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arXiv · 1304.0084

Faster Algorithms for Markov Decision Processes with Low Treewidth

Krishnendu Chatterjee·Jakub Łącki
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Abstract

We consider two core algorithmic problems for probabilistic verification: the maximal end-component decomposition and the almost-sure reachability set computation for Markov decision processes (MDPs). For MDPs with treewidth $k$, we present two improved static algorithms for both the problems that run in time $O(n \cdot k^{2.38} \cdot 2^k)$ and $O(m \cdot \log n \cdot k)$, respectively, where $n$ is the number of states and $m$ is the number of edges, significantly improving the previous known $O(n\cdot k \cdot \sqrt{n\cdot k})$ bound for low treewidth. We also present decremental algorithms for both problems for MDPs with constant treewidth that run in amortized logarithmic time, which is a huge improvement over the previously known algorithms that require amortized linear time.

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Krishnendu Chatterjee, Jakub Łącki. 2013-03-30. Faster Algorithms for Markov Decision Processes with Low Treewidth. https://arxiv.org/abs/1304.0084

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