Connecting Vertices by Independent Trees
We study the paramereteized complexity of the following connectivity problem. For a vertex subset U of a graph G, trees T_1,...,T_s of G are completely independent spanning trees of U if each of them contains U, and for every two distinct vertices u,v in U, the paths from u to v in T_1,...,T_s are pairwise vertex disjoint except for end-vertices u and v. Then for a given s >= 2 and a parameter k, the task is to decide if a given n-vertex graph G contains a set U of size at least k such that there are s completely independent spanning trees of U. The problem is known to be NP-complete already for s=2. We prove the following results: (*) For s=2 the problem is solvable in time 2^{O(k)}*n^{O(1)}. (*) For s=2 the problem does not admit a polynomial kernel unless NP subseteq coNP/poly. (*) For arbitrary s, we show that the problem is solvable in time f(s,k)n^{O(1)} for some function f of s and k only.
Parameterized complexity
FPT-algorithms
completely independent spanning trees
73-84
Regular Paper
Manu
Basavaraju
Manu Basavaraju
Fedor V.
Fomin
Fedor V. Fomin
Petr A.
Golovach
Petr A. Golovach
Saket
Saurabh
Saket Saurabh
10.4230/LIPIcs.FSTTCS.2014.73
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