Free Submeshes Research Articles

A New Compacting Non-Contiguous Processor Allocation Algorithm for 2D Mesh Multicomputers

In non-contiguous allocation, a job request can be split into smaller parts that are allocated possibly 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 likely to increase. The extra communication overhead depends on how the allocation request is partitioned and assigned to free sub-meshes. In this paper, a new non-contiguous processor allocation strategy, referred to as Compacting Non-Contiguous Processor Allocation Strategy (CNCPA), is suggested for the 2D mesh multicomputers. In the proposed strategy, a job is compacted into free locations. The selection of the free locations has for goal leaving large free sub-meshes in the system. To evaluate the performance improvement achieved by the proposed strategy and compare it against well-known existing non-contiguous allocation strategies, the authors conducted extensive simulation experiments. The results show that the proposed strategy can improve performance in terms of job turnaround times and system utilization.

Corner-Boundary Processor Allocation for 3D Mesh-Connected Multicomputers

This research paper presents a new contiguous allocation strategy for 3D mesh-connected multicomputers. The proposed strategy maintains a list of maximal free sub-meshes and gives priority to allocating corner and boundary free sub-meshes. The goal of corner and boundary allocation is to decrease the number of leftover free sub-meshes and increase their sizes, which is expected to reduce processor fragmentation and improve overall system performance. The proposed strategy, which is referred to as Turning Corner-Boundary Free List (TCBFL) strategy, is compared, using extensive simulation experiments, to several existing allocation strategies for 3D meshes. These are the First-Fit (FF), Turning First-Fit Free List (TFFFL), and Turning Busy List (TBL) allocation strategies. The simulation results show that TCBFL produces average turnaround times and mean system utilization values that are superior to those of previous strategies.

Performance evaluation of noncontiguous allocation algorithms for 2D mesh interconnection networks

Several noncontiguous allocation strategies have been proposed for 2D mesh-connected multicomputers. These allocation strategies differ in their ability to detect free submeshes and in the degree of contiguity that exists among the submeshes they allocate to the same job. The previous Adaptive Noncontiguous Allocation (ANCA) policy was evaluated based on a proposed formula that estimates the job execution time when the job is allocated noncontiguous submeshes. Using this formula, simulation results had shown that ANCA could outperform the preceding Multiple Buddy Strategy (MBS). However, the execution times of jobs under noncontiguous allocation depend on message sizes, the number of messages sent, message contention and distances messages traverse. In this paper, we evaluate ANCA for different communication patterns using an event-driven simulator operating at the flit level, which allows for a more realistic evaluation that takes into account the shape of allocation and contention among messages. Moreover, we compare the performance of ANCA with that of other noncontiguous allocation strategies, MBS, Greedy Available Busy List (GABL), and Paging(0). The results show that ANCA is inferior to the remaining strategies, and that GABL has the best performance results, expressed in terms of the average turnaround time and mean system utilization performance parameters.

A new window-based job scheduling scheme for 2D mesh multicomputers

Allocating submeshes to jobs in mesh-connected multicomputers in a FCFS fashion can lead to poor system performance (e.g., long job waiting delays) because the job at the head of the waiting queue can prevent the allocation of free submeshes to other waiting jobs with smaller submesh requirements. However, serving jobs aggressively out-of-order can lead to excessive waiting delays for jobs with large allocation requests. In this paper, we propose a scheduling scheme that uses a window of consecutive jobs from which it selects jobs for allocation and execution. This window starts with the current oldest waiting job and corresponds to the lookahead of the scheduler. The performance of the proposed window-based scheme has been compared to that of FCFS and other previous job scheduling schemes. Extensive simulation results based on synthetic workloads and real workload traces indicate that the new scheduling strategy exhibits good performance when the scheduling window size is large. In particular, it is substantially superior to FCFS in terms of system utilization, average job turnaround times, and maximum waiting delays under medium to heavy system loads. Also, it is superior to aggressive out-of-order scheduling in terms of maximum job waiting delays. Window-based job scheduling can improve both overall system performance and fairness (i.e., maximum job waiting delays) by adopting large lookahead job scheduling windows.

