S. Goldman, J. Parwatikar and S. Suri, "On-line Scheduling with Hard Deadlines," Journal of Algorithms, Vol. 34, pp. 370-389, 2000.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....each one may produce little surplus. If we set deterministically any higher than 1, it is possible the algorithms will miss every pair, and have no surplus even when the optimal matching has surplus. Instead, as in [7] and similar to the Classify and Randomly Select approach [16, 1] see also [11]) we will choose randomly according to an exponential distribution. Speci cally, for all x 2 [1; p max p min ] let Pr[ x] ln(x) 1 The paraphrasing of this last point is a bit more extreme than the others, but it turns out that if there exists a perfect matching on W and a perfect ....

S. Goldman, J. Parwatikar, and S. Suri. On-line scheduling with hard deadlines. Journal of Algorithms, 34:370-389, 2000.

....each one may produce little surplus. If we set 0 deterministically any higher than 1, it is possible the algorithms will miss every pair, and have no surplus even when the optimal matching has surplus. Instead, as in [7] and similar to the Classify andRandomly Select approach [16, 1] see also [11]) we will choose 0 randomly according to an exponential distribution. Specifically, for all x C [1,p . Pi] let ln( 1 Pr[0 ln(p . 1 . Observe that this is where Pr[O = 1] h(p . p . a valid probability distribution. Let OPT be the surplus achieved by the optimal ....

S. Goldman, J. Parwatikar, and S. Suri. On-line scheduling with hard deadlines. Journal of Algorithms, 34:370 389, 2000.

....each one may produce little surplus. If we set # deterministically any higher than 1, it is possible the algorithms will miss every pair, and have no surplus even when the optimal matching has surplus. Instead, as in [7] and similar to the Classify and Randomly Select approach [16, 1] see also [11]) we will choose # randomly according to an exponential distribution. Specifically, for all [1,p max p min ] let The paraphrasing of this last point is a bit more extreme than the others, but it turns out that if there exists a perfect matching on W and a perfect matching on W # W ....

S. Goldman, J. Parwatikar, and S. Suri. On-line scheduling with hard deadlines. Journal of Algorithms, 34:370--389, 2000.

....of intervals on a single machine (resource) where the objective is to maximize the resource utilization. They gave an O(log R) competitive (O( log R) 1 ffl ) competitive) randomized algorithm for some ffl 0, where R is the (unknown) ratio of longest to shortest interval. Later works [17, 18] consider a variant of the problem, where each interval (job) offers a slack, i.e. the maximal possible delay from the time it arrives until it is scheduled. Call admission. Interval scheduling can be viewed as a call admission problem on a line, where the objective is to maximize the number of ....

S. Goldman, J. Parwatikar, and S. Suri. "On-line Scheduling with Hard Deadlines". In WADS '97, 258-- 271.

.... Adapting their constructions to our model where the value of Delta is known results in bounds R 2 (0; Delta) 2 Gamma 1 Delta and R(0; Delta) is Omega Gamma 49 Delta) Goldman, Parwatikar and Suri extended the model of Lipton and Tomkins, allowing jobs to specify arbitrary slacks [10]. They make no assumptions on the slacks specified by jobs and so this setting corresponds exactly to the case = 0 in our model. The existence of slack acts as a double edged sword for competitive analysis. Clearly the added flexibility can only serve to increase the resource utilization for an ....

....processing times has been studied in several other models. The advantage of patience on competitiveness for scheduling single processors preemptively has been studied. Baruah and Haritsa give almost tight bounds for maximizing the 4 Equal length jobs D 1 ( R 1 ( LB UB LB UB = 0 2 4=3 From [10] From [10] From [10] 0 1 1 bc 1 1 1 2bc 3 (Thm. 19) Thm. 11) Thm. 19) Table 1: The lower upper bounds for the deterministic randomized competitiveness of the problem when all job lengths are equal. The best currently known randomized upper bounds are equivalent to the deterministic ....

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S. Goldman, J. Parwatikar, and S. Suri. On-line scheduling with hard deadlines. J. Algorithms, 34(2):370--389, 2000.

....providing such notification can be nothing but a hindrance to the scheduler. Remarkably though, we are able to give alternate algorithms which provide immediate notification while matching most of the best possible performance bounds achieved by schedulers which provide no advanced notification [10, 11]. There does exist one case for which we are able to give evidence that providing immediate notification may indeed be strictly more difficult. 1.1 Definitions Following the standard notation of Graham et al. 12] we consider a job J i to be a triple of nonnegative integers hr i ; p i ; d i i, ....

....while meeting the same bounds on performance as previous algorithms which do not provide any type of advanced notification. Specifically, we give algorithms providing immediate notification while matching the following competitiveness bounds given by previous algorithms without notification [10, 11]: ffl For the case when all job lengths are equal, we present a deterministic algorithm which provides immediate notification. This algorithm is 2 competitive in general, and is (1 1 bc 1 ) competitive where 0 is the patience of the instance. ffl For the case when arbitrary job lengths ....

