Computing treedepth in polynomial space and linear fpt time
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The treedepth of a graph G is the least possible depth of an elimination forest of G: a rooted forest on the same vertex set where every pair of vertices adjacent in G is bound by the ancestor/descendant relation. We propose an algorithm that given a graph G and an integer d, either finds an elimination forest of G of depth at most d or concludes that no such forest exists; thus the algorithm decides whether the treedepth of G is at most d. The running time is 2^O(d^2)· n^O(1) and the space usage is polynomial in n. Further, by allowing randomization, the time and space complexities can be improved to 2^O(d^2)· n and d^O(1)· n, respectively. This improves upon the algorithm of Reidl et al. [ICALP 2014], which also has time complexity 2^O(d^2)· n, but uses exponential space.
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