An adaptive job scheduling scheme for mesh-connected multicomputers

Allocating submeshes to jobs in mesh-connected multicomputers in an FCFS fashion leads to poor system performance because a large job at the head of the waiting queue can prevent the allocation of free submeshes to other smaller waiting jobs. However, serving jobs aggressively out-of-order can lead to excessive waiting delays for large jobs located at the head of the waiting queue. In this paper, we show that the ability of the job scheduling algorithm to bypass the head of the waiting queue should increase with the load, and we propose a scheduling scheme that can bypass the waiting queue head in a load-dependent adaptive fashion. Also, giving priority to large jobs because they are more difficult to accommodate is investigated. The performance of the proposed scheme has been compared to that of FCFS, aggressive out-of-order scheduling, and other previous job scheduling schemes. Extensive simulation results based on synthetic workloads and real workload traces indicate that our scheduling strategy is a good strategy when both average and maximum job waiting delays are considered. In particular, it is substantially superior to FCFS in terms of mean turnaround times, and to aggressive out-of-order scheduling in terms of maximum waiting delays.

On submesh allocation for 2D mesh multicomputers using the free-list approach: Global placement schemes

Two global placement schemes for contiguous processor allocation in two-dimensional mesh-connected multicomputers are proposed in this paper. The first scheme gives preference to allocating a free peripheral submesh that has the largest number of mesh-boundary processors. This peripheral placement has for goal producing large leftover free submeshes, which can improve system performance. Another characteristic of this scheme is that it reduces the search space by halting the search process when a large-enough multicomputer corner submesh is found. The second proposed scheme considers allocation in the corners of all large-enough free submeshes and allocates a submesh that has the maximum number of allocated neighbors and multicomputer peripheral nodes. Using extensive simulations, we evaluated the proposed schemes and compared them with previous promising schemes. The simulation results show that the peripheral placement scheme produces the best average turnaround times, and its measured allocation and de-allocation times are smaller than those of the previous schemes. The second proposed scheme ranks overall second in terms of turnaround times, however it is last in terms of efficiency.

An efficient non-contiguous processor allocation strategy for 2D mesh connected multicomputers

In non-contiguous allocation, a job request can be split into smaller parts that are allocated possibly 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. In this paper, a new non-contiguous processor allocation strategy, referred to as Greedy-Available-Busy-List, is suggested for the 2D mesh network. Request partitioning in our suggested strategy is based on the sub-meshes available for allocation. To evaluate the performance improvement achieved by our strategy and compare it against well-known existing non-contiguous and contiguous strategies, we conduct extensive simulation runs under the assumption of wormhole routing and three communication patterns, notably one-to-all, all-to-all and random. The results show that the new strategy can reduce the communication overhead and substantially improve performance in terms of job turnaround time and system utilization.

A new processor allocation strategy with a high degree of contiguity in mesh-connected multicomputers

Relaxing the contiguity condition in non-contiguous allocation can reduce processor fragmentation and increase processor utilization. However, communication overhead could increase due to the potential increase in message distances. The communication overhead depends on how the allocation request is partitioned and allocated to free sub-meshes. In this paper, a new non-contiguous processor allocation strategy, referred to as Greedy-Available-Busy-List (GABL for short), is suggested for the mesh network, and is compared against the existing non-contiguous and contiguous allocation strategies. To demonstrate the performance gains achieved by our proposed strategy, we have conducted simulation runs under the assumption of wormhole routing technique. The results have revealed that the new strategy can reduce communication overhead and considerably improve performance in terms of the job turnaround time, system utilization, and jobs finish time.

