Abstract
The paper considers a generalization of the well known random placement of balls into bins. Given n circular arcs of lengths α 1, ...,α n we study the maximum number of overlapping arcs on a circle if the starting points of the arcs are chosen randomly. We give almost exact tail bounds on the maximum overlap of the arcs. These tail bounds yield a characterization of the expected maximum overlap that is tight up to constant factors in the lower order terms. We illustrate the strength of our results by presenting new performance guarantees for several application: Minimizing rotational delays of disks, scheduling accesses to parallel disks and allocating memory to limit cache interference misses.
Partially supported by the Future and Emerging Technologies programme of the EU under contract number IST-1999-14186 (ALCOM-FT).
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Sanders, P., Vöcking, B. (2002). Random Arc Allocation and Applications. In: Penttonen, M., Schmidt, E.M. (eds) Algorithm Theory — SWAT 2002. SWAT 2002. Lecture Notes in Computer Science, vol 2368. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45471-3_13
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DOI: https://doi.org/10.1007/3-540-45471-3_13
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