Balancing Minimum Spanning and Shortest Path Trees

This paper give a simple linear-time algorithm that, given a weighted digraph, finds a spanning tree that simultaneously approximates a shortest-path tree and a minimum spanning tree. The algorithm provides a continuous trade-off: given the two trees and epsilon > 0, the algorithm returns a spanning tree in which the distance between any vertex and the root of the shortest-path tree is at most 1+epsilon times the shortest-path distance, and yet the total weight of the tree is at most 1+2/epsilon times the weight of a minimum spanning tree. This is the best tradeoff possible. The paper also describes a fast parallel implementation.Comment: conference version: ACM-SIAM Symposium on Discrete Algorithms (1993

Fast and Compact Distributed Verification and Self-Stabilization of a DFS Tree

We present algorithms for distributed verification and silent-stabilization of a DFS(Depth First Search) spanning tree of a connected network. Computing and maintaining such a DFS tree is an important task, e.g., for constructing efficient routing schemes. Our algorithm improves upon previous work in various ways. Comparable previous work has space and time complexities of $O(n\log \Delta)$ bits per node and $O(nD)$ respectively, where $\Delta$ is the highest degree of a node, $n$ is the number of nodes and $D$ is the diameter of the network. In contrast, our algorithm has a space complexity of $O(\log n)$ bits per node, which is optimal for silent-stabilizing spanning trees and runs in $O(n)$ time. In addition, our solution is modular since it utilizes the distributed verification algorithm as an independent subtask of the overall solution. It is possible to use the verification algorithm as a stand alone task or as a subtask in another algorithm. To demonstrate the simplicity of constructing efficient DFS algorithms using the modular approach, We also present a (non-sielnt) self-stabilizing DFS token circulation algorithm for general networks based on our silent-stabilizing DFS tree. The complexities of this token circulation algorithm are comparable to the known ones

Developmental changes associated with cross-language similarity in bilingual children

Online publication 30/9/2015The main goal of the present study was to investigate how the degree of orthographic overlap between translation equivalents influences bilingual word recognition processes at different stages of reading development. Spanish–Basque bilingual children with ages ranging from 8 to 15 years were tested in an explicit translation recognition task with a large set of items. Critically, the degree of cross-language similarity (i.e. the cognate status) between the references and the correct targets was manipulated along a continuum in order to investigate how the reliance on crosslanguage orthographic overlap varies as a function of reading experience. Results showed that younger children were significantly more sensitive to the cognate status of words than older children while recognising translation equivalents, and that this difference did not depend on the speed of response of the participants. These results demonstrate that the influence of cross-language similarity progressively diminishes as a function of increased exposure to print together with the maturation of the mechanisms responsible for language interference suppression, as suggested by developmental models of bilingual lexical access.This research has been partially funded by the Spanish Government [grant number PSI2012-32123], the European Research Council [grant number ERC-AdG-295362], and by the AThEME project funded by the European Union [grant number 613465]

SU(5) D-brane realizations, Yukawa couplings and proton stability

We discuss SU(5) Grand Unified Theories in the context of orientifold compactifications. Specifically, we investigate two and three D-brane stack realizations of the Georgi-Glashow and the flipped SU(5) model and analyze them with respect to their Yukawa couplings. As pointed out in arXiv:0909.0271 the most economical Georgi-Glashow realization based on two stacks generically suffers from a disastrous large proton decay rate. We show that allowing for an additional U(1) D-brane stack this as well as other phenomenological problems can be resolved. We exemplify with globally consistent Georgi-Glashow models based on RCFT that these D-brane quivers can be indeed embedded in a global setting. These globally consistent realizations admit rigid O(1) instantons inducing the perturbatively missing coupling 10105^H. Finally we show that flipped SU(5) D-brane realizations even with multiple U(1) D-brane stacks are plagued by severe phenomenological drawbacks which generically cannot be overcome.Comment: 34 pages v2 minor correction

Separating Hierarchical and General Hub Labelings

In the context of distance oracles, a labeling algorithm computes vertex labels during preprocessing. An $s,t$ query computes the corresponding distance from the labels of $s$ and $t$ only, without looking at the input graph. Hub labels is a class of labels that has been extensively studied. Performance of the hub label query depends on the label size. Hierarchical labels are a natural special kind of hub labels. These labels are related to other problems and can be computed more efficiently. This brings up a natural question of the quality of hierarchical labels. We show that there is a gap: optimal hierarchical labels can be polynomially bigger than the general hub labels. To prove this result, we give tight upper and lower bounds on the size of hierarchical and general labels for hypercubes.Comment: 11 pages, minor corrections, MFCS 201

Particle models from orientifolds at Gepner-orbifold points

We consider configurations of stacks of orientifold planes and D-branes wrapped on a non trivial internal space of the structure {(Gepner model)^{c=3n} x T^{2(3-n)}}/Z_N, for n=1,2,3. By performing simple moddings by discrete symmetries of Gepner models at orienti fold points, consistent with a Z_N orbifold action, we show that projection on D-brane configurations can be achieved, generically leading to chiral gauge theories. Either supersymmetric or non-supersymmetric (tachyon free) models can be obtained. We illustrate the procedure through some explicit examples.Comment: 36 pages, no figures Corrected sign of eq. 6.26 references added, minor correction

Применение генетического алгоритма в задачах адаптации структур данных

Представлена разработанная схема адаптации структур данных в оперативной памяти. Для поиска адаптированной структуры данных предложено применение генетического алгоритма. Определены его особенности. Для растровых изображений с соответствующими заголовками выполнены экспериментальные исследования временной эффективности адаптированных структур данных, времени сходимости генетического алгоритма и условия целесообразности применения адаптации.Представлена розроблена схема адаптації структур даних в оперативній пам’яті. Для пошуку адаптованої структури даних запропоновано застосування генетичного алгоритму. Визначені його особливості. Для растрових зображень з відповідними заголовками виконані експериментальні дослідження часової ефективності адаптованих структур даних, часу збіжності генетичного алгоритму та умови доцільності застосування адаптації.The developed scheme of data structures adaptation in memory is given. To search for an adapted data structure, genetic algorithm is proposed and its characteristics are defined. For raster images with the appropriate headings, experimental studies of the time efficiency of adapted data structures, the convergence time of the genetic algorithm and conditions for feasibility of adapting are performed