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34
(Incremental) Priority algorithms
, 2003
"... We study the question of which optimization problems can be optimally or approximately solved by "greedylike " algorithms. For definiteness, we will limit the present discussion to some wellstudied scheduling problems although the underlying issues apply in a much more general ..."
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Cited by 42 (10 self)
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We study the question of which optimization problems can be optimally or approximately solved by &quot;greedylike &quot; algorithms. For definiteness, we will limit the present discussion to some wellstudied scheduling problems although the underlying issues apply in a much more general setting. Of course, the main benefit of greedy algorithms lies in both their conceptual simplicity and their computational efficiency. Based on the experience from online competitive analysis, it seems plausible that we should be able to derive approximation bounds for &quot;greedylike &quot; algorithms exploiting only the conceptual simplicity of these algorithms. To this end, we need (and will provide) a precise definition of what we mean by greedy and greedylike.
A Lower Bound for OnLine Scheduling on Uniformly Related Machines
, 1999
"... We consider the problem of online scheduling of jobs arriving one by one on uniformly related machines, with or without preemption. We prove a lower bound of 2, both with and without preemption, for randomized algorithms working for an arbitrary number of machines. For a constant number of machines ..."
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Cited by 29 (13 self)
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We consider the problem of online scheduling of jobs arriving one by one on uniformly related machines, with or without preemption. We prove a lower bound of 2, both with and without preemption, for randomized algorithms working for an arbitrary number of machines. For a constant number of machines we give new lower bounds for the preemptive case.
Randomized Online Scheduling on Two Uniform Machines
"... We study the problem of online scheduling on two uniform machines withspeeds 1 and s * 1. A OE ss 1.61803 competitive deterministic algorithm was already known. We present the first randomized results for this problem: We show that randomization does not help for speeds s * 2, but does help for al ..."
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Cited by 26 (15 self)
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We study the problem of online scheduling on two uniform machines withspeeds 1 and s * 1. A OE ss 1.61803 competitive deterministic algorithm was already known. We present the first randomized results for this problem: We show that randomization does not help for speeds s * 2, but does help for all s! 2. We present a simple memoryless randomized algorithm with competitive ratio (4 \Gamma s)(1 + s)=4 ^ 1.56250. We analyze other randomized algorithms that demonstrate that the randomized competitive ratio is at most 1.52778 for any s. Thesealgorithms are barely random, i.e., they use only a constant number of random bits. Finally, we present a 1 + s/(s² + s + 1) competitive deterministic algorithm for the preemptive version of this problem. For any s, it is best possible evenamong randomized preemptive algorithms.
Online scheduling for sorting buffers
 In Proceedings of the 10th European Symposium on Algorithms (ESA
, 2002
"... Abstract. We introduce the online scheduling problem for sorting buffers. A service station and a sorting buffer are given. An input sequence of items which are only characterized by a specific attribute has to be processed by the service station which benefits from consecutive items with the same a ..."
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Cited by 22 (2 self)
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Abstract. We introduce the online scheduling problem for sorting buffers. A service station and a sorting buffer are given. An input sequence of items which are only characterized by a specific attribute has to be processed by the service station which benefits from consecutive items with the same attribute value. The sorting buffer which is a random access buffer with storage capacity for k items can be used to rearrange the input sequence. The goal is to minimize the cost of the service station, i.e., the number of maximal subsequences in its sequence of items containing only items with the same attribute value. This problem is motivated by many applications in computer science and economics. The strategies are evaluated in a competitive analysis in which the cost of the online strategy is compared with the cost of an optimal offline strategy. Our main result is a deterministic strategy that achieves a competitive ratio of O(log 2 k). In addition, we show that several standard strategies are unsuitable for this problem, i.e., we prove a lower bound of Ω ( √ k) on the competitive ratio of the First In First Out (FIFO) and Least Recently Used (LRU) strategy and of Ω(k) on the competitive ratio of the Largest Color First (LCF) strategy. 1
Optimal Preemptive SemiOnline Scheduling to Minimize Makespan on Two Related Machines
 Operations Research Letters
, 2002
"... We study a preemptive semionline scheduling problem. Jobs with nonincreasing sizes arrive one by one to be scheduled on two uniformly related machines. We analyze the algorithms as a function of the speed ratio (q 1) between the two machines. We design algorithms of optimal competitive ratio ..."
