Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Hitting Set Relaxation for $k$-Server and an Extension to Time-Windows   We study the $k$-server problem with time-windows. In this problem, each
request $i$ arrives at some point $v_i$ of an $n$-point metric space at time
$b_i$ and comes with a deadline $e_i$. One of the $k$ servers must be moved to
$v_i$ at some time in the interval $[b_i, e_i]$ to satisfy this request. We
give an online algorithm for this problem with a competitive ratio of ${\rm
polylog} (n,\Delta)$, where $\Delta$ is the aspect ratio of the metric space.
Prior to our work, the best competitive ratio known for this problem was $O(k
\cdot {\rm polylog}(n))$ given by Azar et al. (STOC 2017). Our algorithm is
based on a new covering linear program relaxation for $k$-server on HSTs. This
LP naturally corresponds to the min-cost flow formulation of $k$-server, and
easily extends to the case of time-windows. We give an online algorithm for
obtaining a feasible fractional solution for this LP, and a primal dual
analysis framework for accounting the cost of the solution. Together, they
yield a new $k$-server algorithm with poly-logarithmic competitive ratio, and
extend to the time-windows case as well. Our principal technical contribution
lies in thinking of the covering LP as yielding a {\em truncated} covering LP
at each internal node of the tree, which allows us to keep account of server
movements across subtrees. We hope that this LP relaxation and the
algorithm/analysis will be a useful tool for addressing $k$-server and related
problems.

35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
19
The categories of this paper are: eess
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat