Performance guarantee for online deadline scheduling in the presence of overload

Earliest deadline first (EDF) is a widely-used online algorithm for scheduling jobs with deadlines in real-time systems. Yet, existing results on the performance guarantee of EDF are limited to underloaded systems [6,12,14]. This paper initiates the study of EDF for overloaded systems, attaining similar performance guarantees as in the underloaded setting. Specifically, we show that EDF with a simple form of admission control is optimal for scheduling on both uniprocessor and multiprocessors when moderately faster processors are available (our analysis actually admits a tradeoff between speed and extra processors). This is the first result attaining optimality under overload. Another contribution of this paper is an improved analysis of the competitiveness for weighted deadline scheduling.published_or_final_versio

Improved parallel algorithms for finding connected components

Finding the connected components of a graph is a basic computational problem. In recent years, there were several exciting results in breaking the log2 n-time barrier to finding connected components on parallel machines using shared memory without concurrent-write capability. This paper further presents two new parallel algorithms both using less than log2 n time. The merit of the first algorithm is that it uses only a sublinear number of processors, yet retains the time complexity of the fastest existing algorithm. The second algorithm is slightly slower but its work (i.e., the time-processor product) is closer to optimal than all previous algorithms using less than log2 n time.published_or_final_versio

Extra processors versus future information in optimal deadline scheduling

This paper is concerned with the extra-resource analysis of online scheduling algorithms. In particular, it studies how to make use of multiple processors to counteract the lack of future information in online deadline scheduling. Our results extend the previous work that are primarily based on using a faster processor to obtain a performance guarantee. The challenge arises from the fact that jobs are sequential in nature and cannot be executed on more than one processor at the same time. Thus, a faster processor can speed up a job while multiple unit-speed processors cannot help.postprin

Competitive deadline scheduling via additional or faster processors

This paper studies on-line scheduling in a single-processor system that allows preemption. The aim is to maximize the total value of jobs completed by their deadlines. It is known that if the on-line scheduler is given a processor faster (say, two times faster) than the off-line scheduler, then there exists an on-line algorithm called SLACKER that can achieve an O(1) competitive ratio. In this paper, we show that using additional unit-speed processors instead of a faster processor is a possible but not cost effective way to achieve an O(1) competitive ratio. Specifically, we find that-θ(log k) unit-speed processors are required, where k is the importance ratio. Another contribution of this paper is an improved analysis of the competitiveness of SLACKER; this new analysis enables us to show that SLACKER, when extended to multi-processor systems, can still guarantee an O(1) competitive ratio.postprin

Nonmigratory online deadline scheduling on multiprocessors

In this paper we consider multiprocessor scheduling with hard deadlines and investigate the cost of eliminating migration in the online setting. Let I be any set of jobs that can be completed by some migratory offline schedule on m processors. We show that I can also be completed by a nonmigratory online schedule using m speed-5.828 processors (i.e., processors 5.828 times faster). This result supplements the previous results that I can also be completed by a non-migratory offline schedule using 6m unit-speed processors [B. Kalyanasundaram and K. R. Pruhs, J. Algorithms, 38 (2001), pp. 2-24] or a migratory online schedule using m speed-2 processors [C. A. Phillips et al., Algorithmica. 32 (2002), pp. 163-200]. Our result is based on a simple conservative scheduling algorithm called PARK, which commits a processor to a job only when the processor has zero commitment before its deadline. A careful analysis of PARK further shows that the processor speed can be reduced arbitrarily close to 1 by exploiting more processors (say, using 16m speed-1.8 processors). PARK also finds application in overloaded systems; it gives the first online nonmigratory algorithm that can exploit moderately faster processors to match the performance of any migratory offline algorithm. © 2005 Society for Industrial and Applied Mathematics.published_or_final_versio

A simple and economical method for improving whole genome alignment

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Extra unit-speed machines are almost as powerful as speedy machines for flow time scheduling

We study online scheduling of jobs to minimize the flow time and stretch on parallel machines. We consider algorithms that are given extra resources so as to compensate for the lack of future information. Recent results show that a modest increase in machine speed can provide very competitive performance; in particular, using O(1) times faster machines, the algorithm SRPT (shortest remaining processing time) is 1-competitive for both flow time [C. A. Phillips et al., in Proceedings of STOC, ACM, New York, 1997, pp. 140-149] and stretch [W. T. Chan et al., in Proceedings of MFCS, Springer-Verlag, Berlin, 2005, pp. 236-247] and HDF (highest density first) is O(1)-competitive for weighted flow time [L. Becchetti et al., in Proceedings of RANDOM-APPROX, Springer-Verlag, Berlin, 2001, pp. 36-47]. Using extra unit-speed machines instead of faster machines to achieve competitive performance is more challenging, as a faster machine can speed up a job but extra unit-speed machines cannot. This paper gives a nontrivial relationship between the extra-speed and extra-machine analyses. It shows that competitive results via faster machines can be transformed to similar results via extra machines, hence giving the first algorithms that, using O(1) times unit-speed machines, are 1-competitive for flow time and stretch and O(1)-competitive for weighted flow time. © 2008 Society for Industrial and Applied Mathematics.published_or_final_versio

Dynamic bin packing of unit fractions items

LNCS v. 3580 entitled: Automata, Languages and Programming: 32nd International Colloquium, ICALP 2005, Lisbon, Portugal, July 11-15, 2005. ProceedingsThis paper studies the dynamic bin packing problem, in which items arrive and depart at arbitrary time. We want to pack a sequence of unit fractions items (i.e., items with sizes 1/ω for some integer w ≥ 1) into unit-size bins such that the maximum number of bins used over all time is minimized. Tight and almost-tight performance bounds are found for the family of any-fit algorithms, including first-fit, best-fit, and worst-fit. We show that the competitive ratio of best-fit and worst-fit is 3, which is tight, and the competitive ratio of first-fit lies between 2.45 and 2.4985. We also show that no on-line algorithm is better than 2.428-competitive. This result improves the lower bound of dynamic bin packing problem even for general items. © Springer-Verlag Berlin Heidelberg 2005.postprin

A tighter extra-resource analysis of online deadline scheduling

This paper is concerned with online algorithms for scheduling jobs with deadlines on a single processor. It has been known for long that unless the system is underloaded, no online scheduling algorithm can be 1-competitive, i.e., matching the performance of the optimal offline algorithm. Nevertheless, recent work has revealed that some online algorithms using a moderately faster processor (or extra processors) can guarantee very competitive performance Kalyanasundaram and Pruhs, 2000 or even be 1-competitive Koo et al., 2002; Lam and To, 2001. This paper takes a further step to investigate online scheduling algorithms with an even higher performance guarantee (i.e., better than 1-competitive algorithms) and in particular, presents an extra-resource analysis of the earliest-deadline-first strategy (EDF) with respect to such a higher performance guarantee. © 2005 Springer Science + Business Media, Inc.postprin

PnpProbs: A better multiple sequence alignment tool by better handling of guide trees

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