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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Computing 56 (1996), S. 95-104 
    ISSN: 1436-5057
    Keywords: 68M20 ; Probabilistic algorithm ; online scheduling ; interval ; busy time
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Wir betrachten das Problem der Zuteilung von Aufgaben bestimmter Rechenzeit auf einem Rechner, um so seine Auslastung zu maximieren. Die Aufgabe besteht darin, einen probabilistischen Online-Algorithmus mit vernünftigem worst-case Performance-Verhältnis zu finden. Wir geben die Antwort auf ein offenes Problem von Lipton und Tompkins, das das bestmögliche Verhältnis betrifft. Weiter verallgemeinern wir ihre Ergebnisse auf einm-Maschinen-Analogon. Schließlich wird eine Variante des Problems analysiert, in dem der Rechner mit einem Zwischenspeicher für einen Job versehen ist.
    Notes: Abstract We consider the problem of scheduling tasks requiring certain processing times on one machine so that the busy time of the machine is maximized. The problem is to find a probabilistic online algorithm with reasonable worst case performance ratio. We answer an open problem of Lipton and Tompkins concerning the best possible ratio that can be achieved. Furthermore, we extend their results to anm-machine analogue. Finally, a variant of the problem is analyzed, in which the machine is provided with a buffer to store one job.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Mathematical methods of operations research 46 (1997), S. 131-142 
    ISSN: 1432-5217
    Keywords: Ellipsoid method ; linear programming ; simplex ; volume
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract Yamnitsky and Levin proposed a variant of Khachiyan's ellopsoid method for testing feasibility of systems of linear inequalities that also runs in polynomial time but uses simplices instead of ellipsoids. Starting with then-simplexS and the half-space {x¦a Tx ≤ β}, the algorithm finds a simplexS YL of small volume that enclosesS ∩ {x¦a Tx ≤ β}. We interpretS YL as a simplex obtainable by point-sliding and show that the smallest such simplex can be determined by minimizing a simple strictly convex function. We furthermore discuss some numerical results. The results suggest that the number of iterations used by our method may be considerably less than that of the standard ellipsoid method.
    Type of Medium: Electronic Resource
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