Interconnection Networks Embeddings and Efficient Parallel Computations.

To obtain a greater performance, many processors are allowed to cooperate to solve a single problem. These processors communicate via an interconnection network or a bus. The most essential function of the underlying interconnection network is the efficient interchanging of messages between processes in different processors. Parallel machines based on the hypercube topology have gained a great respect in parallel computation because of its many attractive properties. Many versions of the hypercube have been introduced by many researchers mainly to enhance communications. The twisted hypercube is one of the most attractive versions of the hypercube. It preserves the important features of the hypercube and reduces its diameter by a factor of two. This dissertation investigates relations and transformations between various interconnection networks and the twisted hypercube and explore its efficiency in parallel computation. The capability of the twisted hypercube to simulate complete binary trees, complete quad trees, and rings is demonstrated and compared with the hypercube. Finally, the fault-tolerance of the twisted hypercube is investigated. We present optimal algorithms to simulate rings in a faulty twisted hypercube environment and compare that with the hypercube

Routing in Mobius Cubes

Möbius cube je zajímavou topologií, která vznikla z topologie hypercube. Největší výhoda oproti hypercube je v přibližně polovičním průměru Möbius cube. V této práci je popsán algoritmus nejkratšího routování a jsou popsány i jeho klady a zápory. Velkou nevýhodou je možnost pádu do stavu uzamknutí (deadlock). Proto je v práci představen nový deadlock-free algoritmus a porovnán s předchozím algoritmem. Dále je v práci popsána možnost použití hypercubického multicast 1-portového wormhole algoritmu na Möbius cube.The Möbius cube is an interesting topology created from the hypercube. Its main advantage is the which that is around one half of the diameter of the hypercube. In this thesis, the shortest path algorithm is described as well as its properties and drawbacks. One major drawback is the possibility of a deadlock. Therefore, a new deadlock-free routing algorithm is introduced and compared to the previous algorithm. Later, usage of hypercube's multicast 1-port wormhole algorithm on the Möbius cube is described

Small-world interconnection networks for large parallel computer systems

The use of small-world graphs as interconnection networks of multicomputers is proposed and analysed in this work. Small-world interconnection networks are constructed by adding (or modifying) edges to an underlying local graph. Graphs with a rich local structure but with a large diameter are shown to be the most suitable candidates for the underlying graph. Generation models based on random and deterministic wiring processes are proposed and analysed. For the random case basic properties such as degree, diameter, average length and bisection width are analysed, and the results show that a fast transition from a large diameter to a small diameter is experienced when the number of new edges introduced is increased. Random traffic analysis on these networks is undertaken, and it is shown that although the average latency experiences a similar reduction, networks with a small number of shortcuts have a tendency to saturate as most of the traffic flows through a small number of links. An analysis of the congestion of the networks corroborates this result and provides away of estimating the minimum number of shortcuts required to avoid saturation. To overcome these problems deterministic wiring is proposed and analysed. A Linear Feedback Shift Register is used to introduce shortcuts in the LFSR graphs. A simple routing algorithm has been constructed for the LFSR and extended with a greedy local optimisation technique. It has been shown that a small search depth gives good results and is less costly to implement than a full shortest path algorithm. The Hilbert graph on the other hand provides some additional characteristics, such as support for incremental expansion, efficient layout in two dimensional space (using two layers), and a small fixed degree of four. Small-world hypergraphs have also been studied. In particular incomplete hypermeshes have been introduced and analysed and it has been shown that they outperform the complete traditional implementations under a constant pinout argument. Since it has been shown that complete hypermeshes outperform the mesh, the torus, low dimensional m-ary d-cubes (with and without bypass channels), and multi-stage interconnection networks (when realistic decision times are accounted for and with a constant pinout), it follows that incomplete hypermeshes outperform them as well

Building Machines That Learn and Think Like People

Recent progress in artificial intelligence (AI) has renewed interest in building systems that learn and think like people. Many advances have come from using deep neural networks trained end-to-end in tasks such as object recognition, video games, and board games, achieving performance that equals or even beats humans in some respects. Despite their biological inspiration and performance achievements, these systems differ from human intelligence in crucial ways. We review progress in cognitive science suggesting that truly human-like learning and thinking machines will have to reach beyond current engineering trends in both what they learn, and how they learn it. Specifically, we argue that these machines should (a) build causal models of the world that support explanation and understanding, rather than merely solving pattern recognition problems; (b) ground learning in intuitive theories of physics and psychology, to support and enrich the knowledge that is learned; and (c) harness compositionality and learning-to-learn to rapidly acquire and generalize knowledge to new tasks and situations. We suggest concrete challenges and promising routes towards these goals that can combine the strengths of recent neural network advances with more structured cognitive models.Comment: In press at Behavioral and Brain Sciences. Open call for commentary proposals (until Nov. 22, 2016). https://www.cambridge.org/core/journals/behavioral-and-brain-sciences/information/calls-for-commentary/open-calls-for-commentar

Automorphisms generating disjoint Hamilton cycles in star graphs

In the first part of the thesis we define an automorphism φn for each star graph Stn of degree n − 1, which yields permutations of labels for the edges of Stn taken from the set of integers {1, . . . , bn/2c}. By decomposing these permutations into permutation cycles, we are able to identify edge-disjoint Hamilton cycles that are automorphic images of a known two-labelled Hamilton cycle H1 2(n) in Stn. Our main result is an improvement from the existing lower bound of bϕ(n)/10c to b2ϕ(n)/9c, where ϕ is Euler’s totient function, for the known number of edge-disjoint Hamilton cycles in Stn for all odd integers n. For prime n, the improvement is from bn/8c to bn/5c. We extend this result to the cases when n is the power of a prime other than 3 and 7. The second part of the thesis studies ‘symmetric’ collections of edge-disjoint Hamilton cycles in Stn, i.e. collections that comprise images of H1 2(n) under general label-mapping automorphisms. We show that, for all even n, there exists a symmetric collection of bϕ(n)/2c edge-disjoint Hamilton cycles, and Stn cannot have symmetric collections of greater than bϕ(n)/2c such cycles for any n. Thus, Stn is not symmetrically Hamilton decomposable if n is not prime. We also give cases of even n, in terms of Carmichael’s reduced totient function λ, for which ‘strongly’ symmetric collections of edge-disjoint Hamilton cycles, which are generated from H1 2(n) by a single automorphism, can and cannot attain the optimum bound bϕ(n)/2c for symmetric collections. In particular, we show that if n is a power of 2, then Stn has a spanning subgraph with more than half of the edges of Stn, which is strongly symmetrically Hamilton decomposable. For odd n, it remains an open problem as to whether the bϕ(n)/2c can be achieved for symmetric collections, but we are able to show that, for certain odd n, a ϕ(n)/4 bound is achievable and optimal for strongly symmetric collections. The search for edge-disjoint Hamilton cycles in star graphs is important for the design of interconnection network topologies in computer science. All our results improve on the known bounds for numbers of any kind of edge-disjoint Hamilton cycles in star graphs

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