples illustrate its use.