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  • 1
    Digitale Medien
    Digitale Medien
    Springer
    Probability theory and related fields 102 (1995), S. 105-121 
    ISSN: 1432-2064
    Schlagwort(e): 60D05 ; 05B40 ; 52A22
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary Letn random intervalsI 1, ...,I n be chosen by selecting endpoints independently from the uniform distribution on [0.1]. Apacking is a pairwise disjoint subset of the intervals; itswasted space is the Lebesgue measure of the points of [0,1] not covered by the packing. In any set of intervals the packing with least wasted space is computationally easy to find; but its expected wasted space in the random case is not obvious. We show that with high probability for largen, this “best” packing has wasted space $$O(\frac{{\log ^2 n}}{n})$$ . It turns out that if the endpoints 0 and 1 are identified, so that the problem is now one of packing random arcs in a unit-circumference circle, then optimal wasted space is reduced toO(1/n). Interestingly, there is a striking difference between thesizes of the best packings: about logn intervals in the unit interval case, but usually only one or two arcs in the circle case.
    Materialart: Digitale Medien
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  • 2
    Digitale Medien
    Digitale Medien
    Springer
    Algorithmica 9 (1993), S. 253-277 
    ISSN: 1432-0541
    Schlagwort(e): Average-case analysis ; Cutting stock problems ; Two-dimensional packing ; Bin packing
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract New approximation algorithms for packing rectangles into a semi-infinite strip are introduced in this paper. Within a standard probability model, an asymptotic average-case analysis is given for the wasted space in the packings produced by these algorithms. An off-line algorithm is presented along with a proof that it wastes θ(√/n)space on the average, wheren is the number of rectangles packed. This result is known to apply to optimal packings as well. Several on-line shelf algorithms are also analyzed. Withn assumed known in advance, one such algorithm is described and shown to waste θ(n 2/3) space on the average. It is proved that this result also characterizes optimal on-line shelf packings. For a very general class of linear-time algorithms, it is shown that a constant (nonzero) fraction of the space must be wasted on the average for alln, and a lower bound on this fraction in terms of algorithm parameters is given. Finally, the paper discusses the implications of the above results for dynamic packing and two-dimensional bin-packing problems.
    Materialart: Digitale Medien
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  • 3
    Digitale Medien
    Digitale Medien
    Springer
    Queueing systems 1 (1986), S. 129-168 
    ISSN: 1572-9443
    Schlagwort(e): Computer storage devices ; auxiliary storage systems ; queueing analyses of computer secondary storage ; stochastic models of computer auxiliary memory systems
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik
    Notizen: Abstract Queueing theory has occupied an important role in the analysis of computer storage structures and algorithms. In this survey we focus on secondary or auxiliary storage devices, which often comprise the principal bottleneck in the overall performance of computer systems. We begin with descriptions of the more important devices, such as disks and drums, and a general discussion of related queueing models. Server motion and dependent successive services are salient features of these models. Widely used, generic results are presented and then applied to specific devices. The paper concludes with a discussion of open problems.
    Materialart: Digitale Medien
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  • 4
    Digitale Medien
    Digitale Medien
    Springer
    Queueing systems 2 (1987), S. 115-145 
    ISSN: 1572-9443
    Schlagwort(e): Polling systems ; disk systems ; disk SCAN policy ; shortest-seek-time-first disk scheduling ; moving-server systems
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik
    Notizen: Abstract A single server moves with speed υ on a line interval (or a circle) of length (circumference)L. Customers, requiring service of constant durationb, arrive on the interval (or circle) at random at mean rate λ customers per unit length per unit time. A customer's mean wait for service depends partly on the rules governing the server's motion. We compare two different servers: thepolling server and thegreedy server. Without knowing the locations of waiting customers, a polling server scans endlessly back and forth across the interval (or clockwise around the circle), stopping only where it encounters a waiting customer. Knowing where customers are waiting, a greedy server always travels toward the current nearest one. Except for certain extreme values of υ,L, b, andλ, the polling and greedy servers are roughly equally effective. Indeed, the simpler polling server is often the better. Theoretical results show, in most cases, that the polling server has a high probability of moving toward the nearest customer, i.e. moving as a greedy server would. The greedy server is difficult to analyze, but was simulated on a computer.
