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- W3185200786 abstract "Finding a consistent DAG extension for a given partially directed acyclic graph (PDAG) is a basic building block used in graphical causal analysis. In 1992, Dor and Tarsi proposed an algorithm with time complexity $O(n^4)$, which has been widely used in causal theory and practice so far. It is a long-standing open question whether an extension can be computed faster and, in particular, it was conjectured that a linear-time method may exist. The main contributions of our work are two-fold: Firstly, we propose a new algorithm for the extension problem for PDAGs which runs in time $O(n^3)$; secondly, we show that, under a computational intractability assumption, our cubic algorithm is optimal. Thus, our impossibility result disproves the conjecture that a linear-time method exists. Based on these results, we present a full complexity landscape for finding extensions in various causal graphical models. We extend the techniques to recognition problems and apply them to design an effective algorithm for closing a PDAG under the orientation rules of Meek." @default.
- W3185200786 created "2021-08-02" @default.
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- W3185200786 date "2021-07-27" @default.
- W3185200786 modified "2023-09-25" @default.
- W3185200786 title "Extendability of Causal Graphical Models: Algorithms and Computational Complexity" @default.
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