Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Faster O(|V|^2|E|W)-Time Energy Algorithms for Optimal Strategy
  Synthesis in Mean Payoff Games   This study strengthens the links between Mean Payoff Games (\MPG{s}) and
Energy Games (EG{s}). Firstly, we offer a faster $O(|V|^2|E|W)$
pseudo-polynomial time and $\Theta(|V|+|E|)$ space deterministic algorithm for
solving the Value Problem and Optimal Strategy Synthesis in \MPG{s}. This
improves the best previously known estimates on the pseudo-polynomial time
complexity to: \[ O(|E|\log |V|) + \Theta\Big(\sum_{v\in
V}\texttt{deg}_{\Gamma}(v)\cdot\ell_{\Gamma}(v)\Big) = O(|V|^2|E|W), \] where
$\ell_{\Gamma}(v)$ counts the number of times that a certain energy-lifting
operator $\delta(\cdot, v)$ is applied to any $v\in V$, along a certain
sequence of Value-Iterations on reweighted \EG{s}; and
$\texttt{deg}_{\Gamma}(v)$ is the degree of $v$. This improves significantly
over a previously known pseudo-polynomial time estimate, i.e.
$\Theta\big(|V|^2|E|W + \sum_{v\in
V}\texttt{deg}_{\Gamma}(v)\cdot\ell_{\Gamma}(v)\big)$ \citep{CR15, CR16}, as
the pseudo-polynomiality is now confined to depend solely on $\ell_\Gamma$.
Secondly, we further explore on the relationship between Optimal Positional
Strategies (OPSs) in \MPG{s} and Small Energy-Progress Measures (SEPMs) in
reweighted \EG{s}. It is observed that the space of all OPSs,
$\texttt{opt}_{\Gamma}\Sigma^M_0$, admits a unique complete decomposition in
terms of extremal-SEPM{s} in reweighted EG{s}. This points out what we called
the "Energy-Lattice $\mathcal{X}^*_{\Gamma}$ associated to
$\texttt{opt}_{\Gamma}\Sigma^M_0$". Finally, it is offered a pseudo-polynomial
total-time recursive procedure for enumerating (w/o repetitions) all the
elements of $\mathcal{X}^*_{\Gamma}$, and for computing the corresponding
partitioning of $\texttt{opt}_{\Gamma}\Sigma^M_0$.

12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
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The categories of this paper are: q-bio
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The categories of this paper are: stat
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
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The categories of this paper are: eess
31
The categories of this paper are: ao-sci