General broadcasting algorithms in one-port wormhole routed hypercubes

Wormhole routing has been accepted as an efficient switching mechanism in point-to-point interconnection networks. Here the network resource, i.e. node buffers and communication channels, are effectively utilized to deliver message across the network; We consider the problem of broadcasting a message in the hypercue equipped with the wormhole switching mechanism. The model is a generalization of an earlier work and considers a broadcast path-length of {dollar}m\ (1\leq m\leq n{dollar}) in the n-cube with a single-port communication capability. In this thesis, the scheme of e-cube and a Gray code path routing and intermediate reception capability have been adopted in order to solve the problem of broadcasting in one-port wormhole routed hypercubes. Two methods have been suggested; one is based on utilizing the Gray codes (Gray code path-based routing), while the other is based on the recursive partitioning of the cube (cube-based routing). The number of routing steps in both methods are compared to those in the previous results, as well as to the lower bounds derived based on the path-length m assumption. A cube-based and a path-based algorithm give {dollar}T(R)+(k\sb{c}+1)T(m){dollar} and {dollar}k\sb{G} +T(m){dollar} routing steps, respectively. By comparison with routing steps of both algorithms, the performance of the path-based algorithm shows better than that of the cube-based; The results of this work are significant and can be used for immediate implementation in contemporary machines most of which are equipped with wormhole routing and serial communication capability

On strong fault tolerance (or strong Menger-connectivity) of multicomputer networks

As the size of networks increases continuously, dealing with networks with faulty nodes becomes unavoidable. In this dissertation, we introduce a new measure for network fault tolerance, the strong fault tolerance (or strong Menger-connectivity)in multicomputer networks, and study the strong fault tolerance for popular multicomputer network structures. Let G be a network in which all nodes have degree d. We say that G is strongly fault tolerant if it has the following property: Let Gf be a copy of G with at most d - 2 faulty nodes. Then for any pair of non-faulty nodes u and v in Gf , there are min{degf (u), degf (v)} node-disjoint paths in Gf from u to v, where degf (u) and degf (v) are the degrees of the nodes u and v in Gf, respectively. First we study the strong fault tolerance for the popular network structures such as star networks and hypercube networks. We show that the star networks and the hypercube networks are strongly fault tolerant and develop efficient algorithms that construct the maximum number of node-disjoint paths of nearly optimal or optimal length in these networks when they contain faulty nodes. Our algorithms are optimal in terms of their time complexity. In addition to studying the strong fault tolerance, we also investigate a more realistic concept to describe the ability of networks for tolerating faults. The traditional definition of fault tolerance, sustaining at most d - 1faulty nodes for a regular graph G of degree d, reflects a very rare situation. In many cases, there is a chance that a routing path between two given nodes can be constructed though the network may have more faulty nodes than its degree. In this dissertation, we study the fault tolerance of hypercube networks under a probability model. When each node of the n-dimensional hypercube network has an independent failure probability p, we develop algorithms that, with very high probability, can construct a fault-free path when the hypercube network can sustain up to 2np faulty nodes

Interconnection Networks Based on Gaussian and Eisenstein-Jacobi Integers

Quotient rings of Gaussian and Eisenstein-Jacobi(EJ) integers can be deployed to construct interconnection networks with good topological properties. In this thesis, we propose deadlock-free deterministic and partially adaptive routing algo­rithms for hexagonal networks, one special class of EJ networks. Then we discuss higher dimensional Gaussian networks as an alternative to classical multidimen­sional toroidal networks. For this topology, we explore many properties including distance distribution and the decomposition of higher dimensional Gaussian net­ works into Hamiltonian cycles. In addition, we propose some efficient communi­cation algorithms for higher dimensional Gaussian networks including one-to-all broadcasting and shortest path routing. Simulation results show that the rout­ing algorithm proposed for higher dimensional Gaussian networks outperforms the routing algorithm of the corresponding torus networks with approximately the same number of nodes. These simulation results are expected since higher dimen­sional Gaussian networks have a smaller diameter and a smaller average message latency as compared with toroidal networks. Finally, we introduce a degree-three interconnection network obtained from pruning a Gaussian network. This network shows possible performance improve­ment over other degree-three networks since it has a smaller diameter compared to other degree-three networks. Many topological properties of degree-three pruned Gaussian network are explored. In addition, an optimal shortest path routing algorithm and a one-to-all broadcasting algorithm are given

