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  • Articles: DFG German National Licenses  (3)
  • 05B40  (1)
  • Cutting stock problems  (1)
  • disk systems  (1)
  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Queueing systems 2 (1987), S. 115-145 
    ISSN: 1572-9443
    Keywords: Polling systems ; disk systems ; disk SCAN policy ; shortest-seek-time-first disk scheduling ; moving-server systems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: 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.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Probability theory and related fields 102 (1995), S. 105-121 
    ISSN: 1432-2064
    Keywords: 60D05 ; 05B40 ; 52A22
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: 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.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Algorithmica 9 (1993), S. 253-277 
    ISSN: 1432-0541
    Keywords: Average-case analysis ; Cutting stock problems ; Two-dimensional packing ; Bin packing
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: 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.
    Type of Medium: Electronic Resource
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