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== Title ==
An $O(\log k)$-competitive Algorithm for Generalized Caching
== Speaker ==
Harald Räcke, University of Warwick
== Abstract ==
In the generalized caching problem, we have a set of pages and a cache
of size $k$. Each page $p$ has a size $w_p\ge1$ and fetching cost $c_p$
for loading the page into the cache. At any point in time, the sum of
the sizes of the pages stored in the cache cannot exceed $k$. The input
consists of a sequence of page requests. If a page is not present in the
cache at the time it is requested, it has to be loaded into the cache
incurring a cost of $c_p$.
We give a randomized $O(\log k)$-competitive online algorithm for the
generalized caching problem, improving the previous bound of
$O(\log^2 k)$ by Bansal, Buchbinder, and Naor. This improved bound is
tight and of the same order as the known bounds for the classic problem
with uniform weights and sizes. We use the same LP based techniques as
Bansal et al.\ but provide improved and slightly simplified methods for
rounding fractional solutions online.
This is joint work with Anna Adamaszek, Artur Czumaj, and Matthias Englert.
An $O(\log k)$-competitive Algorithm for Generalized Caching
== Speaker ==
Harald Räcke, University of Warwick
== Abstract ==
In the generalized caching problem, we have a set of pages and a cache
of size $k$. Each page $p$ has a size $w_p\ge1$ and fetching cost $c_p$
for loading the page into the cache. At any point in time, the sum of
the sizes of the pages stored in the cache cannot exceed $k$. The input
consists of a sequence of page requests. If a page is not present in the
cache at the time it is requested, it has to be loaded into the cache
incurring a cost of $c_p$.
We give a randomized $O(\log k)$-competitive online algorithm for the
generalized caching problem, improving the previous bound of
$O(\log^2 k)$ by Bansal, Buchbinder, and Naor. This improved bound is
tight and of the same order as the known bounds for the classic problem
with uniform weights and sizes. We use the same LP based techniques as
Bansal et al.\ but provide improved and slightly simplified methods for
rounding fractional solutions online.
This is joint work with Anna Adamaszek, Artur Czumaj, and Matthias Englert.