An efficient free-list submesh allocation scheme for two-dimensional mesh-connected multicomputers

This paper presents an efficient free-list submesh allocation scheme for two-dimensional mesh-connected systems. The scheme maintains an unordered list of free submeshes. For allocation, it selects the first free submesh that has at least the same size as the request, and when the selected submesh is larger than the request the part actually allocated is one that has the largest number of busy neighbors and mesh boundary processors. Whereas the best previously proposed schemes have time complexities that are either quadratic or cubic in the number of free or allocated submeshes, the time complexity of the proposed scheme is linear in the number of free submeshes. To evaluate the effectiveness of the scheme, its system performance in terms of parameters such as the average job turnaround time was compared to that of promising previously proposed schemes. Simulation results show that the scheme performs at least as well as these schemes, yet it has the lowest time complexity.

태스크와 서브메쉬의 유형별 분류에 기반한 서브메쉬 할당방법

본 논문에서는 메쉬 구조 다중컴퓨터 시스템을 위한 새로운 서브메쉬 할당방법을 제안한다. 이 할당방법의 특징은 유형별 가용 서브메쉬 리스트를 사용하여 가용 서브메쉬의 탐색시간을 줄이는 것이다. 이 할당방법은 메쉬 구조에서 탐색한 독립 가용 서브메쉬들을 유형(정방형, 가로 직사각형, 세로 직사각형)에 따라 분류하여 유형별 가용 서브메쉬 리스트를 생성한다. 그리고 태스크의 유형과 동일한 유형별 가용 서브메쉬 리스트에서 먼저 최적의 서브메쉬를 찾음으로써 서브메쉬의 탐색시간을 줄인다. 만약 가용 서브메쉬를 찾지 못할 경우에는 각 독립 가용 서브메쉬의 속성으로 저장된 확장지수를 사용하여 서브메쉬의 크기를 확장한 후 최적의 가용 서브메쉬를 찾는다. 시뮬레이션을 통하여 본 논문에서 제안하는 서브메쉬 할당방법이 서브메쉬 탐색시간을 줄이는 면에서 기존의 할당방법에 비해 우수함을 보인다. This paper presents a new submesh allocation scheme for mesh-connected multicomputer systems. The key idea in the proposed allocation scheme is to reduce the submesh search time using classified free submesh lists (CFSL). This scheme reduces the submesh search time by classifying independent free submeshes according to their types (square, horizontal rectangle, vertical rectangle) and searching the best-fit submesh from the classified free submesh list. When no suitable submesh is found, the search can be continued by using the expansion index (El), which is stored as an attribute of each submesh, is used to form a larger submesh. Through simulation, we show that the proposed strategy improves the performance compared to previous strategies with respect to submesh search time.

Processor allocation in the mesh multiprocessors using the leapfrog method

The mesh-connected multiprocessor has become popular because of its simple and regular structure. A new data structure, the R-array, is proposed to represent the mesh at first. The element in the R-array stores statistical information about occupied conditions of the mesh. Statistical information of the R-array can direct the allocation process to jump to the processes that can serve as a base of a free submesh. Based on a simple and reasonable assumption, we develop a stochastic process to analyze behaviors of the proposed scheme. The proposed scheme is the first whose probabilities of locating free submeshes under different workloads are precisely computed. These results can be applied to each full-recognition scheme. In addition, the execution costs of the proposed scheme can also be accurately calculated. Finally, simulations are performed which show that the proposed schemes are faster than most.

An efficient submesh allocation scheme for two-dimensional meshes with little overhead

This paper presents a submesh allocation scheme for two-dimensional mesh systems. The submesh detection process considers only those available free submeshes that border from the left on some allocated submeshes or have their left boundaries aligned with that of the mesh. Fragmentation in the system can be reduced as a result. More importantly, we present an efficient approach to facilitate the detection of such available submeshes. The basic idea of the approach is to place the allocated submeshes of the busy set in a certain order so as to reduce the complexity of subtraction operations required for submesh detection. The method is simple and causes an amount of overhead which is only a fraction of that produced by previous algorithms. Extensive simulation has been conducted to evaluate the performance of the proposed scheme. The results show that when allocation overhead is considered, the proposed scheme may outperform previous methods.

