Performance analysis of parallel branch and bound search with the hypercube architecture

With the availability of commercial parallel computers, researchers are examining new classes of problems which might benefit from parallel computing. This paper presents results of an investigation of the class of search intensive problems. The specific problem discussed is the Least-Cost Branch and Bound search method of deadline job scheduling. The object-oriented design methodology was used to map the problem into a parallel solution. While the initial design was good for a prototype, the best performance resulted from fine-tuning the algorithm for a specific computer. The experiments analyze the computation time, the speed up over a VAX 11/785, and the load balance of the problem when using loosely coupled multiprocessor system based on the hypercube architecture

Subcube embeddability and fault tolerance of augmented hypercubes

Hypercube networks have received much attention from both parallel processing and communications areas over the years since they offer a rich interconnection structure with high bandwidth, logarithmic diameter, and high degree of fault tolerance. They are easily partitionable and exhibit a high degree of fault tolerance. Fault-tolerance in hypercube and hypercube-based networks received the attention of several researchers in recent years; The primary idea of this study is to address and analyze the reliability issues in hypercube networks. It is well known that the hypercube can be augmented with one dimension to replace any of the existing dimensions should any dimension fail. In this research, it is shown that it is possible to add i dimensions to the standard hypercube, Qn to tolerate (i - 1) dimension failures, where 0 \u3c i ≤ n. An augmented hypercube, Qn +(n) with n additional dimensions is introduced and compared with two other hypercube networks with the same amount of redundancy. Reliability analysis for the three hypercube networks is done using the combinatorial and Markov modeling. The MTTF values are calculated and compared for all three networks. Comparison between similar size hypercube networks show that the augmented hypercube is more robust than the standard hypercube; As a related problem, we also look at the subcube embeddability. Subcube embeddability of the hypercube can be enhanced by introducing an additional dimension. A set of new dimensions, characterized by the Hamming distance between the pairs of nodes it connects, is introduced using a measure defined as the magnitude of a dimension. An enumeration of subcubes of various sizes is presented for a dimension parameterized by its magnitude. It is shown that the maximum number of subcubes for a Qn can only be attained when the magnitude of dimension is n - 1 or n. It is further shown that the latter two dimensions can optimally increase the number of subcubes among all possible choices

Efficient mapping algorithms for scheduling robot inverse dynamics computation on a multiprocessor system

Two efficient mapping algorithms for scheduling the robot inverse dynamics computation consisting of m computational modules with precedence relationship to be executed on a multiprocessor system consisting of p identical homogeneous processors with processor and communication costs to achieve minimum computation time are presented. An objective function is defined in terms of the sum of the processor finishing time and the interprocessor communication time. The minimax optimization is performed on the objective function to obtain the best mapping. This mapping problem can be formulated as a combination of the graph partitioning and the scheduling problems; both have been known to be NP-complete. Thus, to speed up the searching for a solution, two heuristic algorithms were proposed to obtain fast but suboptimal mapping solutions. The first algorithm utilizes the level and the communication intensity of the task modules to construct an ordered priority list of ready modules and the module assignment is performed by a weighted bipartite matching algorithm. For a near-optimal mapping solution, the problem can be solved by the heuristic algorithm with simulated annealing. These proposed optimization algorithms can solve various large-scale problems within a reasonable time. Computer simulations were performed to evaluate and verify the performance and the validity of the proposed mapping algorithms. Finally, experiments for computing the inverse dynamics of a six-jointed PUMA-like manipulator based on the Newton-Euler dynamic equations were implemented on an NCUBE/ten hypercube computer to verify the proposed mapping algorithms. Computer simulation and experimental results are compared and discussed

Efficient processor management strategies for multicomputer systems

Multicomputers are cost-effective alternatives to the conventional supercomputers. Contemporary processor management schemes tend to underutilize the processors and leave many of the processors in the system idle while jobs are waiting for execution;Instead of designing faster processors or interconnection networks, a substantial performance improvement can be obtained by implementing better processor management strategies. This dissertation studies the performance issues related to the processor management schemes and proposes several ways to enhance the multicomputer systems by means of processor management. The proposed schemes incorporate the concepts of size-reduction, non-contiguous allocation, as well as job migration. Job scheduling using a bypass-queue is also studied. All the proposed schemes are proven effective in improving the system performance via extensive simulations. Each proposed scheme has different implementation cost and constraints. In order to take advantage of these schemes, judicious selection of system parameters is important and is discussed

An efficient processor allocation strategy that maintains a high degree of contiguity among processors in 2D mesh connected multicomputers

Two strategies are used for the allocation of jobs to processors connected by mesh topologies: contiguous allocation and non-contiguous allocation. In non-contiguous allocation, a job request can be split into smaller parts that are allocated to non-adjacent free sub-meshes rather than always waiting until a single sub-mesh of the requested size and shape is available. Lifting the contiguity condition is expected to reduce processor fragmentation and increase system utilization. However, the distances traversed by messages can be long, and as a result the communication overhead, especially contention, is increased. The extra communication overhead depends on how the allocation request is partitioned and assigned to free sub-meshes. This paper presents a new Non-contiguous allocation algorithm, referred to as Greedy-Available-Busy-List (GABL for short), which can decrease the communication overhead among processors allocated to a given job. The simulation results show that the new strategy can reduce the communication overhead and substantially improve performance in terms of parameters such as job turnaround time and system utilization. Moreover, the results reveal that the Shortest-Service-Demand-First (SSD) scheduling strategy is much better than the First-Come-First-Served (FCFS) scheduling strategy

Isomorphic Strategy for Processor Allocation in k-Ary n-Cube Systems

Due to its topological generality and flexibility, the k-ary n-cube architecture has been actively researched for various applications. However, the processor allocation problem has not been adequately addressed for the k-ary n-cube architecture, even though it has been studied extensively for hypercubes and meshes. The earlier k-ary n-cube allocation schemes based on conventional slice partitioning suffer from internal fragmentation of processors. In contrast, algorithms based on job-based partitioning alleviate the fragmentation problem but require higher time complexity. This paper proposes a new allocation scheme based on isomorphic partitioning, where the processor space is partitioned into higher dimensional isomorphic subcubes. The proposed scheme minimizes the fragmentation problem and is general in the sense that any size request can be supported and the host architecture need not be isomorphic. Extensive simulation study reveals that the proposed scheme significantly outperforms earlier schemes in terms of mean response time for practical size k-ary and n-cube architectures. The simulation results also show that reduction of external fragmentation is more substantial than internal fragmentation with the proposed scheme

Isomorphic Strategy for Processor Allocation in k-Ary n-Cube Systems

Due to its topological generality and flexibility, the k-ary n-cube architecture has been actively researched for various applications. However, the processor allocation problem has not been adequately addressed for the k-ary n-cube architecture, even though it has been studied extensively for hypercubes and meshes. The earlier k-ary n-cube allocation schemes based on conventional slice partitioning suffer from internal fragmentation of processors. In contrast, algorithms based on job-based partitioning alleviate the fragmentation problem but require higher time complexity. This paper proposes a new allocation scheme based on isomorphic partitioning, where the processor space is partitioned into higher dimensional isomorphic subcubes. The proposed scheme minimizes the fragmentation problem and is general in the sense that any size request can be supported and the host architecture need not be isomorphic. Extensive simulation study reveals that the proposed scheme significantly outperforms earlier schemes in terms of mean response time for practical size k-ary and n-cube architectures. The simulation results also show that reduction of external fragmentation is more substantial than internal fragmentation with the proposed scheme