Treasure hunt : a framework for cooperative, distributed parallel optimization

Orientador: Prof. Dr. Daniel WeingaertnerCoorientadora: Profa. Dra. Myriam Regattieri DelgadoTese (doutorado) - Universidade Federal do Paraná, Setor de Ciências Exatas, Programa de Pós-Graduação em Informática. Defesa : Curitiba, 27/05/2019Inclui referências: p. 18-20Área de concentração: Ciência da ComputaçãoResumo: Este trabalho propõe um framework multinível chamado Treasure Hunt, que é capaz de distribuir algoritmos de busca independentes para um grande número de nós de processamento. Com o objetivo de obter uma convergência conjunta entre os nós, este framework propõe um mecanismo de direcionamento que controla suavemente a cooperação entre múltiplas instâncias independentes do Treasure Hunt. A topologia em árvore proposta pelo Treasure Hunt garante a rápida propagação da informação pelos nós, ao mesmo tempo em que provê simutaneamente explorações (pelos nós-pai) e intensificações (pelos nós-filho), em vários níveis de granularidade, independentemente do número de nós na árvore. O Treasure Hunt tem boa tolerância à falhas e está parcialmente preparado para uma total tolerância à falhas. Como parte dos métodos desenvolvidos durante este trabalho, um método automatizado de Particionamento Iterativo foi proposto para controlar o balanceamento entre explorações e intensificações ao longo da busca. Uma Modelagem de Estabilização de Convergência para operar em modo Online também foi proposto, com o objetivo de encontrar pontos de parada com bom custo/benefício para os algoritmos de otimização que executam dentro das instâncias do Treasure Hunt. Experimentos em benchmarks clássicos, aleatórios e de competição, de vários tamanhos e complexidades, usando os algoritmos de busca PSO, DE e CCPSO2, mostram que o Treasure Hunt melhora as características inerentes destes algoritmos de busca. O Treasure Hunt faz com que os algoritmos de baixa performance se tornem comparáveis aos de boa performance, e os algoritmos de boa performance possam estender seus limites até problemas maiores. Experimentos distribuindo instâncias do Treasure Hunt, em uma rede cooperativa de até 160 processos, demonstram a escalabilidade robusta do framework, apresentando melhoras nos resultados mesmo quando o tempo de processamento é fixado (wall-clock) para todas as instâncias distribuídas do Treasure Hunt. Resultados demonstram que o mecanismo de amostragem fornecido pelo Treasure Hunt, aliado à maior cooperação entre as múltiplas populações em evolução, reduzem a necessidade de grandes populações e de algoritmos de busca complexos. Isto é especialmente importante em problemas de mundo real que possuem funções de fitness muito custosas. Palavras-chave: Inteligência artificial. Métodos de otimização. Algoritmos distribuídos. Modelagem de convergência. Alta dimensionalidade.Abstract: This work proposes a multilevel framework called Treasure Hunt, which is capable of distributing independent search algorithms to a large number of processing nodes. Aiming to obtain joint convergences between working nodes, Treasure Hunt proposes a driving mechanism that smoothly controls the cooperation between the multiple independent Treasure Hunt instances. The tree topology proposed by Treasure Hunt ensures quick propagation of information, while providing simultaneous explorations (by parents) and exploitations (by children), on several levels of granularity, regardless the number of nodes in the tree. Treasure Hunt has good fault tolerance and is partially prepared to full fault tolerance. As part of the methods developed during this work, an automated Iterative Partitioning method is proposed to control the balance between exploration and exploitation as the search progress. A Convergence Stabilization Modeling to operate in Online mode is also proposed, aiming to find good cost/benefit stopping points for the optimization algorithms running within the Treasure Hunt instances. Experiments on classic, random and competition benchmarks of various sizes and complexities, using the search algorithms PSO, DE and CCPSO2, show that Treasure Hunt boosts the inherent characteristics of these search algorithms. Treasure Hunt makes algorithms with poor performances to become comparable to good ones, and algorithms with good performances to be capable of extending their limits to larger problems. Experiments distributing Treasure Hunt instances in a cooperative network up to 160 processes show the robust scaling of the framework, presenting improved results even when fixing a wall-clock time for the instances. Results show that the sampling mechanism provided by Treasure Hunt, allied to the increased cooperation between multiple evolving populations, reduce the need for large population sizes and complex search algorithms. This is specially important on real-world problems with time-consuming fitness functions. Keywords: Artificial intelligence. Optimization methods. Distributed algorithms. Convergence modeling. High dimensionality

LIPIcs, Volume 248, ISAAC 2022, Complete Volume

LIPIcs, Volume 248, ISAAC 2022, Complete Volum

Proceedings of the Workshop on Change of Representation and Problem Reformulation

The proceedings of the third Workshop on Change of representation and Problem Reformulation is presented. In contrast to the first two workshops, this workshop was focused on analytic or knowledge-based approaches, as opposed to statistical or empirical approaches called 'constructive induction'. The organizing committee believes that there is a potential for combining analytic and inductive approaches at a future date. However, it became apparent at the previous two workshops that the communities pursuing these different approaches are currently interested in largely non-overlapping issues. The constructive induction community has been holding its own workshops, principally in conjunction with the machine learning conference. While this workshop is more focused on analytic approaches, the organizing committee has made an effort to include more application domains. We have greatly expanded from the origins in the machine learning community. Participants in this workshop come from the full spectrum of AI application domains including planning, qualitative physics, software engineering, knowledge representation, and machine learning

Scheduling and reconfiguration of interconnection network switches

Interconnection networks are important parts of modern computing systems, facilitating communication between a system\u27s components. Switches connecting various nodes of an interconnection network serve to move data in the network. The switch\u27s delay and throughput impact the overall performance of the network and thus the system. Scheduling efficient movement of data through a switch and configuring the switch to realize a schedule are the main themes of this research. We consider various interconnection network switches including (i) crossbar-based switches, (ii) circuit-switched tree switches, and (iii) fat-tree switches. For crossbar-based input-queued switches, a recent result established that logarithmic packet delay is possible. However, this result assumes that packet transmission time through the switch is no less than schedule-generation time. We prove that without this assumption (as is the case in practice) packet delay becomes linear. We also report results of simulations that bear out our result for practical switch sizes and indicate that a fast scheduling algorithm reduces not only packet delay but also buffer size. We also propose a fast mesh-of-trees based distributed switch scheduling (maximal-matching based) algorithm that has polylog complexity. A circuit-switched tree (CST) can serve as an interconnect structure for various computing architectures and models such as the self-reconfigurable gate array and the reconfigurable mesh. A CST is a tree structure with source and destination processing elements as leaves and switches as internal nodes. We design several scheduling and configuration algorithms that distributedly partition a given set of communications into non-conflicting subsets and then establish switch settings and paths on the CST corresponding to the communications. A fat-tree is another widely used interconnection structure in many of today\u27s high-performance clusters. We embed a reconfigurable mesh inside a fat-tree switch to generate efficient connections. We present an R-Mesh-based algorithm for a fat-tree switch that creates buses connecting input and output ports corresponding to various communications using that switch