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S. Goldman, J. Parwatikar, and S. Suri. On-line scheduling with hard deadlines. Journal of Algorithms, 34(2):370--389, Feb. 2000. 16

....each one may produce little surplus. If we set deterministically any higher than 1, it is possible the algorithms will miss every pair, and have no surplus even when the optimal matching has surplus. Instead, as in [7] and similar to the Classify andRandomly Select approach [16, 1] see also [11]) we will choose randomly according to an exponential distribution. Specifically, for all x 2 [1; pmax Gamma pmin ] let Pr[ x] ln(x) 1 ln(p max Gamma pmin ) 1 ; where P r[ 1] 1 ln(pmax Gammap min) 1 . Observe that this is a valid probability distribution. Let OPT be the ....

S. Goldman, J. Parwatikar, and S. Suri. On-line scheduling with hard deadlines. Journal of Algorithms, 34:370--389, 2000.

....[23] considered the non preemptive version of the on line problem, while Koren and Shasha [19] and Baruah et al. 7] considered the preemptive version. The special cases where the weight of a job is proportional to the processing time were considered in the on line setting in several papers [5, 10, 12, 15, 16, 6]. Our combinatorial algorithm for arbitrary weights borrows some of the techniques used in the on line case. Some of our algorithms are based on rounding a fractional solution obtained from a linear programming (LP) relaxation of the problem. In the LP formulation for a single machine we have a ....

S.A. Goldman, J. Parwatikar and S. Suri, On-line scheduling with hard deadlines, Proc. 5th International Workshop on Algorithms and Data Structures, Lecture Notes in Computer Science, Vol. 1272, pp. 258-271, 1997.

.... A special case of this problem, studied by Lipton and Tomkins, is when all jobs have delay exactly zero, and thus immediately need to be scheduled or else lost [8] This model was then generalized to include delays by Goldman et al. where they allow each job to specify an arbitrary delay [6]. Notice that the existence of delays, in general, acts as a double edged sword. Clearly, the existence of delays can only help a scheduler in increasing the resource utilization, as it offers more flexibility for scheduling jobs. However in terms of competitive analysis, delays may create more ....

....which does not depend on the maximum length job. We provide a lower bound showing that this is the best possible deterministic result, even when all jobs have one of three distinct lengths. In the special case where all jobs are required to have the same length (e.g. packets in an ATM network) [6], we generalize previous results, showing that the natural greedy algorithm is 1 1 b c 1 competitive, and again that this is the best possible deterministic result. In the case where jobs have one of two distinct lengths, we give tight bounds improving slightly on the (2 1 ) bound for ....

[Article contains additional citation context not shown here]

S. Goldman, J. Parwatikar, and S. Suri. On-line scheduling with hard deadlines. In Proc. of the Workshop on Algorithms and Data Structures, volume 1272 of Lecture Notes in Computer Science, pages 258--271. Springer-Verlag, 1997.

....time or laxity by previous researchers. 2 customer requesting 5 hours of time must be willing to wait at least 15 minutes instead. Measuring the slack in relation to a job s processing time is quite natural for admission control and similar restrictions have been examined in related models [4, 6, 8, 10]. The main result of our paper is that the competitiveness of online scheduling algorithms is significantly improved when instances have non zero patience. When arbitrary slacks are allowed (i.e. when # = 0) a previous lower bound shows that even if randomization is allowed, the competitiveness ....

....are required to have the same length (e.g. packets in an ATM network) we show that the natural greedy algorithm is (1 1 ### 1 ) competitive, and again that this is the best possible deterministic result. This result generalizes a previous bound of 2 competiveness for the case when # = 0 [10]. In the case where jobs have one of two distinct lengths, we give tight upper and lower bounds which improve slightly on the (2 1 # ) bound for arbitrary lengths. A complete summary of our upper and lower bounds when parameterized by # is given in Table 1. A more complete set of bounds when ....

[Article contains additional citation context not shown here]

S. Goldman, J. Parwatikar, and S. Suri. On-line scheduling with hard deadlines. In Proceedings of the Workshop on Algorithms and Data Structures, volume 1272 of Lecture Notes in Computer Science, pages 258-- 271. Springer-Verlag, 1997.

....is given with competitive ratio O(min(log Phi; log Delta) and this is shown to be optimal. In [1] a nonconstant deterministic lower bound for the case that = 1 is given. For nonpreemptive scheduling with Phi = 1, there is an O(log Delta) competitive randomized algorithm and this is optimal [3, 9]. Faults completely change the nature of these scheduling problems. There seems to be little research that uses competitive analysis to study fault tolerance. In [4] fault tolerant scheduling of jobs without deadlines is studied, and optimal deterministic and randomized algorithms are given for ....

S. Goldman, J. Parwatikar, S. Suri, "On-line scheduling with hard deadlines", Workshop on Algorithms and Data Structures, 258--271, 1997.

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S. Goldman, J. Parwatikar and S. Suri, "On-line Scheduling with Hard Deadlines," Journal of Algorithms, Vol. 34, pp. 370-389, 2000.

No context found.

S.A. Goldman, J. Parwatikar and S. Suri, On-line scheduling with hard deadlines, Proc. 5th International Workshop on Algorithms and Data Structures, Lecture Notes in Computer Science, Vol. 1272, pp. 258--271, 1997.

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