Efficient adaptive collect algorithms

Dynamical Computing Power Balancing for Adaptive Mesh Refinement Applications

The complete subcube recognition problem is defined as, given a collection of available processors on an n-dimensional hypercube, locate a subcube of dimension k that consists entirely of available processors, if one exists. Despite many algorithms proposed so far on this subject, improving the time complexity of this problem remains a challenge. Efficiency limits that can be reached have not been exhausted yet. This paper proposes a novel algorithm to recognize all the overlapping subcubes available on an n-dimensional hypercube whose processors are partially allocated. Given P=2/sup n/, as the total number of processors in the hypercube, the new algorithm runs in O(n-3/sup n/) or O(P(log/sub 2/) /sup 3/log/sub 2/ P) time which is an improvement over previously proposed strategies, such as multiple-graycode, missing combination, maximal set of subcubes, and tree collapsing.

This paper shows an important exception against the common perception that three-dimensional meshes are more powerful than two-dimensional ones: Let N be the total number of processors. Then permutation routing over three-dimensional mesh computers needs Θ(N2/3) steps while it takes Θ(N1/2) steps over two-dimensional ones under the following condition: (1) The path of each packet must be determined solely by its initial position and destination, i.e., the algorithm must be oblivious. (2) Each path must be “elementary,” i.e., it must be shortest and as straight as possible. Thus the conditions are quite reasonable in practice, under which, little surprisingly, three-dimensional meshes are significantly less powerful than two-dimensional ones for the fundamental network operation.

In a Distributed Consensus protocol n processors, of which at most t may be faulty, are given initial binary values; after exchanging messages all the processors that are correct must agree on one of the initial values. We measure the quality of a consensus protocol by the following parameters: the total number of processors n, the number of rounds of message exchange r, and the communication complexity, given by the maximal message size.

Large-scale parallel viscous flow computations using an unstructured multigrid algorithm

Presents a parallel hash join algorithm that is based on the concept of hierarchical hashing, to address the problem of data skew. The proposed algorithm splits the usual hash phase into a hash phase and an explicit transfer phase, and adds an extra scheduling phase between these two. During the scheduling phase, a heuristic optimization algorithm, using the output of the hash phase, attempts to balance the load across the multiple processors in the subsequent join phase. The algorithm naturally identifies the hash partitions with the largest skew values and splits them as necessary, assigning each of them to an optimal number of processors. Assuming for concreteness a Zipf-like distribution of the values in the join column, a join phase which is CPU-bound, and a shared nothing environment, the algorithm is shown to achieve good join phase load balancing, and to be robust relative to the degree of data skew and the total number of processors. The overall speedup due to this algorithm is compared to some existing parallel hash join methods. The proposed method does considerably better in high skew situations.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Three main parameters characterize the efficiency of algorithms that solve the Consensus Problem. The ratio between the total number of processors and the maximum number of faulty processors (n and t, respectively), the number of rounds, and the size of any single message. Lower bounds exist for each one of the three. In this paper we present two families of algorithms, each achieving the lower bound for one parameter and a trade-off between the other two. The first family includes algorithms where, given an integer k, the algorithm always requires the minimal possible number of rounds (t+1), with n=k(3t+1) processors and messages of size at most t O(t/k). To the second family belong algorithms in which all messages are of one bit size, the number of processors is t O((k+1)/k) and the number of rounds is t+t O ((k−1)/k). These two families are based on a very simple algorithm with (2t+1)(t+1) processors using the minimal number of rounds and the minimal message size (one bit).

7 - Conclusions

In the near future, semiconductor technology will allow the integration of multiple processors on a chip or multichip-module (MCM). In this paper we investigate the architecture and partitioning of resources between processors and cache memory for single chip and MCM-based multiprocessors. We study the performance of a cluster-based multiprocessor architecture in which processors within a cluster are tightly coupled via a shared cluster cache for various processor-cache configurations. Our results show that for parallel applications, clustering via shared caches provides an effective mechanism for increasing the total number of processors in a system, without increasing the number of invalidations. Combining these results with cost estimates for shared cluster cache implementations leads to two conclusions: 1) For a four cluster multiprocessor with single chip clusters, two processors per cluster with a smaller cache provides higher performance and better cost/performance than a single processor with a larger cache and 2) this four cluster configuration can be scaled linearly in performance by adding processors to each cluster using MCM packaging techniques.

The problem of optimal scheduling n tasks in a parallel processor system is studied. The tasks are malleable, i.e., a task may be executed by several processors simultaneously and the processing speed of a task is a nonlinear function of the number of processors allocated to it. The total number of processors is m and it is an upper bound on the number of processors that can be used by all the tasks simultaneously. It is assumed that the number of processors is sufficient to process all the tasks simultaneously, i.e. n≤m. The objective is to find a task schedule and a processor allocation such that the overall task completion time, i.e. the makespan, is minimized. The problem is motivated by real-life applications of parallel computer systems in scientific computing of highly parallelizable tasks. An O(n) algorithm is presented to solve this problem when all the processing speed functions are convex. If these functions are all concave and the number of tasks is a constant, the problem can be solved in polynomial time. A relaxed problem, in which the number of processors allocated to each task is not required to be integer, can be solved in O(nmax {m,nlog 2 m}) time. It is proved that the minimum makespan values for the original and relaxed problems coincide. For n=2 or n=3, an optimal solution for the relaxed problem can be converted into an optimal solution for the original problem in a constant time.

