Selection, Routing and Sorting on the Star Graph

We consider the problems of selection, routing and sorting on an n-star graph (with n! nodes), an interconnection network which has been proven to possess many special properties. We identify a tree like subgraph (which we call as a \u27(k, l, k) chain network\u27) of the star graph which enables us to design efficient algorithms for the above mentioned problems. We present an algorithm that performs a sequence of n prefix computations in O(n2) time. This algorithm is used as a subroutine in our other algorithms. In addition we offer an efficient deterministic sorting algorithm that runs in O(n3lg n) steps. Though an algorithm with the same time bound has been proposed before, our algorithm is very simple and is based on a different approach. We also show that sorting can be performed on the n star graph in time O(n3) and that selection of a set of uniformly distributed n keys can be performed in O(n2) time with high probability. Finally, we also present a deterministic (non oblivious) routing algorithm that realizes any permutation in O(n3) steps on the n-star graph. There exists an algorithm in the literature that can perform a single prefix computation in O(n lg n) time. The best known previous algorithm for sorting has a run time of O(n3 lg n) and is deterministic. To our knowledge, the problem of selection has not been considered before on the star graph

Online Permutation Routing in Partitioned Optical Passive Star Networks

This paper establishes the state of the art in both deterministic and randomized online permutation routing in the POPS network. Indeed, we show that any permutation can be routed online on a POPS network either with $O(\frac{d}{g}\log g)$ deterministic slots, or, with high probability, with $5c\lceil d/g\rceil+o(d/g)+O(\log\log g)$ randomized slots, where constant $c=\exp (1+e^{-1})\approx 3.927$. When $d=\Theta(g)$, that we claim to be the "interesting" case, the randomized algorithm is exponentially faster than any other algorithm in the literature, both deterministic and randomized ones. This is true in practice as well. Indeed, experiments show that it outperforms its rivals even starting from as small a network as a POPS(2,2), and the gap grows exponentially with the size of the network. We can also show that, under proper hypothesis, no deterministic algorithm can asymptotically match its performance

Distributed Data Summarization in Well-Connected Networks

We study distributed algorithms for some fundamental problems in data summarization. Given a communication graph G of n nodes each of which may hold a value initially, we focus on computing sum_{i=1}^N g(f_i), where f_i is the number of occurrences of value i and g is some fixed function. This includes important statistics such as the number of distinct elements, frequency moments, and the empirical entropy of the data. In the CONGEST~ model, a simple adaptation from streaming lower bounds shows that it requires Omega~(D+ n) rounds, where D is the diameter of the graph, to compute some of these statistics exactly. However, these lower bounds do not hold for graphs that are well-connected. We give an algorithm that computes sum_{i=1}^{N} g(f_i) exactly in {tau_{G}} * 2^{O(sqrt{log n})} rounds where {tau_{G}} is the mixing time of G. This also has applications in computing the top k most frequent elements. We demonstrate that there is a high similarity between the GOSSIP~ model and the CONGEST~ model in well-connected graphs. In particular, we show that each round of the GOSSIP~ model can be simulated almost perfectly in O~({tau_{G}}) rounds of the CONGEST~ model. To this end, we develop a new algorithm for the GOSSIP~ model that 1 +/- epsilon approximates the p-th frequency moment F_p = sum_{i=1}^N f_i^p in O~(epsilon^{-2} n^{1-k/p}) roundsfor p >= 2, when the number of distinct elements F_0 is at most O(n^{1/(k-1)}). This result can be translated back to the CONGEST~ model with a factor O~({tau_{G}}) blow-up in the number of rounds

Path Planning in Multi-AGVs Using a Modified A-star Algorithm

The problem of path planning is a hot and exclusive research topic on multiple Automatic Guided Vehicles (multi-AGVs) systems. Many research results have been reported, but outrightly solving path planning problem from the perspective of reducing traffic congestion have faced obstacles. A collision-free path planning procedure based on a modified A-star Algorithm for multi-AGVs logistics sorting system is proposed in this paper. AGVs are now a poplar way to handle materials in latest smart warehouses. Many researches have been conducted and new technologies are still being developed. There is wide scale research on algorithms to help in scheduling, routing and path planning. Multi-AGVs are used to load goods automatically in a packaging factory. To ensure an effective and safe collision free path planning, this work investigates movement, scheduling and routing, speed manipulation and efficiency of machinery to target positions. The A-star algorithm with grid method to map out a typical warehouse scenario into multiple nodes was used. To have the shortest possible path, for obstacle avoidance, we employed the Braitenberg model. The waiting strategy is used for conflict resolution at intersections

