1,541 research outputs found
Kernelization and Parameterized Algorithms for 3-Path Vertex Cover
A 3-path vertex cover in a graph is a vertex subset such that every path
of three vertices contains at least one vertex from . The parameterized
3-path vertex cover problem asks whether a graph has a 3-path vertex cover of
size at most . In this paper, we give a kernel of vertices and an
-time and polynomial-space algorithm for this problem, both new
results improve previous known bounds.Comment: in TAMC 2016, LNCS 9796, 201
New Results on Directed Edge Dominating Set
We study a family of generalizations of Edge Dominating Set on directed
graphs called Directed -Edge Dominating Set. In this problem an arc
is said to dominate itself, as well as all arcs which are at distance
at most from , or at distance at most to .
First, we give significantly improved FPT algorithms for the two most
important cases of the problem, -dEDS and -dEDS (that correspond
to versions of Dominating Set on line graphs), as well as polynomial kernels.
We also improve the best-known approximation for these cases from logarithmic
to constant. In addition, we show that -dEDS is FPT parameterized by
, but W-hard parameterized by (even if the size of the optimal is
added as a second parameter), where is the treewidth of the underlying
graph of the input.
We then go on to focus on the complexity of the problem on tournaments. Here,
we provide a complete classification for every possible fixed value of ,
which shows that the problem exhibits a surprising behavior, including cases
which are in P; cases which are solvable in quasi-polynomial time but not in P;
and a single case which is NP-hard (under randomized reductions) and
cannot be solved in sub-exponential time, under standard assumptions
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