Adaptive control in rollforward recovery for extreme scale multigrid

With the increasing number of compute components, failures in future exa-scale computer systems are expected to become more frequent. This motivates the study of novel resilience techniques. Here, we extend a recently proposed algorithm-based recovery method for multigrid iterations by introducing an adaptive control. After a fault, the healthy part of the system continues the iterative solution process, while the solution in the faulty domain is re-constructed by an asynchronous on-line recovery. The computations in both the faulty and healthy subdomains must be coordinated in a sensitive way, in particular, both under and over-solving must be avoided. Both of these waste computational resources and will therefore increase the overall time-to-solution. To control the local recovery and guarantee an optimal re-coupling, we introduce a stopping criterion based on a mathematical error estimator. It involves hierarchical weighted sums of residuals within the context of uniformly refined meshes and is well-suited in the context of parallel high-performance computing. The re-coupling process is steered by local contributions of the error estimator. We propose and compare two criteria which differ in their weights. Failure scenarios when solving up to $6.9\cdot10^{11}$ unknowns on more than 245\,766 parallel processes will be reported on a state-of-the-art peta-scale supercomputer demonstrating the robustness of the method

On quantifying fault patterns of the mesh interconnect networks

One of the key issues in the design of Multiprocessors System-on-Chip (MP-SoCs), multicomputers, and peerto- peer networks is the development of an efficient communication network to provide high throughput and low latency and its ability to survive beyond the failure of individual components. Generally, the faulty components may be coalesced into fault regions, which are classified into convex and concave shapes. In this paper, we propose a mathematical solution for counting the number of common fault patterns in a 2-D mesh interconnect network including both convex (|-shape, | |-shape, ý-shape) and concave (L-shape, Ushape, T-shape, +-shape, H-shape) regions. The results presented in this paper which have been validated through simulation experiments can play a key role when studying, particularly, the performance analysis of fault-tolerant routing algorithms and measure of a network fault-tolerance expressed as the probability of a disconnection

Embedding cube-connected cycles graphs into faulty hypercubes

We consider the problem of embedding a cube-connected cycles graph (CCC) into a hypercube with edge faults. Our main result is an algorithm that, given a list of faulty edges, computes an embedding of the CCC that spans all of the nodes and avoids all of the faulty edges. The algorithm has optimal running time and tolerates the maximum number of faults (in a worst-case setting). Because ascend-descend algorithms can be implemented efficiently on a CCC, this embedding enables the implementation of ascend-descend algorithms, such as bitonic sort, on hypercubes with edge faults. We also present a number of related results, including an algorithm for embedding a CCC into a hypercube with edge and node faults and an algorithm for embedding a spanning torus into a hypercube with edge faults

Resilient Routing Implementation in 2D Mesh NoC

With the rapid shrinking of technology and growing integration capacity, the probability of failures in Networks-on-Chip (NoCs) increases and thus, fault tolerance is essential. Moreover, the unpredictable locations of these failures may influence the regularity of the underlying topology, and a regular 2D mesh is likely to become irregular. Thus, for these failure-prone networks, a viable routing framework should comprise a topology-agnostic routing algorithm along with a cost-effective, scalable routing mechanism able to handle failures, irrespective of any particular failure patterns. Existing routing techniques designed to route irregular topologies efficiently lack flexibility (logic-based), scalability (table-based) or relaxed switch design (uLBDR-based). Designing an efficient routing implementation technique to address irregular topologies remains a pressing research problem. To address this, we present a fault resilient routing mechanism for irregular 2D meshes resulting from failures. To handle irregularities, it avoids using routing tables and employs a few fixed configuration bits per switch resulting in a scalable approach. Experiments demonstrate that the proposed approach is guaranteed to tolerate all locations of single and double-link failures and most multiple failures. Also, unlike uLBDR it is not restricted to any particular switching technique and does not replicate any extra messages. Along with fault tolerance, the proposed mechanism can achieve better network performance in fault-free cases. The proposed technique achieves graceful performance degradation during failure. Compared to uLBDR, our method has 14% less area requirements and 16% less overall power consumption

New Fault Tolerant Multicast Routing Techniques to Enhance Distributed-Memory Systems Performance

Distributed-memory systems are a key to achieve high performance computing and the most favorable architectures used in advanced research problems. Mesh connected multicomputer are one of the most popular architectures that have been implemented in many distributed-memory systems. These systems must support communication operations efficiently to achieve good performance. The wormhole switching technique has been widely used in design of distributed-memory systems in which the packet is divided into small flits. Also, the multicast communication has been widely used in distributed-memory systems which is one source node sends the same message to several destination nodes. Fault tolerance refers to the ability of the system to operate correctly in the presence of faults. Development of fault tolerant multicast routing algorithms in 2D mesh networks is an important issue. This dissertation presents, new fault tolerant multicast routing algorithms for distributed-memory systems performance using wormhole routed 2D mesh. These algorithms are described for fault tolerant routing in 2D mesh networks, but it can also be extended to other topologies. These algorithms are a combination of a unicast-based multicast algorithm and tree-based multicast algorithms. These algorithms works effectively for the most commonly encountered faults in mesh networks, f-rings, f-chains and concave fault regions. It is shown that the proposed routing algorithms are effective even in the presence of a large number of fault regions and large size of fault region. These algorithms are proved to be deadlock-free. Also, the problem of fault regions overlap is solved. Four essential performance metrics in mesh networks will be considered and calculated; also these algorithms are a limited-global-information-based multicasting which is a compromise of local-information-based approach and global-information-based approach. Data mining is used to validate the results and to enlarge the sample. The proposed new multicast routing techniques are used to enhance the performance of distributed-memory systems. Simulation results are presented to demonstrate the efficiency of the proposed algorithms