Abstract
The width measure treedepth, also known as vertex ranking, centered coloring and elimination tree height, is a well-established notion which has recently seen a resurgence of interest. We present an algorithm which—given as input an n-vertex graph, a tree decomposition of width w, and an integer t—decides whether the input graph has treedepth at most t in time 2O(wt) ·n. We use this to construct further algorithms which do not require a tree decomposition as part of their input: A simple algorithm which decides treedepth in linear time for a fixed t, thus answering an open question posed by Ossona de Mendez and Nešetřil as to whether such an algorithm exists, a fast algorithm with running time \(2^{O(t^2)} \cdot n\) and an algorithm for chordal graphs with running time 2O(t logt)·n.
Research funded by DFG-Project RO 927/13-1 “Pragmatic Parameterized Algorithms”.
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Reidl, F., Rossmanith, P., Villaamil, F.S., Sikdar, S. (2014). A Faster Parameterized Algorithm for Treedepth. In: Esparza, J., Fraigniaud, P., Husfeldt, T., Koutsoupias, E. (eds) Automata, Languages, and Programming. ICALP 2014. Lecture Notes in Computer Science, vol 8572. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-43948-7_77
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