Computing the Fréchet Distance with a Retractable Leash

All known algorithms for the Fréchet distance between curves proceed in two steps: first, they construct an efficient oracle for the decision version; second, they use this oracle to find the optimum from a finite set of critical values. We present a novel approach that avoids the detour through the decision version. This gives the first quadratic time algorithm for the Fréchet distance between polygonal curves in (Formula presented.) under polyhedral distance functions (e.g., (Formula presented.) and (Formula presented.)). We also get a (Formula presented.)-approximation of the Fréchet distance under the Euclidean metric, in quadratic time for any fixed (Formula presented.). For the exact Euclidean case, our framework currently yields an algorithm with running time (Formula presented.). However, we conjecture that it may eventually lead to a faster exact algorithm

Mechanistic Insights into Ring-Opening and Decarboxylation of 2-Pyrones in Liquid Water and Tetrahydrofuran

2-Pyrones, such as triacetic acid lactone, are a promising class of biorenewable platform chemicals that provide access to an array of chemical products and intermediates. We illustrate through the combination of results from experimental studies and first-principle density functional theory calculations that key structural features dictate the mechanisms underlying ring-opening and decarboxylation of 2-pyrones, including the degree of ring saturation, the presence of C═C bonds at the C4═C5 or C5═C6 positions within the ring, as well as the presence of a β-keto group at the C4 position. Our results demonstrate that 2-pyrones undergo a range of reactions unique to their structure, such as retro-Diels–Alder reactions and nucleophilic addition of water. In addition, the reactivity of 2-pyrones and the final products formed is shown to depend on the solvent used and the acidity of the reaction environment. The mechanistic insights obtained here provide guidance for the selective conversion of 2-pyrones to targeted chemicals.Reprinted (adapted) with permission from Journal of American Chemical Society, 135(15); 5699-5708. Doi: 10.1021/ja312075r. Copyright 2013 American Chemical Society. </p

Reprint of : Memory-constrained algorithms for simple polygons

A constant-work-space algorithm has read-only access to an input array and may use only O(1) additional words of bits, where n is the input size. We show how to triangulate a plane straight-line graph with n vertices in O(n2) time and constant work-space. We also consider the problem of preprocessing a simple polygon P for shortest path queries, where P is given by the ordered sequence of its n vertices. For this, we relax the space constraint to allow s words of work-space. After quadratic preprocessing, the shortest path between any two points inside P can be found in O(n2/s) time. Keywords: Space–time trade-off; Constant workspace; Triangulation; Shortest path; Simple polygon Tetsuo Asano, Kevin Buchin, Maike Buchin, Matias Korman, Wolfgang Mulzer, Günter Rote, André Schulz Memory-constrained algorithms for simple polygons Computational Geometry, Volume 46, Issue 8, October 2013, Pages 959-969 http://dx.doi.org/10.1016/j.comgeo.2013.04.00

НЕОДНОРОДНОСТЬ ХИМИЧЕСКОГО СОСТАВА МЕЖЗВЕЗДНОЙ СРЕДЫ ПО ДАННЫМ HDE 226868 (Cyg X-1) И α Cam // Ученые записки КФУ. Физико-математические науки 2011 N2

Методом моделирования синтетического спектра с учетом не-ЛТР-эффектов определены химические составы атмосфер О-сверхгигантов HDE 226868 (оптический компонент Cyg X-1) и α Cam, имеющих близкие физические характеристики, но расположенных на расстоянии 2.5-2.7 кпк друг от друга. Среднее содержание элементов группы CNO, а также Al, S и Zn в HDE 226868 на 0.15-0.30 dex превосходит содержание этих элементов в α Cam. Установленное различие содержаний находится в качественном соответствии с распределением тяжелых элементов в диске Галактики, полученным в работе Лака и др. в результате исследования 50 галактических цефеид. Данный факт является подтверждением неоднородности распределения тяжелых элементов на масштабе порядка 2 кпк и соответствует представлениям о сохранении индивидуальных характеристик <<сверхоблаков>> в межзвездной среде на шкале времени более одного миллиарда лет

Interference minimization in asymmetric sensor networks

A fundamental problem in wireless sensor networks is to connect a given set of sensors while minimizing the receiver interference. This is modeled as follows: each sensor node corresponds to a point in R^d and each transmission range corresponds to a ball. The receiver interference of a sensor node is defined as the number of transmission ranges it lies in. Our goal is to choose transmission radii that minimize the maximum interference while maintaining a strongly connected asymmetric communication graph. For the two-dimensional case, we show that it is NP-complete to decide whether one can achieve a receiver interference of at most 5 . In the one-dimensional case, we prove that there are optimal solutions with nontrivial structural properties. These properties can be exploited to obtain an exact algorithm that runs in quasi-polynomial time. This generalizes a result by Tan et al. to the asymmetric case