Abstract
The paper investigates a version of the resource allocation problem arising in the wireless networking, namely in the OVSF code reallocation process. In this setting a complete binary tree of a given height n is considered, together with a sequence of requests which have to be served in an online manner. The requests are of two types: an insertion request requires to allocate a complete subtree of a given height, and a deletion request frees a given allocated subtree. In order to serve an insertion request it might be necessary to move some already allocated subtrees to other locations in order to free a large enough subtree. We are interested in the worst case average number of such reallocations needed to serve a request.
In [4] the authors delivered bounds on the competitive ratio of online algorithm solving this problem, and showed that the ratio is between 1.5 and O(n). We partially answer their question about the exact value by giving an O(1)-competitive online algorithm.
In [3], authors use the same model in the context of memory management systems, and analyze the number of reallocations needed to serve a request in the worst case. In this setting, our result is a corresponding amortized analysis.
The research has been supported by grant APVV-0433-06 and VEGA 1/3106/06.
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Forišek, M. et al. (2007). Online Bandwidth Allocation. In: Arge, L., Hoffmann, M., Welzl, E. (eds) Algorithms – ESA 2007. ESA 2007. Lecture Notes in Computer Science, vol 4698. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75520-3_49
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DOI: https://doi.org/10.1007/978-3-540-75520-3_49
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