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- W2517752011 abstract "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|) + ThetaBig(sum_{vin V}texttt{deg}_{Gamma}(v)cdotell_{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 $vin V$, 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. $Thetabig(|V|^2|E|W + sum_{vin V}texttt{deg}_{Gamma}(v)cdotell_{Gamma}(v)big)$ 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 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 $texttt{opt}_{Gamma}Sigma^M_0$." @default.
- W2517752011 created "2016-09-16" @default.
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- W2517752011 creator A5061874157 @default.
- W2517752011 date "2016-09-06" @default.
- W2517752011 modified "2023-09-27" @default.
- W2517752011 title "Faster O(|V|^2|E|W)-Time Energy Algorithms for Optimal Strategy Synthesis in Mean Payoff Games" @default.
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