Scheduling to Maximize the Minimum Processor Finish Time in a Multiprocessor System

Deuermeyer, Bryan L.; Friesen, Donald K.; Langston, Michael A.

doi:10.1137/0603019

Cited by 103 publications

(56 citation statements)

References 4 publications

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“…Regarding the worst-case behavior of the LPT-heuristic applied to the C min -maximization problem, Deuermeyer et al [5] showed that the minimum completion time of the LPT-schedule is never less than 3/4 times the optimal minimum completion time. This bound is asymptotically tight when m tends to infinity.…”

Section: Previous Work and Intention Of The Papermentioning

confidence: 99%

Comparing the minimum completion times of two longest-first scheduling-heuristics

Walter

2011

Cent Eur J Oper Res

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For the problem of non-preemptively scheduling n independent jobs on m identical parallel machines so that the minimum (or earliest) machine completion time is maximized, we compare two well-known longest-first heuristics -the LPT-(longest processing time) and the RLPT-heuristic (restricted LPT).We prove that the minimum completion time of the LPT-schedule is at least as long as the minimum completion time of the RLPT-schedule. Furthermore, we show that the minimum completion time of the RLPT-heuristic always remains within a factor of 1/m of the optimal minimum completion time. The paper finishes with a conjecture on the probabilistic behavior of the RLPT-heuristic compared to the LPT-heuristic in case of two machines.

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Section: Previous Work and Intention Of The Papermentioning

confidence: 99%

Comparing the minimum completion times of two longest-first scheduling-heuristics

Walter

2011

Cent Eur J Oper Res

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“…It should be noted, that an additional, much stronger, semi-online variant was studied as well, where it is assumed that jobs arrive sorted by non-increasing processing time. In this variant, which is much closer to an offline problem than our model, the approximation ratio is at most 4 3 [11,12]. For uniformly related machines, no algorithm with finite approximation ratio exists even for two machines [4].…”

Section: Introductionmentioning

confidence: 99%

“…[18,12,11,24,6,15,17,2]). For identical machines, it is known that any online algorithm for identical machines has an approximation ratio of at least m (the proof is folklore, see [24,4]), and this bound can be achieved using a greedy algorithm which assigns each job to the least loaded machine, as was shown by Woeginger [24].…”

Section: Introductionmentioning

confidence: 99%

Max-min Online Allocations with a Reordering Buffer

Epstein

Levin

Stee³

2010

Automata, Languages and Programming

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Abstract. We consider online scheduling so as to maximize the minimum load, using a reordering buffer which can store some of the jobs before they are assigned irrevocably to machines. For m identical machines, we show an upper bound of Hm−1 + 1 for a buffer of size m − 1. A competitive ratio below Hm is not possible with any finite buffer size, and it requires a buffer of sizeΩ(m) to get a ratio of O(log m). For uniformly related machines, we show that a buffer of size m + 1 is sufficient to get an approximation ratio of m, which is best possible for any finite sized buffer. Finally, for the restricted assignment model, we show lower bounds identical to those of uniformly related machines, but using different constructions. In addition, we design an algorithm of approximation ratio O(m) which uses a finite sized buffer. We give tight bounds for two machines in all the three models. These results sharply contrast to the (previously known) results which can be achieved without the usage of a reordering buffer, where it is not possible to get a ratio below an approximation ratio of m already for identical machines, and it is impossible to obtain an algorithm of finite approximation ratio in the other two models, even for m = 2. Our results strengthen the previous conclusion that a reordering buffer is a powerful tool and it allows a significant decrease in the competitive ratio of online algorithms for scheduling problems. Another interesting aspect of our results is that our algorithm for identical machines imitates the behavior of the greedy algorithm on (a specific set of) related machines, whereas our algorithm for related machines completely ignores the speeds until the end, and then only uses the relative order of the speeds.

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“…Deuermeyer et al (1982) show that the longest processing time (LPT) heuristic has a performance guarantee of 3/4. This analysis has been tightened by Csirik et al (1992) who show that the exact worst-case ratio of LPT is (3m − 1)/(4m − 2).…”

Section: Introductionmentioning

confidence: 99%

“…This problem has been first described by Deuermeyer et al (1982) and is formally described as follows: a set J of n jobs has to be scheduled on m identical parallel machines (with n > m ≥ 2). Each job j ∈ J has to be processed non-preemptively for p j units of time.…”

Section: Introductionmentioning

confidence: 99%