Woeginger, G. (1994), `On-line scheduling of jobs with fixed start and end times', Theoretical Computer Science 130, 5--16.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....algorithm that can guarantee to attain more than one fourth of the processor utilization of the optimal offline algorithm. Another way to express this result is that the competitive ratio of any on line algorithm is at least 4. This lower bound is tight as matching algorithms are also known [1, 9, 14]. In recent years, there are a number of exciting results on improving performance guarantee without making assumption on future inputs; the basic idea is to allow the online scheduler to have more resources than the adversary (e.g. 3, 6 8, 10 12] For the single processor deadline ....

G. Woeginer. On-line scheduling of jobs with fixed start and end time. Theoretical Computer Science, 130:5--16, 1994.

....right endpoint. However, it is easy to see that single pass algorithms that process the intervals in order of non increasing weight or in order of non decreasing left endpoint do not have a finite worst case ratio (even in the case when each job consists of one interval only, see Woeginger [28], and even if randomization is allowed, see Canetti and Irani [6] Therefore, we investigate in this paper the special class of single pass algorithms, which we call myopic algorithms, that arise when the intervals are processed in order of non decreasing right endpoint. Thus, myopic algorithms ....

G. Woeginger. On-line scheduling of jobs with fixed start and end times. Theoretical Computer Science, 130:5--16, 1994.

....able to accept and complete all orders. An order selection policy is needed to help the manufacturer determine which orders to accept and reject. Some previous work has been done on combined order selection and scheduling to maximize total revenue or the total value of the accepted orders ( 2] 9] [23]) These papers assume that orders have strict release times and due dates within which they must be completed. In most of these papers, the required due date is equal to the arrival time of the order plus the processing time, hence, an order must be processed as soon as it ariSyes, or it is lost. ....

Woeginger, G.J., "On-line scheduling of jobs with fixed start and end times", Theoretical Computer Science, Vol. 130, 1994, 5-16.

....where a schedule is a subset of non overlapping intervals. Lipton and Tomkins [6] study a variant where the input intervals are sorted by their left endpoints. They give a randomized scheduler that is 2 competitive. As we will see, our problem is di#erent from theirs in several ways. Woeginger [10] studied a problem that has several of the features of our problem. Other online interval packing problems can be found in [11, 5] Outline. In the next section, we formulate our on line scheduling problem and give two schedulers, FirstFit and EndFit. FirstFit is based on a heuristic which always ....

G. J. Woeginger. On-line scheduling of jobs with fixed start and end times. Theor. Computer Science, 130:5--16, 1994.

....computes the maximum matching with small change that comprimises two opposing goals: maximum matching and minimization of aborts of scheduled jobs. This upper bound is compensated by the lower bounds 8 #, which is obtained by extending the lower bound 4 in the interval scheduling problem [12]. Related Work There have been many researches on the problem of scheduling communication jobs without deadlines. In general, they adopted the discrete model of time and aimed to minimize the total time required for the completion of all communication jobs. Gopal and Wong [4] formulated this ....

....ratio 7 6 . Jain, et al. 7, 6, 8] studied many variants of this problem raised in I O platform. However, in these works, neither deadline constraints nor online algorithms were considered. Our problem is an extension of the interval scheduling problem, which was introduced by Woeginger [12]. In the interval scheduling problem, entire system includes only two communication nodes (thus, every communication jobs occur between the two nodes and at most one communication job can be scheduled at a time) and the expiration time x j of a job J j equals the release time r j (usually termed ....

[Article contains additional citation context not shown here]

G.J. Woeginger. On-line scheduling of jobs with fixed start and end times. Theoretical Computer Science, 130:5--16, 1994.

....where a schedule is a subset of non overlapping intervals. Lipton and Tomkins [6] study a variant where the input intervals are sorted by their left endpoints. They give a randomized scheduler that is 2 competitive. As we will see, our problem is di#erent from theirs in several ways. Woeginger [10] studied a problem that has several of the features of our problem. Other online interval packing problems can be found in [11, 5] Outline. In the next section, we formulate our on line scheduling problem and give two schedulers, FirstFit and EndFit. FirstFit is based on a heuristic which always ....

G. J. Woeginger. On-line scheduling of jobs with fixed start and end times. Theor. Computer Science, 130:5--16, 1994.

....A schedule here is a subset of non overlapping intervals. Lipton and Tomkins [9] study a variant where the input intervals are sorted by their left endpoints. They give a randomized scheduler that is 2 competitive. As we will see, our problem is di#erent from theirs in several ways. Woeginger [15] studied a problem that has several of the features of our problem (see below) Other online interval packing problems can be found in [13, 8] Outline. In the next section, we formulate our on line scheduling problem and give two schedulers, FirstFit and EndFit. We then generalize both ....

