Properties and Algorithms of the KCube Graphs

The KCube interconnection topology was rst introduced in 2010. The KCube graph is a compound graph of a Kautz digraph and hypercubes. Compared with the at- tractive Kautz digraph and well known hypercube graph, the KCube graph could accommodate as many nodes as possible for a given indegree (and outdegree) and the diameter of interconnection networks. However, there are few algorithms designed for the KCube graph. In this thesis, we will concentrate on nding graph theoretical properties of the KCube graph and designing parallel algorithms that run on this network. We will explore several topological properties, such as bipartiteness, Hamiltonianicity, and symmetry property. These properties for the KCube graph are very useful to develop efficient algorithms on this network. We will then study the KCube network from the algorithmic point of view, and will give an improved routing algorithm. In addition, we will present two optimal broadcasting algorithms. They are fundamental algorithms to many applications. A literature review of the state of the art network designs in relation to the KCube network as well as some open problems in this field will also be given.

Properties and Algorithms of the KCube Interconnection Networks

The KCube interconnection network was first introduced in 2010 in order to exploit the good characteristics of two well-known interconnection networks, the hypercube and the Kautz graph. KCube links up multiple processors in a communication network with high density for a fixed degree. Since the KCube network is newly proposed, much study is required to demonstrate its potential properties and algorithms that can be designed to solve parallel computation problems. In this thesis we introduce a new methodology to construct the KCube graph. Also, with regard to this new approach, we will prove its Hamiltonicity in the general KC(m; k). Moreover, we will find its connectivity followed by an optimal broadcasting scheme in which a source node containing a message is to communicate it with all other processors. In addition to KCube networks, we have studied a version of the routing problem in the traditional hypercube, investigating this problem: whether there exists a shortest path in a Qn between two nodes 0n and 1n, when the network is experiencing failed components. We first conditionally discuss this problem when there is a constraint on the number of faulty nodes, and subsequently introduce an algorithm to tackle the problem without restrictions on the number of nodes.

Properties and algorithms of the (n, k)-star graphs

The (n, k)-star interconnection network was proposed in 1995 as an attractive alternative to the n-star topology in parallel computation. The (n, k )-star has significant advantages over the n-star which itself was proposed as an attractive alternative to the popular hypercube. The major advantage of the (n, k )-star network is its scalability, which makes it more flexible than the n-star as an interconnection network. In this thesis, we will focus on finding graph theoretical properties of the (n, k )-star as well as developing parallel algorithms that run on this network. The basic topological properties of the (n, k )-star are first studied. These are useful since they can be used to develop efficient algorithms on this network. We then study the (n, k )-star network from algorithmic point of view. Specifically, we will investigate both fundamental and application algorithms for basic communication, prefix computation, and sorting, etc. A literature review of the state-of-the-art in relation to the (n, k )-star network as well as some open problems in this area are also provided.

Properties and algorithms of the (n, k)-arrangement graphs

The (n, k)-arrangement interconnection topology was first introduced in 1992. The (n, k )-arrangement graph is a class of generalized star graphs. Compared with the well known n-star, the (n, k )-arrangement graph is more flexible in degree and diameter. However, there are few algorithms designed for the (n, k)-arrangement graph up to present. In this thesis, we will focus on finding graph theoretical properties of the (n, k)- arrangement graph and developing parallel algorithms that run on this network. The topological properties of the arrangement graph are first studied. They include the cyclic properties. We then study the problems of communication: broadcasting and routing. Embedding problems are also studied later on. These are very useful to develop efficient algorithms on this network. We then study the (n, k )-arrangement network from the algorithmic point of view. Specifically, we will investigate both fundamental and application algorithms such as prefix sums computation, sorting, merging and basic geometry computation: finding convex hull on the (n, k )-arrangement graph. A literature review of the state-of-the-art in relation to the (n, k)-arrangement network is also provided, as well as some open problems in this area.

Properties and algorithms of the hyper-star graph and its related graphs

The hyper-star interconnection network was proposed in 2002 to overcome the drawbacks of the hypercube and its variations concerning the network cost, which is defined by the product of the degree and the diameter. Some properties of the graph such as connectivity, symmetry properties, embedding properties have been studied by other researchers, routing and broadcasting algorithms have also been designed. This thesis studies the hyper-star graph from both the topological and algorithmic point of view. For the topological properties, we try to establish relationships between hyper-star graphs with other known graphs. We also give a formal equation for the surface area of the graph. Another topological property we are interested in is the Hamiltonicity problem of this graph. For the algorithms, we design an all-port broadcasting algorithm and a single-port neighbourhood broadcasting algorithm for the regular form of the hyper-star graphs. These algorithms are both optimal time-wise. Furthermore, we prove that the folded hyper-star, a variation of the hyper-star, to be maixmally fault-tolerant.

