Broadcastings and digit tilings on three-dimensional torus networks

AbstractA tiling in a finite abelian group H is a pair (T,L) of subsets of H such that any h∈H can be uniquely represented as t+l where t∈T and l∈L. This paper studies a finite analogue of self-affine tilings in Euclidean spaces and applies it to a problem of broadcasting on circuit switched networks. We extend the tiling argument of Peters and Syska [Joseph G. Peters, Michel Syska, Circuit switched broadcasting in torus networks, IEEE Trans. Parallel Distrib. Syst., 7 (1996) 246–255] to 3-dimensional torus networks

Broadcasting in Hypercubes under Circuit Switched Model

International audienceIn this paper, we propose a method which enables to construct almost optimal broadcast schemes on an n-dimensional hypercube in the circuit switched,-port model. In this model, an initiator must inform all the nodes of the network in a sequence of rounds. During a round, vertices communicate along arc-disjoint dipaths. Our construction is based on particular sequences of nested binary codes having the property that each code can inform the next one in a single round. This last property is insured by a ow technique and results about symmetric ow networks. We apply the method to design optimal schemes improving and generalizing the previous results

Line broadcasting in cycles

AbstractBroadcasting is the process of transmitting information from an originating node (processor) in a network to all other nodes in the network. A local broadcast scheme only allows a node to send information along single communication links to adjacent nodes, while a line broadcast scheme allows nodes to use paths of several communication links to call distant nodes. The minimum time possible for broadcasting in a network of n nodes when no node is involved in more than one communication at any given time is ⌊ log n⌋ phases. Local broadcasting is not sufficient, in general, for broadcasting to be completed in minimum time; line broadcasting is always sufficient. An optimal line broadcast is a minimum-time broadcast that uses the smallest possible total number of communication links. In this paper, we give a complete characterization of optimal line broadcasting in cycles, and we develop efficient methods for constructing optimal line broadcast schemes

Circuit-Switched Gossiping in the 3-Dimensional Torus Networks

In this paper we describe, in the case of short messages, an efficient gossiping algorithm for 3-dimensional torus networks (wrap-around or toroidal meshes) that uses synchronous circuit-switched routing. The algorithm is based on a recursive decomposition of a torus. The algorithm requires an optimal number of rounds and a quasi-optimal number of intermediate switch settings to gossip in an $7^i \times 7^i \times 7^i$ torus

Symmetric flows and broadcasting in hypercubes

International audienceIn this paper, we propose a method which enables to construct almost optimal broadcast schemes on an n-dimensional hypercube in the circuit switched,-port model. In this model, an initiator must inform all the nodes of the network in a sequence of rounds. During a round, vertices communicate along arc-disjoint dipaths. Our construction is based on particular sequences of nested binary codes having the property that each code can inform the next one in a single round. This last property is insured by a ow technique and results about symmetric ow networks. We apply the method to design optimal schemes improving and generalizing the previous results

Model-driven approach for supporting the mapping of parallel algorithms to parallel computing platforms

The trend from single processor to parallel computer architectures has increased the importance of parallel computing. To support parallel computing it is important to map parallel algorithms to a computing platform that consists of multiple parallel processing nodes. In general different alternative mappings can be defined that perform differently with respect to the quality requirements for power consumption, efficiency and memory usage. The mapping process can be carried out manually for platforms with a limited number of processing nodes. However, for exascale computing in which hundreds of thousands of processing nodes are applied, the mapping process soon becomes intractable. To assist the parallel computing engineer we provide a model-driven approach to analyze, model, and select feasible mappings. We describe the developed toolset that implements the corresponding approach together with the required metamodels and model transformations. We illustrate our approach for the well-known complete exchange algorithm in parallel computing. © 2013 Springer-Verlag

Una contribució al càlcul de valors i vectors propis i a l'anàlisi de l'escalabilitat

El càlcul de valors i vectors propis és un nucli computacional que forma part de diverses aplicacions de tipus científic i tècnic que requereixen una potència de càlcul molt gran. Aquestes aplicacions no poden resoldre's en sistemes monoprocessadors perquè aquests sistemes no proporcionen la potència de càlcul suficient per resoldre el problema amb un temps raonable. Una solució possible a aquest problema és la utilització de sistemes paral·lels.El contingut d'aquest treball pot dividir-se en quatre parts ben diferenciades; en les tres primeres parts dels valors i vectors propis en sistemes multicomputadors amb diferents topologies: hipercub, malla i torus; en l'última part del treball es proposa una metodologia d'anàlisis de l'escalabilitat de sistemes paral·lels.- En la primera part del treball es proposen un conjunt d'algorismes paral·lels per hipercubs: BR segmentat, alfa-optimal i Grau-4. Tots aquests algorismes es basen en l'algorisme Block Recursive proposat a [42]. Els nous algorismes proposats tenen la capacitat d'utilitzar de forma més eficient el potencial paral·lelisme de comunicacions que ofereix una arquitectura multiple-port amb els que s'aconsegueix una reducció del cost de la comunicació considerable respecte al cost de comunicació de l'algorisme original.- En la segona part del treball es proposa un nou algorisme amb una topologia de comunicació en malla bidimensional (2D). Aquest algorimse l'hem anomenat algorisme 2D. Es veurà que aquest nou algorisme aconsegueix reduir el cost total considerablement respecte als algorismes que han estat proposats per altres autors per malles i torus.- En la tercera part, s'estudia l'eficiència de l'algorisme BR-segmentat (algorisme amb una topologia de comunicació en hipercub proposat en la primera part de la tesi) un cop mapejat en un multicomputador amb una topologia en malla o en torus. A l'hora de realitzar el mapeig s'ha aplicat i ampliat una metodologia desenvolupada en el grup de treball que ens permet realitzar el mapeig de forma eficient i sistemàtic d'una topologia en hipercub a una topologia en malla o torus. El cost de la comunicació del nou algorisme es compara amb el cost de l'algorisme 2D proposat en la segona part del treball.- Finalment, en l'última part d'aquest treball es proposa una metodologia d'anàlisi de l'escalabilitat de sistemes paral·lels orientada a l'usuari final del sistema. S'utilitza l'algorisme 2D mapejat en una línia per mostrar un exemple d'aplicació de la metodologia