A faster parameterized algorithm for treedepth
F Reidl, P Rossmanith, FS Villaamil… - … Colloquium on Automata …, 2014 - Springer
F Reidl, P Rossmanith, FS Villaamil, S Sikdar
International Colloquium on Automata, Languages, and Programming, 2014•SpringerThe 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 2 O (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 …
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 2 O (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 …
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 2 O(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 and an algorithm for chordal graphs with running time 2 O(t logt)·n.
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