Resource placement with multiple adjacency constraints in k-ary n-cubes

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Reliable low latency I/O in torus-based interconnection networks

In today's high performance computing environment I/O remains the main bottleneck in achieving the optimal performance expected of the ever improving processor and memory technologies. Interconnection networks therefore combines processing units, system I/O and high speed switch network fabric into a new paradigm of I/O based network. It decouples the system into computational and I/O interconnections each allowing "any-to-any" communications among processors and I/O devices unlike the shared model in bus architecture. The computational interconnection, a network of processing units (compute-nodes), is used for inter-processor communication in carrying out computation tasks, while the I/O interconnection manages the transfer of I/O requests between the compute-nodes and the I/O or storage media through some dedicated I/O processing units (I /O-nodes). Considering the special functions performed by the I/O nodes, their placement and reliability become important issues in improving the overall performance of the interconnection system. This thesis focuses on design and topological placement of I/O-nodes in torus based interconnection networks, with the aim of reducing I/O communication latency between compute-nodes and I/O-nodes even in the presence of faulty I/O-nodes. We propose an efficient and scalable relaxed quasi-perfect placement scheme using Lee distance error correction code such that compute-nodes are at distance-t or at most distance-t+1 from an I/O-node for a given t. This scheme provides a better and optimal alternative placement than quasi perfect placement when perfect placement cannot be found for a particular torus. Furthermore, in the occurrence of faulty I/O-nodes, the placement scheme is also used in determining other alternative I/O-nodes for rerouting I/O traffic from affected compute-nodes with minimal slowdown. In order to guarantee the quality of service required of inter-processor communication, a scheduling algorithm was developed at the router level to prioritize message forwarding according to inter-process and I/O messages with the former given higher priority. Our simulation results show that relaxed quasi-perfect outperforms quasi-perfect and the conventional I/O placement (where I/O nodes are concentrated at the base of the torus interconnection) with little degradation in inter-process communication performance. Also the fault tolerant redirection scheme provides a minimal slowdown, especially when the number of faulty I/O nodes is less than half of the initial available I/O nodes

Resource placement, data rearrangement, and Hamiltonian cycles in torus networks

Many parallel machines, both commercial and experimental, have been/are being designed with toroidal interconnection networks. For a given number of nodes, the torus has a relatively larger diameter, but better cost/performance tradeoffs, such as higher channel bandwidth, and lower node degree, when compared to the hypercube. Thus, the torus is becoming a popular topology for the interconnection network of a high performance parallel computers. In a multicomputer, the resources, such as I/O devices or software packages, are distributed over the networks. The first part of the thesis investigates efficient methods of distributing resources in a torus network. Three classes of placement methods are studied. They are (1) distant-t placement problem: in this case, any non-resource node is at a distance of at most t from some resource nodes, (2) j-adjacency problem: here, a non-resource node is adjacent to at least j resource nodes, and (3) generalized placement problem: a non-resource node must be a distance of at most t from at least j resource nodes. This resource placement technique can be applied to allocating spare processors to provide fault-tolerance in the case of the processor failures. Some efficient spare processor placement methods and reconfiguration schemes in the case of processor failures are also described. In a torus based parallel system, some algorithms give best performance if the data are distributed to processors numbered in Cartesian order; in some other cases, it is better to distribute the data to processors numbered in Gray code order. Since the placement patterns may be changed dynamically, it is essential to find efficient methods of rearranging the data from Gray code order to Cartesian order and vice versa. In the second part of the thesis, some efficient methods for data transfer from Cartesian order to radix order and vice versa are developed. The last part of the thesis gives results on generating edge disjoint Hamiltonian cycles in k-ary n-cubes, hypercubes, and 2D tori. These edge disjoint cycles are quite useful for many communication algorithms