On submesh allocation for mesh multicomputers: a best-fit allocation and a virtual submesh allocation for faulty meshes

The submesh allocation problem is to recognize and locate a free submesh that can accommodate a request for a submesh of a specified size. In this paper, we propose a new best-fit submesh allocation strategy for mesh-connected multiprocessor systems. The proposed strategy maintains and uses a free submesh list for an efficient allocation. For an allocation request, the strategy selects the best-fit submesh which causes the least amount of potential processor fragmentation. As many large free submeshes as possible are preserved for later allocations. For this purpose, we introduce a novel function quantifying the degree of potential fragmentation of submeshes. The proposed strategy has the capability of recognizing a complete submesh. We also propose an allocation strategy for faulty meshes which can maintain and allocate virtual submeshes derived from faulty submeshes. Extensive simulation is carried out to compare the proposed strategy with previous strategies. The proposed strategy has the best performance: a 6-50 percent improvement over the previous best strategy.

Submesh Allocation in Mesh Multicomputers Using Busy-List: A Best-Fit Approach with Complete Recognition Capability

A new approach is proposed for dynamic submesh allocation in mesh-connected multicomputer system, which supports a multiuser environment. The proposed strategy effectively prunes the search space by searching for free submeshes on the corners of allocated (busy) submeshes along with the four corners of the mesh system. A submesh is selected with the potential of causing the least amount of fragmentation in the system. The proposed strategy possesses complete submesh recognition capability; it is a best-fit strategy, as well. Existing strategies do not provide this combination of capabilities. The deallocation time and memory overhead are shown to be constant in that they do not grow with the size of the mesh. To demonstrate effectiveness, the performance of the proposed strategy is compared against all existing schemes. Simulation results indicate that the proposed strategy outperforms existing ones in terms of parameters such as average delay in honoring a request, standard deviation of delay, average allocation time, average deallocation time, and amount of memory required. The proposed scheme achieves a 20 to 30% improvement in the average waiting delay over the best performing existing algorithm to date. Our scheme is shown to be applicable to torus-connected multicomputers as well, with only minor modifications. The scheme can also be used for submesh allocation with failures.

ON THE BEST FIT SUBMESH ALLOCATION STRATEGY IN MESH-CONNECTED MULTICOMPUTERS

The submesh allocation problem is to recognize and locate a free submesh that can accommodate a request for a submesh of a specified size. An efficient submesh allocation strategy is required for achieving high performance on mesh multicomputers. In this paper, we propose a new best fit submesh allocation strategy. The proposed strategy maintains and uses a free submesh list to get global information for free submeshes. For an allocation request, the strategy tries to allocate a best fit submesh which causes the least amount of potential fragmentation so as to preserve the large free submeshes to be as many as possible and to prevent processor fragmentation for later requests. For this purpose, we introduce a novel function for quantifying the degree of potential fragmentation of submeshes. The proposed strategy has the complete submesh recognition capability. Extensive simulation is carried out to compare it with the previous strategies, and experimental results indicate that it exhibits the best performance along with an about 30% average improvement over the previous best strategy.

FREE SUBMESH LIST STRATEGY: A BEST FIT SUBMESH ALLOCATION IN MESH CONNECTED MULTICOMPUTERS

The submesh allocation problem is to recognize and locate a free submesh that can accommodate a request for a submesh of a specified size. In this paper, we propose a new best-fit submesh allocation strategy. The proposed strategy maintains and uses a free submesh list to get global information for free submeshes. For an allocation request, the proposed strategy tries to allocate a best-fit submesh which causes the least amount of potential processor fragmentation so as to reserve the large free submeshes as many as possible for later requests. For this purpose, we introduce a novel function for quantifying the degree of potential fragmentation of submeshes. The proposed strategy has the complete submesh recognition capability. Extensive simulation is carried out to compare the proposed strategy with the previous strategies and it is shown that the proposed strategy exhibits the best performance.