With the rapid advancement of wireless networking technology, networks have evolved from static to dynamic. Reliability of dynamic networks has virtually become an important issue. Fortunately, a solution to the above issue can be derived from solutions to the Byzantine Agreement (BA) problem. BA problem can be solved by protocols that make processors reach an agreement through message exchange. Protocols used to solve the problem can be divided into Immediate Byzantine Agreement (IBA) protocols and Eventual Byzantine Agreement (EBA) protocols. In IBA protocols, the number of rounds of message exchange is determined by the total number of processors in the network. Even if no faulty processor is present in the network, IBA protocols still require a fixed number of rounds of message exchange, causing a waste of time. In contrast, EBA protocols dynamically adjust the number of rounds of message exchange according to the interference of faulty processors. In terms of efficiency, EBA protocols certainly outperform IBA protocols. Due to the fact that the existing EBA protocols have been designed for static networks, they cannot work on dynamic networks. In this paper, we revisit the EBA problem in dynamic networks to increase the reliability of dynamic networks. Simulations will be conducted to validate that the proposed protocol requires the minimum rounds of message exchange and can tolerate the maximum number of malicious faulty processors compared to other existing protocols.

Diagnosis is an essential subject for the reliability of a multiprocessor system. Under the comparison diagnosis model, Sengupta and Dahbura proposed a polynomial-time algorithm with time complexity O(N5) to identify all the faulty processors for a given syndrome in a system with N processors. In this paper, we present a novel idea on system diagnosis called node diagnosability. The node diagnosability can be viewed as a local strategy toward system diagnosability. There is a strong relationship between the node diagnosability and the traditional diagnosability. For this local sense, we focus more on a single processor and require only identifying the status of this particular processor correctly. Under the comparison diagnosis model, we propose a sufficient condition to determine the node diagnosability of a given processor. Furthermore, we propose a useful local structure called an extended star to guarantee the node diagnosability and provide an efficient algorithm to determine the faulty or fault-free status of each processor based on this structure. For a multiprocessor system with total number of processors N, the time complexity of our algorithm to diagnose a given processor is O(\log N) and that to diagnose all the faulty processors is O(N\log N) under the comparison model, provided that there is an extended star structure at each processor and that the time for looking up the testing result of a comparator in the syndrome table is constant.

We present an algorithm for regular, personalized all- to- all communication, in which every processor has an individual message to deliver to every other processor. Our machine model is a cluster of processing nodes where each node, possibly consisting of several processors, can participate in only one communication operation with another node at a time. The nodes may have different numbers of processors. This general model is important for the implementation of all-to-all communication in libraries such as MPI where collective communication may take place over arbitrary subsets of processors. The algorithm is optimal up to an additive term that is small if the total number of processors is large compared to the maximal number of processors in a node.

Virtual reality (VR) technology is commonly used in entertainment applications; however, it has also been deployed in practical applications in more serious aspects of our lives, such as safety. To support people working in dangerous industries, VR can ensure operators manipulate standardized tasks and work collaboratively to deal with potential risks. Surprisingly, little research has focused on how people can collaboratively work in VR environments. Few studies have paid attention to the cognitive load of operators in their collaborative tasks. Once task demands become complex, many researchers focus on optimizing the design of the interaction interfaces to reduce the cognitive load on the operator. That approach could be of merit; however, it can actually subject operators to a more significant cognitive load and potentially more errors and a failure of collaboration. In this paper, we propose a new collaborative VR system to support two teleoperators working in the VR environment to remote control an uncrewed ground vehicle. We use a compared experiment to evaluate the collaborative VR systems, focusing on the time spent on tasks and the total number of operations. Our results show that the total number of processes and the cognitive load during operations were significantly lower in the two-person group than in the single-person group. Our study sheds light on designing VR systems to support collaborative work with respect to the flow of work of teleoperators instead of simply optimizing the design outcomes.

A parallel hash join algorithm based on the concept of hierarchical hashing is proposed to address the problem data skew. The proposed algorithm adds an extra scheduling phase to the usual hash and join phases. During the scheduling phase, a heuristic optimization algorithm, using the output of the hash phase, attempts to balance the load across the multiple processors in the subsequent join phase. The algorithm naturally identifies the hash partitions with the largest skew elements, splits them up, and assigns each of them to an optimal number of processors. Assuming a Zipf-like distribution of the elements in the join column, the algorithm is shown to achieve good load balancing for the join phase in a CPU-bound environment, and it is shown to be fairly robust relative to the degree of data skew and the total number of processors. The overall speedup due to this algorithm is compared with conventional parallel hash join methods and the considerable advantage of the proposed method is demonstrated even when the additional scheduling phase is taken into account. >