Gerhard J. Woeginger. On-line scheduling of jobs with fixed start and end times. Theoretical Computer Science, 130:5--16, 1994. 15

....A schedule here is a subset of non overlapping intervals. Lipton and Tomkins [8] study a variant where the input intervals are sorted by their left endpoints. They give a randomized scheduler that is 2 competitive. As we will see, our problem is different from theirs in several ways. Woeginger [14] studied a problem that has several of the features of our problem (see below) Other online interval packing problems can be found in [12, 7] 2 Problem Formulation We formalize our problem as a reservation problem. Each (reservation) request q has five parameters q = r; s; t; v; w) where r ....

....served. The reservation nature of q comes from the fact that r can be less than s, and the request has an explicit span. Multimedia applications such as video on demand need such reservation properties: a customer may request for one hour of viewing time in some future time. Woeginger [14] study the case r = s and t Gamma s = v. Write rt(q) st(q) dl(q) sz(q) wt(q) for the above parameters of q, respectively. An instance I is a sequence (q 1 ; q 2 ; q n ) of requests where the release times of the q i s are in increasing order: note that we allow rt(q i ) rt(q i 1 ) ....

Gerhard J. Woeginger. On-line scheduling of jobs with fixed start and end times. Theoretical Computer Science, 130:5--16, 1994.

....is very different from the previous three. For example, it is meaningless to measure the length of the schedule, as it is essentially fixed; instead we measure the weight (or the number) of accepted jobs. We do not cover this paradigm in this survey. It is studied for example in the papers [83, 62, 32], and it is also related to load balancing [5] 2.3 Objective functions The most common objective function is the makespan, which is the length of the schedule, or equivalently the time when the last job is completed. In one of the variations we allow jobs to be rejected at a certain penalty, in ....

G. J. Woeginger. On-line scheduling of jobs with fixed start and end times. Theoretical Comput. Sci., 130:5--16, 1994. This article was processed using the L a T E X macro package with LLNCS style

....algorithm [13] Hence, Lawler s algorithm runs in polynomial time on the unit benefit versions of these problems. For the online version of 1 j r i ; pmtn j P x i (1 Gamma U i ) there is a 4 competitive deterministic algorithm, and this is optimal for deterministic online algorithms [2, 15]. There is no constant competitive deterministic or randomized online algorithm for 1 j r i ; pmtn j P (1 Gamma U i )w i [9, 12] However, in [8] it is shown that if the online scheduler is given a faster processor than the adversary, then there is a relatively simple deterministic online ....

G. Woeginger, "On-line scheduling of jobs with fixed start and end time", Theoretical Computer Science, 130, 5--16, 1994..

....show that no randomized on line algorithm can have a lower competitive ratio. 1 Introduction 1.1 Problem Statement We consider randomized algorithms for on line real time scheduling in a multi processor system that may experience processor faults. We model this problem in the standard way (e.g. [1, 2, 3, 4, 6]) The setting is a collection P = fP 1 ; Pm g of processors that see over time a collection J = fJ 1 ; J n g of jobs. Each job J i has a release time r i , a length x i , a deadline d i , and a benefit b i . The on line algorithm is unaware of J i until time r i . At time r i the ....

....characteristic we consider is the ratio of the length of the longest job to the length of the shortest job. We denote this ratio by Delta. Another useful parameter will be = min( Phi; Delta) An important special case, called the uniform value density case, of this problem is when Phi = 1 [1, 2, 6], In this case, under the assumption that running a job that will eventually be abandoned is not useful, the multiplicative inverse of the competitive ratio indicates the fraction of time that the processors were doing useful work. 1.2 Previous Results We first survey prior work that assumed ....

[Article contains additional citation context not shown here]

G. Woeginger, "On-line scheduling of jobs with fixed start and end time", to appear, Theoretical Computer Science.

....University of Pittsburgh, Pittsburgh, PA 15260. E Mail: kalyan cs.pitt.edu y Department of Computer Science, University of Pittsburgh, Pittsburgh, PA 15260. E Mail: kirk cs.pitt.edu 1. 1 Problem Statement We adopt best effort firm real time scheduling, a standard model of real time computation [1, 2, 5, 7, 8, 11], as our model of real time computation. The setting is a collection P 1 ; Pm of unit speed processors. The scheduler sees over time a collection J 1 ; J n of jobs. Each job J i has a release time r i , a processing time x i , a deadline d i , and a benefit b i . Unless we state ....

