Abstract
We consider the model of online computation with advice [5]. In particular, we study the k-server problem under this model. We prove two upper bounds for this problem. First, we show a \(\Big\lceil\frac{\lceil\log k\rceil}{b-2}\Big\rceil \)-competitive online algorithm for general metric spaces with b bits of advice per request, where 3 ≤ b ≤ logk. This improves upon the recent result of [1]. Moreover, we believe that our algorithm and our analysis are more intuitive and simpler than those of [1]. Second, we give a 1-competitive online algorithm for trees which uses 2 + 2⌈log(p + 1)⌉ bits of advice per request, where p is the caterpillar dimension of the tree.
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Renault, M.P., Rosén, A. (2012). On Online Algorithms with Advice for the k-Server Problem. In: Solis-Oba, R., Persiano, G. (eds) Approximation and Online Algorithms. WAOA 2011. Lecture Notes in Computer Science, vol 7164. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29116-6_17
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DOI: https://doi.org/10.1007/978-3-642-29116-6_17
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