| M. Livingston and Q. F. Stout. Parallel allocation algorithms for hypercubes and meshes. In Proceedings of the 4th Conference on Hypercube Concurrent Computers and Applications, pages 59--66, 1989. |
....and several runs of the same job result in approximately equal execution times. Examples of contiguous allocation strategies for mesh topologies are 2D Buddy [9] Frame Sliding [5] and First Fit Best Fit [18] For hypercube topologies, examples are Gray Code [4] Partners [1] and Cyclic Buddy [11]. However, contiguous processor allocation strategies suffer from fragmentation. Consider an additional job in Fig. 1 that requests four nodes. Six nodes are unallocated at this time, but there is no contiguous block of four nodes available. The nodes (2,3) 2,4) 3,4) and (4,4) for example are ....
M. Livingston and Q. F. Stout. Parallel allocation algorithms for hypercubes and meshes. In Proceedings of the 4th Conference on Hypercube Concurrent Computers and Applications, pages 59--66, 1989.
....the runtime of the application, and then release the subcubes back to the operating system. The algorithm used by the operating system to handle the requests and relinquishments of subcubes is the processor allocation algorithm and has been the target of of intensive research for the past decade [14, 12, 11, 17, 3]. The key idea to remember is that a subcube is equivalent to a block of addresses that is expressible using a single address expression or mask. This equivalence means that subcube recognition techniques can be applied to the problem of multicast address allocation. Note, however, that while ....
M. Livingston and Q. F. Stout. Parallel allocation algorithms for hypercubes and meshes. In Proceedings of the 4th Conference on Hypercube Concurrent Computers and Applications, 1989.
....faulty (a worst case scenario) and determine the average number of faults required to make each locatable subcube faulty (expected case scenario) where the faults are assumed to be distributed uniformly randomly and independently. We contend that the cyclic buddy scheme, which we introduced in [15], should be the method of choice for subcube location in hypercubes. This scheme can be implemented in parallel with almost no system overhead [15] and, as our results here will show, it yields a substantial improvement in fault tolerance over the buddy and gray coded buddy schemes. In Section 2, ....
....where the faults are assumed to be distributed uniformly randomly and independently. We contend that the cyclic buddy scheme, which we introduced in [15] should be the method of choice for subcube location in hypercubes. This scheme can be implemented in parallel with almost no system overhead [15], and, as our results here will show, it yields a substantial improvement in fault tolerance over the buddy and gray coded buddy schemes. In Section 2, we describe the subcube location schemes we will study. The schemes under consideration are the buddy, double buddy, gray coded buddy, double ....
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M.L. Livingston and Q.F. Stout, "Parallel allocation algorithms for hypercubes and meshes" in Proc. 4th Conf. on Hypercube Concurrent Computers and Appl. (1989), pp. 59-66.
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