http://www.mdpi.com/journal/algorithms/special_issues/algorithms-applied-math/ Submission All papers should be submitted to algorithms@mdpi.com. To be published continuously until the deadline and papers will be listed together at the special issue website. Submitted papers should not have been published nor be under consideration for publication elsewhere. All papers are refereed through a peer-review process. A guide for authors is available on the Instructions for Authors page. Algorithms is an international peer-reviewed quarterly journal published by MDPI. Article Processing Charges (APC) will be waived for well prepared manuscripts of invited papers. For the first three volumes of this new journal the APC are of 300 CHF (or 550 CHF per paper for those papers that require extensive additional formatting and/or English corrections) for papers submitted before 31 December 2010. http://www.mdpi.com/1999-4893/3/3/311/ 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 and the antiderivative. Computational results indicate that second-derivative-based 5-point-window L1 splines preserve shape as well as or better than the other types of L1 splines. To calculate second-derivative-based 5-point-window L1 splines, we introduce an analysis-based, parallelizable algorithm. This algorithm is orders of magnitude faster than the previously widely used primal affine algorithm. http://www.mdpi.com/1999-4893/3/3/311/ Fri, 20 Aug 2010 00:00:00 CEST Algorithms 2010-08-20 3 3 Article 311 328 1999-4893 Univariate Cubic L1 Interpolating Splines: Spline Functional, Window Size and Analysis-based Algorithm 2010-08-20 doi: 10.3390/a3030311 Lu Yu Qingwei Jin John E. Lavery Shu-Cherng Fang http://www.mdpi.com/1999-4893/3/3/276/ 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 the windows with linearity, convexity and oscillation properties of the resulting L1 spline. These analytical results provide the basis for a computationally efficient algorithm for calculation of L1 splines on 5-point windows. http://www.mdpi.com/1999-4893/3/3/276/ Fri, 30 Jul 2010 00:00:00 CEST Algorithms 2010-07-30 3 3 Article 276 293 1999-4893 Univariate Cubic L1 Interpolating Splines: Analytical Results for Linearity, Convexity and Oscillation on 5-PointWindows 2010-07-30 doi: 10.3390/a3030276 Qingwei Jin John E. Lavery Shu-Cherng Fang http://www.mdpi.com/1999-4893/3/3/265/ 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. http://www.mdpi.com/1999-4893/3/3/265/ Mon, 26 Jul 2010 00:00:00 CEST Algorithms 2010-07-26 3 3 Article 265 275 1999-4893 Computation of the Metric Average of 2D Sets with Piecewise Linear Boundaries 2010-07-26 doi: 10.3390/a3030265 Shay Kels Nira Dyn Evgeny Lipovetsky http://www.mdpi.com/1999-4893/3/3/224/ 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 n0.5. http://www.mdpi.com/1999-4893/3/3/224/ Mon, 12 Jul 2010 00:00:00 CEST Algorithms 2010-07-12 3 3 Article 224 243 1999-4893 Segment LLL Reduction of Lattice Bases Using Modular Arithmetic 2010-07-12 doi: 10.3390/a3030224 Mehrotra Li http://www.mdpi.com/1999-4893/3/3/216/ 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. http://www.mdpi.com/1999-4893/3/3/216/ Thu, 01 Jul 2010 00:00:00 CEST Algorithms 2010-07-01 3 3 Article 216 223 1999-4893 Algorithmic Solution of Stochastic Differential Equations 2010-07-01 doi: 10.3390/a3030216 Schurz http://www.mdpi.com/1999-4893/3/2/197/ This paper is a review which presents and explains the decomposition of graphs by clique minimal separators. The pace is leisurely, we give many examples and figures. Easy algorithms are provided to implement this decomposition. The historical and theoretical background is given, as well as sketches of proofs of the structural results involved. http://www.mdpi.com/1999-4893/3/2/197/ Fri, 14 May 2010 00:00:00 CEST Algorithms 2010-05-14 3 2 Review 197 215 1999-4893 An Introduction to Clique Minimal Separator Decomposition 2010-05-14 doi: 10.3390/a3020197 Berry Pogorelcnik Simonet