Graph coloring techniques for planning dynamic optical networks

Dynamic optical networks will be crucial in global optical communications in the next 5-10 years.On-demand services, fuelled by applications such as cloud computing and grid computing, are the main drivers for the availability of an increasingly dynamic network infrastructure. Efficient network planning tools that deal with Routing and Wavelength Assignment problems are of paramount relevance in this dynamics cenario. In this work, a simulator for planning dynamic optical networks was developed, and several real networks were tested, such as National Science Foundation Network, British Telecom, US Backbone Network, and also bidirectional ring networks. In this simulator, we have implemented a graph coloring wavelength assignment algorithm named Small-Bucket algorithm that allows recoloring to occur. A comparison performance with the First-fit algorithm is performed in terms of the blocking probability, number of recolorings, number of colors used and simulation time. It is concluded that the Small-Bucket algorithm originate slower blocking probabilities than the ones obtained with the First-fit algorithm. However, to reach these low blocking probabilities, the Small-Bucket algorithm makes use of a larger number of wavelengths and recolorings.As redes ópticas dinâmicas serão cruciais nas comunicações ópticas globais nos proximos 5-10 anos. Os principais impulsionadores deste dinamismo são os serviços on-demand, suportados por aplicações como computação em nuvem e computação em grelha, conduzindo à necessidade de uma infraestrutura de rede cada vez mais dinâmica. Ferramentas de planeamento de rede eficientes, que lidam com os problemas de encaminhamento e atribuição de comprimentos de onda serão de extrema relevância neste cenário dinâmico. Neste trabalho foi desenvolvido um simulador para o planeamento de redes ópticas dinâmicas, e várias redes reais foram testadas, como a National Science Foundation Network, a British Telecom, a US Backbone Network e também redes bidirecionais em anel. Neste simulador, implementa-se um algoritmo de coloração de grafos denominado algoritmo Small-Bucket, que permite a ocorrência de recolorações de nós. Este algoritmo é comparado como algoritmo First-fit, em termos de probabilidade de bloqueio, número de recolorações, número de cores usadas e tempo de simulação. Conclui-se que o algoritmo Small-Bucket produz menores probabilidades de bloqueio do que as obtidas com o algoritmo First-fit. No entanto, para atingir essas baixas probabilidades de bloqueio, o algoritmo Small-Bucket faz uso de um maior número de comprimentos de onda e recolorações

A Concept for an STJ-based Spectrograph

We describe a multi-order spectrograph concept suitable for 8m-class telescopes, using the intrinsic spectral resolution of Superconducting Tunneling Junction detectors to sort the spectral orders. The spectrograph works at low orders, 1-5 or 1-6, and provides spectral coverage with a resolving power of R~8000 from the atmospheric cutoff at 320 nm to the long wavelength end of the infrared H or K band at 1800 nm or 2400 nm. We calculate that the spectrograph would provide substantial throughput and wavelength coverage, together with high time resolution and sufficient dynamic range. The concept uses currently available technology, or technologies with short development horizons, restricting the spatial sampling to two linear arrays; however an upgrade path to provide more spatial sampling is identified. All of the other challenging aspects of the concept - the cryogenics, thermal baffling and magnetic field biasing - are identified as being feasible.Comment: Accepted in Monthly Notices of the Royal Astronomical Society, 12 pages with 10 figure

Distributed Computing on Core-Periphery Networks: Axiom-based Design

Inspired by social networks and complex systems, we propose a core-periphery network architecture that supports fast computation for many distributed algorithms and is robust and efficient in number of links. Rather than providing a concrete network model, we take an axiom-based design approach. We provide three intuitive (and independent) algorithmic axioms and prove that any network that satisfies all axioms enjoys an efficient algorithm for a range of tasks (e.g., MST, sparse matrix multiplication, etc.). We also show the minimality of our axiom set: for networks that satisfy any subset of the axioms, the same efficiency cannot be guaranteed for any deterministic algorithm