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46
Better Bounds For Online Scheduling
 SIAM JOURNAL ON COMPUTING
, 1997
"... We study a classical problem in online scheduling. A sequence of jobs must be scheduled on m identical parallel machines. As each job arrives, its processing time is known. The goal is to minimize the makespan. Bartal, Fiat, Karloff and Vohra [3] gave a deterministic online algorithm that is 1.986c ..."
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Cited by 81 (5 self)
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We study a classical problem in online scheduling. A sequence of jobs must be scheduled on m identical parallel machines. As each job arrives, its processing time is known. The goal is to minimize the makespan. Bartal, Fiat, Karloff and Vohra [3] gave a deterministic online algorithm that is 1.986competitive. Karger, Phillips and Torng [11] generalized the algorithm and proved an upper bound of 1.945. The best lower bound currently known on the competitive ratio that can be achieved by deterministic online algorithms it equal to 1.837. In this paper we present an improved deterministic online scheduling algorithm that is 1.923competitive, for all m 2. The algorithm is based on a new scheduling strategy, i.e., it is not a generalization of the approach by Bartal et al. Also, the algorithm has a simple structure. Furthermore, we develop a better lower bound. We prove that, for general m, no deterministic online scheduling algorithm can be better than 1.852competitive.
Online scheduling
 ONLINE ALGORITHMS, LECTURE NOTES IN COMPUTER SCIENCE 1442
, 1998
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OnLine Scheduling  A Survey
, 1997
"... Scheduling has been studied extensively in many varieties and from many viewpoints. Inspired by applications in practical computer systems, it developed into a theoretical area with many interesting results, both positive and negative. The basic situation we study is the following. We have some sequ ..."
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Cited by 38 (0 self)
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Scheduling has been studied extensively in many varieties and from many viewpoints. Inspired by applications in practical computer systems, it developed into a theoretical area with many interesting results, both positive and negative. The basic situation we study is the following. We have some sequence of jobs that have to be processed on the machines available to us. In the most basic problem, each job is characterized by its running time and has to be scheduled for that time on one of the machines. In other variants there may be additional restrictions or relaxations specifying which schedules are allowed. We want to schedule the jobs as efficiently as possible, which most often means that the total length of the schedule (the makespan) should be as small as possible, but other objective functions are also considered. The notion of an online algorithm is intended to formalize the realistic scenario, where the algorithm does not have the access to the whole inp...
Approximation Schemes for Scheduling on Uniformly Related and Identical Parallel Machines
, 1999
"... We give a polynomial approximation scheme for the problem of scheduling on uniformly related parallel machines for a large class of objective functions that depend only on the machine completion times, including minimizing the l p norm of the vector of completion times. This generalizes and simp ..."
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Cited by 38 (9 self)
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We give a polynomial approximation scheme for the problem of scheduling on uniformly related parallel machines for a large class of objective functions that depend only on the machine completion times, including minimizing the l p norm of the vector of completion times. This generalizes and simplifies many previous results in this area. 1 Introduction Scheduling is one of fundamental areas of combinatorial optimization. Most multiprocessor scheduling problems are known to be hard to solve optimally (NPhard, see below). Thus the research focuses on giving efficient approximation algorithms that produce a solution close to the optimal one. Ideally, one hopes to obtain a family of polynomial algorithms such that for any given " ? 0 the corresponding algorithm is guaranteed to produce a solution with a cost within a factor of (1 + ") of the optimum cost; such a family is called a polynomial approximation scheme. A polynomial scheme for the basic problem of minimization of the total...
Techniques for Scheduling with Rejection
 in Algorithms—ESA ’98, Lecture Notes in Comput. Sci. 1461
, 1998
"... We consider the general problem of scheduling a set of jobs where we may choose not to schedule certain jobs, and thereby incur a penalty for each rejected job. More specifically, we focus on choosing a set of jobs to reject and constructing a schedule for the remaining jobs so as to optimize the su ..."
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Cited by 27 (3 self)
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We consider the general problem of scheduling a set of jobs where we may choose not to schedule certain jobs, and thereby incur a penalty for each rejected job. More specifically, we focus on choosing a set of jobs to reject and constructing a schedule for the remaining jobs so as to optimize the sum of the weighted completion times of the jobs scheduled plus the sum of the penalties of the jobs rejected.
Preemptive Multiprocessor Scheduling with Rejection
 Theoretical Computer Science
, 1999
"... The problem of online multiprocessor scheduling with rejection was introduced by Bartal, Leonardi, MarchettiSpaccamela, Sgall and Stougie [4]. They show that for this problem the competitive ratio is 1+ OE ß 2:61803, where OE is the golden ratio. A modified model of multiprocessor scheduling with r ..."