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Cited by 17 (2 self)
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We study a preemptive semionline scheduling problem. Jobs with nonincreasing sizes arrive one by one to be scheduled on two uniformly related machines. We analyze the algorithms as a function of the speed ratio (q 1) between the two machines. We design algorithms of optimal competitive ratio for all values of q, and show that for q > 2, idle time needs to be introduced. This is the rst preemptive scheduling problem over list, where idle time is provably required.
Preemptive Scheduling in Overloaded Systems (Extended Abstract)
, 2002
"... We study the problem of scheduling a set of preemptive tasks, where each task j is specified by its release time r j , deadline d j , processing time p j , and weight w j representing its profit rate. ..."
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Cited by 14 (1 self)
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We study the problem of scheduling a set of preemptive tasks, where each task j is specified by its release time r j , deadline d j , processing time p j , and weight w j representing its profit rate.
Scheduling parallel jobs to minimize the makespan
, 2006
"... We consider the NPhard problem of scheduling parallel jobs with release dates on identical parallel machines to minimize the makespan. A parallel job requires simultaneously a prespecified, jobdependent number of machines when being processed. We prove that the makespan of any nonpreemptive list ..."
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Cited by 13 (0 self)
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We consider the NPhard problem of scheduling parallel jobs with release dates on identical parallel machines to minimize the makespan. A parallel job requires simultaneously a prespecified, jobdependent number of machines when being processed. We prove that the makespan of any nonpreemptive listschedule is within a factor of 2 of the optimal preemptive makespan. This gives the bestknown approximation algorithms for both the preemptive and the nonpreemptive variant of the problem. We also show that no listscheduling algorithm can achieve a better performance guarantee than 2 for the nonpreemptive problem, no matter which priority list is chosen. Listscheduling also works in the online setting where jobs arrive over time and the length of a job becomes known only when it completes; it therefore yields a deterministic online algorithm with competitive ratio 2 as well. In addition, we consider a different online model in which jobs arrive one by one and need to be scheduled before the next job becomes known. We show that no listscheduling algorithm has a constant competitive ratio. Still, we present the first online algorithm for scheduling parallel jobs with a constant competitive ratio in this context. We also prove a new informationtheoretic lower bound of 2.25 for the competitive ratio of any deterministic online algorithm for this model. Moreover, we show that 6/5 is a lower bound for the competitive ratio of any deterministic online algorithm of the preemptive version of the model jobs arriving over time.
Equilibria Strategies for Selecting Sellers and Satisfying Buyers
 Cooperative Information Agents V, LNAI
, 2001
"... Dynamism of trade activity inevitably results in situations where sellers face local supply shortages. In such cases, sellers need to decide which buyer purchase requests to satisfy. Commonly, sellers satisfy purchase requests based on their arrival order, i.e., First In is First Served (FIFS). ..."
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Cited by 10 (3 self)
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Dynamism of trade activity inevitably results in situations where sellers face local supply shortages. In such cases, sellers need to decide which buyer purchase requests to satisfy. Commonly, sellers satisfy purchase requests based on their arrival order, i.e., First In is First Served (FIFS). In electronic trade, sellers may follow strategies different from FIFS without the buyers being able to detect this difference.
Optimal Preemptive Scheduling on Uniform Processors With NonDecreasing Speed Ratios
 Oper. Res. Lett
, 2000
"... We study preemptive scheduling on uniformly related processors, where jobs are arriving one by one in an online fashion. We consider the class of machine sets where the speed ratios are nondecreasing as speed increases. For each set of machines in this class, we design an algorithm of optimal compe ..."
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Cited by 10 (0 self)
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We study preemptive scheduling on uniformly related processors, where jobs are arriving one by one in an online fashion. We consider the class of machine sets where the speed ratios are nondecreasing as speed increases. For each set of machines in this class, we design an algorithm of optimal competitive ratio. This generalizes the known result for identical machines, and solves other interesting cases. 1 Introduction We consider online scheduling on m uniformly related machines. Jobs arrive online, and each job has to be assigned before the next job arrives. This scheduling model is called "scheduling jobs one by one" (see [9]). Preemption is allowed, hence each job may be cut into a few pieces. These pieces are to be assigned to possibly different machines, in nonoverlapping time slots. (Nonpreemptive algorithms are not allowed to cut the job and have to assign it continuously to one machine.) School of Computer and Media Sciences, The Interdisciplinary Center, P.O.B. 167, 4...