An optimal upper bound on the minimal completion time in distributed supercomputing

Lundberg, Lars; Lennerstad, Håkan

doi:10.1145/181181.181339

Cited by 14 publications

(9 citation statements)

References 9 publications

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“…2 The same proof gives the following n-independent v ersion: THEOREM 4.10 (i) For any program P we have h(P;1; q )(1 R(k; u; q)) h(P;k;u): 12 (ii) For any complete program P we have h(P;1; q )(1 R(k; u; q)) h(P;k;u)< m ( P ) h ( P;1; q ) R ( k; u; q):…”

Section: Resultsmentioning

confidence: 92%

“…We have also derived optimal bounds for static versus dynamic allocation of parallel programs ( [7] and [10]), cluster versus dynamic allocation ( [8] and [11]), for all programs with a specied parallelism [12], for the worst case performance drop at memory reorganization [13], and for the cluster execution time for a program P only knowing one execution time for P, executed with dynamic allocation and any schedule [14]. All these reports provide optimal bounds for NPhard quantities.…”

Section: Introductionmentioning

confidence: 99%

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Optimal Worst Case Formulas Comparing Cache Memory Associativity

Lennerstad¹,

Lundberg²

2000

SIAM J. Comput.

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Consider an arbitrary program P which is to be executed on a computer with two alternative cache memories. The rst cache has k sets and u blocks in each set, this is denoted a (k;u)-cache. The other is a fully associative cache with q block s ; a ( 1 ; q )-cache.We present optimal formulas comparing the performance of a (k;u)-cache compared to a (1; q )-cache for worst case scenarios. Optimal mappings of the program variables to the cache blocks are assumed.Let h(P;k;u)denote the number of cache hits for the program P using a ( k;u)-cache and an optimal mapping. We establish an explicit formula for the function r(n; k; u; q) and prove that inf P h(P;k;u) h(P;1; q ) = 1 r ( n; k; u; q); where the inmum is taken over all programs P which contain n variables.We also deduce a formula for the inmum taken over all programs of any numberofvariables:inf P h(P;k;u) h(P;1; q ) = 1 R ( k; u; q):Further we prove that programs which are extremal for this minimum may have any hit ratio, i.e. any ratio h(P;1; q ) =m(P). Here m(P) is the total number of memory references for the program P. An optimal bound on the hit ratio using a (k;u)-cache, given the hit ratio with a (1; q )-cache, also follows.

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Section: Resultsmentioning

confidence: 92%

Section: Introductionmentioning

confidence: 99%

Optimal Worst Case Formulas Comparing Cache Memory Associativity

Lennerstad¹,

Lundberg²

2000

SIAM J. Comput.

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“…One of these bounds requires complete knowledge of the parallel profile vector corresponding to the program [12]. This kind of input is, in most cases, not available.…”

Section: Discussion and Related Workmentioning

confidence: 99%

Using recorded values for bounding the minimum completion time in multiprocessors

Lundberg¹,

Lennerstad²

1998

IEEE Trans. Parallel Distrib. Syst.

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Abstract-The way the processes in a parallel program are scheduled on the processors of a multiprocessor system affects the performance significantly. Finding a schedule of processes to processors which results in minimum completion time is NP-hard. Therefore, one has to resort to heuristic schedules. However, it is often difficult to determine if a specific schedule is close to the optimal case or if it is worthwhile to look for other schedules.Based on information from previous executions of the parallel program, we present a formula for an upper bound on the minimum completion time of the program. The bound is a function of a set of parameters. Some of these parameters are obtained from the previous executions of the program and the others describe the target multiprocessor architecture for which we want to bound the minimum completion time. The bound is optimal when it is based on information from one previous execution. Using these results, we are able to decide if a certain schedule is close to optimal or if it is worthwhile to look for other schedules. This is demonstrated by evaluating the completion time of a specific schedule of a particular program. The proofs used for obtaining the bound are based on program transformations and combinatorial mathematics.Index Terms-Parallel program scheduling, optimal performance bounds, multiprocessors with clusters, synchronizing processes, information from previous executions.

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“…For dynamic scheduling, the lower bound is the same as the predicted speedup; i.e., for this case the bound holds no interesting information. However, for static scheduling, the lower bound is calculated according to the previously obtained theoretical result (see [9]). If the predicted speedup is lower than the speedup bound we know that the currently investigated static schedule is not optimal for the multithreaded program; e.g., it is worthwhile to look for other static schedules.…”

Section: Methods Overviewmentioning

confidence: 99%

“…Previous results [9] show that, based on certain information about the parallel program, one can obtain a tight upper bound on the minimal completion time using static scheduling; i.e., it is always possible to find a static schedule with a completion time less than or equal to the bound. This bound makes it possible to determine if a certain static schedule is close to the optimal case or if it is worthwhile to look for other schedules.…”

Section: Introductionmentioning

confidence: 99%