Asymmetric Ramsey Properties of Random Graphs Involving Cliques

Consider the following problem: Forgiven graphs G and F(1),..., F(k), find a coloring of the edges of G with k colors such that G does not contain F; in color i. Rodl and Rucinski studied this problem for the random graph G,,, in the symmetric case when k is fixed and F(1) = ... = F(k) = F. They proved that such a coloring exists asymptotically almost surely (a.a.s.) provided that p <= bn(-beta) for some constants b = b(F,k) and beta = beta(F). This result is essentially best possible because for p >= Bn(-beta), where B = B(F, k) is a large constant, such an edge-coloring does not exist. Kohayakawa and Kreuter conjectured a threshold function n(-beta(F1,..., Fk)) for arbitrary F(1), ..., F(k). In this article we address the case when F(1),..., F(k) are cliques of different sizes and propose an algorithm that a.a.s. finds a valid k-edge-coloring of G(n,p) with p <= bn(-beta) for some constant b = b(F(1),..., F(k)), where beta = beta(F(1),..., F(k)) as conjectured. With a few exceptions, this algorithm also works in the general symmetric case. We also show that there exists a constant B = B(F,,..., Fk) such that for p >= Bn(-beta) the random graph G(n,p) a.a.s. does not have a valid k-edge-coloring provided the so-called KLR-conjecture holds. (C) 2008 Wiley Periodicals, Inc. Random Struct. Alg., 34, 419-453, 2009

The CoastColour Round Robin datasets: a database to evaluate the performance of algorithms for the retrieval of water quality parameters in coastal waters

The CoastColour project Round Robin (CCRR) project (http://www.coastcolour.org) funded by the European Space Agency (ESA) was designed to bring together a variety of reference datasets and to use these to test algorithms and assess their accuracy for retrieving water quality parameters. This information was then developed to help end-users of remote sensing products to select the most accurate algorithms for their coastal region. To facilitate this, an inter-comparison of the performance of algorithms for the retrieval of in-water properties over coastal waters was carried out. The comparison used three types of datasets on which ocean colour algorithms were tested. The description and comparison of the three datasets are the focus of this paper, and include the Medium Resolution Imaging Spectrometer (MERIS) Level 2 match-ups, in situ reflectance measurements and data generated by a radiative transfer model (HydroLight). The datasets mainly consisted of 6,484 marine reflectance associated with various geometrical (sensor viewing and solar angles) and sky conditions and water constituents: Total Suspended Matter (TSM) and Chlorophyll-a (CHL) concentrations, and the absorption of Coloured Dissolved Organic Matter (CDOM). Inherent optical properties were also provided in the simulated datasets (5,000 simulations) and from 3,054 match-up locations. The distributions of reflectance at selected MERIS bands and band ratios, CHL and TSM as a function of reflectance, from the three datasets are compared. Match-up and in situ sites where deviations occur are identified. The distribution of the three reflectance datasets are also compared to the simulated and in situ reflectances used previously by the International Ocean Colour Coordinating Group (IOCCG, 2006) for algorithm testing, showing a clear extension of the CCRR data which covers more turbid waters.

The Development of Parallel Resolution Algorithms Using the Graph Representation

The parallel resolution procedures based on graph structures method are presented. OR-, AND- and DCDP- parallel inference on connection graph representation is explored and modifications to these algorithms using heuristic estimation are proposed. The principles for designing these heuristic functions are thoroughly discussed. The colored clause graphs resolution principle is presented. The comparison of efficiency (on the Steamroller problem) is carried out and the results are presented. The parallel unification algorithm used in the parallel inference procedure is briefly outlined in the final part of the paper.

Evaluating the spatial transferability and temporal repeatability of remote-sensing-based lake water quality retrieval algorithms at the European scale: a meta-analysis approach

Many studies have shown the considerable potential for the application of remote-sensing-based methods for deriving estimates of lake water quality. However, the reliable application of these methods across time and space is complicated by the diversity of lake types, sensor configuration, and the multitude of different algorithms proposed. This study tested one operational and 46 empirical algorithms sourced from the peer-reviewed literature that have individually shown potential for estimating lake water quality properties in the form of chlorophyll-a (algal biomass) and Secchi disc depth (SDD) (water transparency) in independent studies. Nearly half (19) of the algorithms were unsuitable for use with the remote-sensing data available for this study. The remaining 28 were assessed using the Terra/Aqua satellite archive to identify the best performing algorithms in terms of accuracy and transferability within the period 2001–2004 in four test lakes, namely Vänern, Vättern, Geneva, and Balaton. These lakes represent the broad continuum of large European lake types, varying in terms of eco-region (latitude/longitude and altitude), morphology, mixing regime, and trophic status. All algorithms were tested for each lake separately and combined to assess the degree of their applicability in ecologically different sites. None of the algorithms assessed in this study exhibited promise when all four lakes were combined into a single data set and most algorithms performed poorly even for specific lake types. A chlorophyll-a retrieval algorithm originally developed for eutrophic lakes showed the most promising results (R2 = 0.59) in oligotrophic lakes. Two SDD retrieval algorithms, one originally developed for turbid lakes and the other for lakes with various characteristics, exhibited promising results in relatively less turbid lakes (R2 = 0.62 and 0.76, respectively). The results presented here highlight the complexity associated with remotely sensed lake water quality estimates and the high degree of uncertainty due to various limitations, including the lake water optical properties and the choice of methods.

Biased Random-key Genetic Algorithms For The Winner Determination Problem In Combinatorial Auctions.