    Materialart: Digitale Medien
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  • 5
    Digitale Medien
    Digitale Medien
    Springer
    Annals of operations research 26 (1990), S. 135-147 
    ISSN: 1572-9338
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Wirtschaftswissenschaften
    Notizen: Abstract We study a single-machine scheduling problem in which the items to be processed have to be batched as well as sequenced. Since processed items become available in batches, flow times are defined to be the same for all items in the same batch. A constant set-up delay is incurred between consecutive batches. For any fixed, but arbitrary item sequence, we present an algorithm that finds a sequence of batches such that the total flow time of the items is minimized; we prove that for a set ofn items, the algorithm runs inO(n) time. We show that, among all sequences, the one leading to the minimum flow time has the items in non-decreasing order of running times. Thus, the optimal algorithm for the combined problem, called thebatch-sizing problem, runs inO(n logn) time. We also prove that this algorithm yields an improved solution to a scheduling problem recently studied by Baker [1].
    Materialart: Digitale Medien
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  • 6
    Digitale Medien
    Digitale Medien
    Springer
    BIT 18 (1978), S. 52-66 
    ISSN: 1572-9125
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract Cody and Coffman have studied the problem of distributing a set of a equal-size records among the sectors of a drum-like storage device so as to minimize the average rotational latency cost. This paper is an extension of that work. We employ the same model but a different latency delay function. Motivated by the NP-completeness of the general problem and the fact that an arbitrary assignment can have an expected latency cost almost twice that of an optimal assignment, we propose and analyze a fast heuristic whose performance compares favorably with that of an optimal algorithm.
    Materialart: Digitale Medien
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  • 7
    Digitale Medien
    Digitale Medien
    Springer
    BIT 10 (1970), S. 443-456 
    ISSN: 1572-9125
    Schlagwort(e): Dewey (17th): 651.8 ; U.D.C.: 007 681.322.025 ; Trees ; search Structures ; data ; file ; tree Information Retrieval
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract An important property of file structures is their behavior when the underlying distribution of access frequencies is non-uniform. In this note we consider methods for structuring files so that initially unknown but non-uniform access frequencies are exploited in a way that reduces mean search times. As a specific illustration a simple algorithm is applied to sequence search trees and shown to produce structures with mean search times that are significantly less than those produced by an algorithm creating tree structures independent of access frequencies. An analytic result is obtained for this improvement when access frequencies are uniform. Samples from the results of Monte Carlo simulations are used to illustrate this improvement when access frequencies are non-uniform.
    Materialart: Digitale Medien
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  • 8
    Digitale Medien
    Digitale Medien
    Springer
    Acta informatica 21 (1984), S. 409-415 
    ISSN: 1432-0525
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik
    Notizen: Summary Let S be a set of positive numbers and m an integer not less than 2. The problem is to partition S into m subsets such that the ratio of the largest subset sum to the smallest is as small as possible. Let ϱ g (S) be the value of this ratio using the greedy or largest-first rule and ϱ 0 (S) be the smallest possible value of this ratio, i.e., the optimal value. The authors prove that $$\frac{{\rho _g \left( S \right)}}{{\rho _0 \left( S \right)}}\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{ \leqslant } {7 \mathord{\left/ {\vphantom {7 5}} \right. \kern-\nulldelimiterspace} 5}$$ , and that this is a best possible bound for all m.
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 9
    Digitale Medien
    Digitale Medien
    Springer
    Acta informatica 9 (1978), S. 263-271 
    ISSN: 1432-0525
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik
    Notizen: Summary We consider a variant of the classical one-dimensional bin-packing problem: The number of bins is fixed and the object is to maximize the number of pieces packed from some given set. Both problems have applications in processor and storage allocation in computer systems in addition to a broad application in operations research. It can easily be shown that both problems are NP-complete; our approach will be to propose and analyze very fast heuristics. We consider a class of algorithms and bound the performance of an arbitrary algorithm in that class. Finally we propose an algorithm, the first-fit-increasing algorithm, and analyze its running time and relative performance.
    Materialart: Digitale Medien
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  • 10
    Digitale Medien
    Digitale Medien
    Springer
    Acta informatica 1 (1971), S. 1-13 
    ISSN: 1432-0525
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik
    Notizen: Summary This paper concerns the problem of obtaining predictions of the extent to which additional core storage would improve the performance of a given paging system based on information that could be obtained from monitoring the system whilst running its normal workload. It is shown that for a large class of replacement algorithms there are efficient techniques for producing exact predictions of the performance improvement, and that for a further class of algorithms statistical predictions can be provided.
    Materialart: Digitale Medien
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