Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Online Connected Dominating Set Leasing   We introduce the \emph{Online Connected Dominating Set Leasing} problem
(OCDSL) in which we are given an undirected connected graph $G = (V, E)$, a set
$\mathcal{L}$ of lease types each characterized by a duration and cost, and a
sequence of subsets of $V$ arriving over time. A node can be leased using lease
type $l$ for cost $c_l$ and remains active for time $d_l$. The adversary gives
in each step $t$ a subset of nodes that need to be dominated by a connected
subgraph consisting of nodes active at time $t$. The goal is to minimize the
total leasing costs. OCDSL contains the \emph{Parking Permit
Problem}~\cite{PPP} as a special subcase and generalizes the classical offline
\emph{Connected Dominating Set} problem~\cite{Guha1998}. It has an $\Omega(\log
^2 n + \log |\mathcal{L}|)$ randomized lower bound resulting from lower bounds
for the \emph{Parking Permit Problem} and the \emph{Online Set Cover}
problem~\cite{Alon:2003:OSC:780542.780558,Korman}, where $|\mathcal{L}|$ is the
number of available lease types and $n$ is the number of nodes in the input
graph. We give a randomized $\mathcal{O}(\log ^2 n + \log |\mathcal{L}| \log
n)$-competitive algorithm for OCDSL. We also give a deterministic algorithm for
a variant of OCDSL in which the dominating subgraph need not be connected, the
\emph{Online Dominating Set Leasing} problem. The latter is based on a simple
primal-dual approach and has an $\mathcal{O}(|\mathcal{L}| \cdot
\Delta)$-competitive ratio, where $\Delta$ is the maximum degree of the input
graph.

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The categories of this paper are: stat
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The categories of this paper are: q-fin
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The categories of this paper are: eess
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The categories of this paper are: hep-th
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The categories of this paper are: chem-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-alg
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The categories of this paper are: plasm-ph
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The categories of this paper are: math-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: bayes-an
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The categories of this paper are: physics