Abstract In this paper, we address the problem of picking a subset of bids in a general combinatorial auction so as to maximize the overall profit using the first-price model. This winner determination problem assumes that a single bidding round is held to determine both the winners and prices to be paid. We introduce six variants of biased random-key genetic algorithms for this problem. Three of them use a novel initialization technique that makes use of solutions of intermediate linear programming relaxations of an exact mixed integer-linear programming model as initial chromosomes of the population. An experimental evaluation compares the effectiveness of the proposed algorithms with the standard mixed linear integer programming formulation, a specialized exact algorithm, and the best-performing heuristics proposed for this problem. The proposed algorithms are competitive and offer strong results, mainly for large-scale auctions.

Assignment of the absolute configuration at the sulfur atom of thioridazine metabolites by the analysis of their chiroptical properties: The case of thioridazine 2-sulfoxide

Thioridazine (THD) is a commonly prescribed phenotiazine neuroleptic drug, which is extensively biotransformed in the organism producing as main metabolites sulfoxides and a sulfone by sulfur oxidation Significant differences have been observed in the activity of the THD enantiomers as well as for its main metabolites, and enantioselectivity phenomena have been proved in the metabolic pathway. Here the assignment of the absolute configuration at the sulfur atom of enantiomeric THD-2-sulfoxide (THD-2-SO) has been carried out by circular dichroism (CD) spectroscopy The stereoisomers were separated by HPLC on Chiralpak AS column, recording the CD spectra for the two collected enantiomeric fractions The theoretical electronic CD spectrum has been obtained by the TDDFT/B3LYP/6-31G*. as Boltzmann averaging of the contributions calculated for the most stable conformations of the drug The comparison of the simulated and experimental spectra allowed the absolute configuration at the sulfur atom of the four THD-2-SO stereoisomers to be assigned The developed method should be useful for a reliable correlation between stereochemistry and activity and/or toxicity

Robust parameter settings of evolutionary algorithms for the optimisation of agricultural systems models

Numerical optimisation methods are being more commonly applied to agricultural systems models, to identify the most profitable management strategies. The available optimisation algorithms are reviewed and compared, with literature and our studies identifying evolutionary algorithms (including genetic algorithms) as superior in this regard to simulated annealing, tabu search, hill-climbing, and direct-search methods. Results of a complex beef property optimisation, using a real-value genetic algorithm, are presented. The relative contributions of the range of operational options and parameters of this method are discussed, and general recommendations listed to assist practitioners applying evolutionary algorithms to the solution of agricultural systems. (C) 2001 Elsevier Science Ltd. All rights reserved.

Using siting algorithms in the design of marine reserve networks

Using benthic habitat data from the Florida Keys (USA), we demonstrate how siting algorithms can help identify potential networks of marine reserves that comprehensively represent target habitat types. We applied a flexible optimization tool-simulated annealing-to represent a fixed proportion of different marine habitat types within a geographic area. We investigated the relative influence of spatial information, planning-unit size, detail of habitat classification, and magnitude of the overall conservation goal on the resulting network scenarios. With this method, we were able to identify many adequate reserve systems that met the conservation goals, e.g., representing at least 20% of each conservation target (i.e., habitat type) while fulfilling the overall aim of minimizing the system area and perimeter. One of the most useful types of information provided by this siting algorithm comes from an irreplaceability analysis, which is a count of the number of, times unique planning units were included in reserve system scenarios. This analysis indicated that many different combinations of sites produced networks that met the conservation goals. While individual 1-km(2) areas were fairly interchangeable, the irreplaceability analysis highlighted larger areas within the planning region that were chosen consistently to meet the goals incorporated into the algorithm. Additionally, we found that reserve systems designed with a high degree of spatial clustering tended to have considerably less perimeter and larger overall areas in reserve-a configuration that may be preferable particularly for sociopolitical reasons. This exercise illustrates the value of using the simulated annealing algorithm to help site marine reserves: the approach makes efficient use of;available resources, can be used interactively by conservation decision makers, and offers biologically suitable alternative networks from which an effective system of marine reserves can be crafted.

Application of genetic algorithms in the design of an electrical potential of fractional order

Fractional calculus (FC) is currently being applied in many areas of science and technology. In fact, this mathematical concept helps the researches to have a deeper insight about several phenomena that integer order models overlook. Genetic algorithms (GA) are an important tool to solve optimization problems that occur in engineering. This methodology applies the concepts that describe biological evolution to obtain optimal solution in many different applications. In this line of thought, in this work we use the FC and the GA concepts to implement the electrical fractional order potential. The performance of the GA scheme, and the convergence of the resulting approximation, are analyzed. The results are analyzed for different number of charges and several fractional orders.

Application of fractional algorithms in the control of a robotic bird

In this paper, it is studied the dynamics of the robotic bird in terms of time response and robustness. It is analyzed the wing angle of attack and the velocity of the bird, the tail influence, the gliding flight and the flapping flight. The results are positive for the construction of flying robots. The development of computational simulation based on the dynamic of the robotic bird should allow testing strategies and different algorithms of control such as integer and fractional controllers.