....of the following results are for a single processor with preemption unless stated otherwise. Let be the ratio of the largest benefit of a job to the minimum benefit of a job. There are 4 competitive algorithms for the cases Phi = 1 or Delta = 1, and this is optimal for deterministic algorithms [2, 11]. The optimal competitive ratio is Theta( Phi) 2, 7] In [2] a 2 competitive algorithm for interval scheduling is given for the case Phi = 1 and m = 2. This immediately yields a 2 competitive randomized algorithm for interval scheduling for Phi = 1 and m = 1. A 3=2 lower bound on the ....

G. Woeginger, "On-line scheduling of jobs with fixed start and end time", Theoretical Computer Science, 130, 5--16, 1994..

....complex and unintuitive and it is not clear how it can benefit from the knowledge of statistical information, such as request popularities. Finally, we should note that allowing preemption of requests can lead to better competitive ratios for on line scheduling and admission control problems [7, 9, 14, 15, 20, 33]. However, the assumption of preemptability is unrealistic in the context of CM applications. 3 Problem Formulation We view a CM database server as a black box capable of offering a sustained bandwidth capacity of B. The input sequence consists of a collection of requests oe = oe 1 ; oe 2 ; ....

Gerhard J. Woeginger. "On-line Scheduling of Jobs with Fixed Start and End Times". Theoretical Computer Science, 130:5--16, 1994.

....deadlines. The literature about scheduling theory is extremely rich. A good introduction is [4] and [2] which also deals with resource constraints. 9] gives a survey about up to date online scheduling research whereas online interval scheduling with fixed start and end times is investigated in [8, 11]. The design of ICMS is a very active area of worldwide theoretical and experimental research (e.g. see [1, 3, 5, 6] The work presented in this paper has been accomplished in the context of the SICMA project. This project, funded by the commission of the European community, aims at developing a ....

....3 . Nevertheless, we want to serve as many requests as possible. So the performance of an algorithm ALG for DAP or RDAP under an input r is the number of successful requests, i.e. the number of delivered data packets, and it is denoted by PALG (r) This objective function follows ideas of [8, 11] where no benefit is paid when a job violates its deadline. Following the well known definition of competitiveness, we say an online algorithm A is ae competitive if there is a constant ff such that for all inputs r POPT (r) ae PA (r) ff : The competitive ratio is then the infimum over ....

G. J. Woeginger. On-line scheduling of jobs with fixed start and end times. Theoretical

....with bounded competitive ratios on all inputs that are not closely correlated with processor speed. 1 Introduction We consider several well known nonclairvoyant scheduling problems, including the problem of minimizing the average response time [13, 15] and besteffort firm real time scheduling [1, 2, 3, 4, 8, 11, 12, 18]. We postpone formally defining these problems until the next section. In nonclairvoyant scheduling some relevant information, e.g. when jobs will arrive in the future, is not available to the scheduling algorithm A. The standard way to measure the adverse effect of this lack of knowledge is ....

....Since this is a maximization problem, the competitive ratio definitions in the introduction have to be modified by inverting the ratios. So for example, the competitive ratio for this problem is then min A max I Opt(I) A(I) The deterministic competitive ratio for this problem is Theta( Phi) [3, 4, 11, 18], and the randomized competitive ratio is Theta(min(log Phi; log Delta) 8, 12] where the importance ratio Phi is the ratio of the maximum value density of a job to the minimum value density of a job, and Delta is the ratio of the length of the longest job to the length of the shortest ....

G. Woeginger, "On-line scheduling of jobs with fixed start and end time", Theoretical Computer Science, 130, 1994.

.... online algorithm [5] If the objective function is to maximize processor utilization (the fraction of time that the processor is working on a job that it will complete by its deadline) then there is a 4 competitive deterministic algorithm, and this is optimal for deterministic online algorithms [2, 12]. It is well known that the algorithm SRPT minimizes the total flow time, which is the sum over all jobs of the completion time minus the release time of that job. If one changes the job environment to disallow preemption then it is easy to see that no constant competitive randomized algorithm ....

G. Woeginger, "On-line scheduling of jobs with fixed start and end time", Theoretical Computer Science, 130, 5--16, 1994..

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Woeginger, G. (1994), `On-line scheduling of jobs with fixed start and end times', Theoretical Computer Science 130, 5--16.

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