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Cited by 27 (3 self)
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The problem of online multiprocessor scheduling with rejection was introduced by Bartal, Leonardi, MarchettiSpaccamela, Sgall and Stougie [4]. They show that for this problem the competitive ratio is 1+ OE ß 2:61803, where OE is the golden ratio. A modified model of multiprocessor scheduling with rejection is presented where preemption is allowed. For this model, it is shown that better performance is possible. An online algorithm which is (4+ p 10)=3 ! 2:38743competitive is presented. We prove that the competitive ratio of any online algorithm is at least 2.12457. We say that an algorithm schedules obliviously if the accepted jobs are scheduled without knowledge of the rejection penalties. We also show a lower bound of 2.33246 on the competitive ratio of any online algorithm which schedules obliviously. As a subroutine in our algorithm, we use a new optimal online algorithm for preemptive scheduling without rejection. This algorithm never acheives a larger makespan than that of the...
SALSA: Strategyproof Online Spectrum Admissions for Wireless Networks
 IEEE Trans. on Computers
, 2010
"... Abstract—It is imperative to design efficient and effective online spectrum allocation methods since requests for spectrums often come in an online fashion. In this paper, we propose SALSA, strategyproof online spectrum admission for wireless networks. We assume that the requests arrival follows the ..."
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Abstract—It is imperative to design efficient and effective online spectrum allocation methods since requests for spectrums often come in an online fashion. In this paper, we propose SALSA, strategyproof online spectrum admission for wireless networks. We assume that the requests arrival follows the Poisson distribution. Upon receiving an online spectrum request, our protocol will decide immediately whether to grant its exclusive usage or not, and how much the request should pay. Preempting existing spectrum usage is not allowed. We proposed two protocols that have guaranteed performances for two different scenarios: 1) randomarrival case: the bid values and requested time durations follow some distributions that can be learned, or 2) semiarbitraryarrival case: the bid values could be arbitrary, but the request arrival sequence is random. We analytically prove that our protocols are strategyproof, and are both approximately social efficient and revenue efficient. Our extensive simulation results show that they perform almost optimum. Our method for semiarbitraryarrival model achieves social efficiency and revenue efficiency almost 2030 percent of the optimum, while it has been proven that no mechanism can achieve social efficiency ratio better than 1=e ’ 37 percent. Our protocol for the randomarrival case even achieves social efficiency and revenue efficiency twosix times the expected performances by the celebrated VCG mechanism. Index Terms—Wireless networks, spectrum, online allocation, competitive ratio, social efficiency, revenue efficiency. Ç 1
Truthful Online Spectrum Allocation and Auction in MultiChannel Wireless Networks
"... Abstract—We propose efficient spectrum channel allocation and auction methods for the online wireless channel scheduling. Assume that each user requests for the exclusive usage of a number of wireless channels for a certain time interval. The scheduler has to decide whether to grant its exclusive us ..."
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Abstract—We propose efficient spectrum channel allocation and auction methods for the online wireless channel scheduling. Assume that each user requests for the exclusive usage of a number of wireless channels for a certain time interval. The scheduler has to decide whether to grant its exclusive usage an how much will be charged. To possibly serve users with higher priority, preemptions are allowed with penalties. We analytically prove that our protocols are efficient, truthful, and they have asymptotically optimum competitive ratios. Our extensive simulations show that they perform almost optimum: most of our methods can achieve more than 50 % of the optimum by offline method. Index Terms—Spectrum, online algorithm, competitive ratio, wireless networks, mechanisms, strategyproof. I.
Online scheduling of unit time jobs with rejection: minimizing the total completion time
, 2002
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TOFU: SemiTruthful Online Frequency Allocation Mechanism for Wireless Networks
, 2009
"... In wireless networks, we need to allocate spectrum efficiently. One challenge is that the spectrum usage requests often come in an online fashion. The second challenge is that the secondary users in a cognitive radio network are often selfish and prefer to maximize their own benefits. In this paper, ..."
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Cited by 10 (3 self)
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In wireless networks, we need to allocate spectrum efficiently. One challenge is that the spectrum usage requests often come in an online fashion. The second challenge is that the secondary users in a cognitive radio network are often selfish and prefer to maximize their own benefits. In this paper, we address these two challenges by proposing TOFU, semitruthful online frequency allocation method for wireless networks when primary users can sublease the spectrums to secondary users. In our protocol, secondary users are required to submit the spectrum bid α timeslots before its usage. Upon receiving an online spectrum request, our protocol will decide whether to grant its exclusive usage or not, within at least γ timeslots of requests’ arrival. We assume that existing spectrum usage can be preempted with some compensation. For various possible known information, we analytically prove that the competitive ratios of our methods are within small constant factors of the optimum online method. Furthermore, in our mechanisms, no selfish users will gain benefits by bidding lower than its willing payment. Our extensive simulation results show that they perform almost optimum: our methods get a total profit that is more than 95 % of the offline optimum when γ is about the duration of spectrum usage ∆.