
Parameterized Complexity of Geodetic Set
A vertex set S of a graph G is geodetic if every vertex of G lies on a s...
read it

Hitting Long Directed Cycles is FixedParameter Tractable
In the Directed Long Cycle Hitting Set problem we are given a directed g...
read it

Experimental Evaluation of Parameterized Algorithms for Feedback Vertex Set
Feedback Vertex Set is a classic combinatorial optimization problem that...
read it

Structural Parameterizations for Equitable Coloring
An nvertex graph is equitably kcolorable if there is a proper coloring...
read it

Dynamic Parameterized Problems and Algorithms
Fixedparameter algorithms and kernelization are two powerful methods to...
read it

Diversity in Kemeny Rank Aggregation: A Parameterized Approach
In its most traditional setting, the main concern of optimization theory...
read it

How Bad is the Freedom to FloodIt?
FixedFloodIt and FreeFloodIt are combinatorial problems on graphs th...
read it
Preprocessing to Reduce the Search Space: Antler Structures for Feedback Vertex Set
The goal of this paper is to open up a new research direction aimed at understanding the power of preprocessing in speeding up algorithms that solve NPhard problems exactly. We explore this direction for the classic Feedback Vertex Set problem on undirected graphs, leading to a new type of graph structure called antler decomposition, which identifies vertices that belong to an optimal solution. It is an analogue of the celebrated crown decomposition which has been used for Vertex Cover. We develop the graph structure theory around such decompositions and develop fixedparameter tractable algorithms to find them, parameterized by the number of vertices for which they witness presence in an optimal solution. This reduces the search space of fixedparameter tractable algorithms parameterized by the solution size that solve Feedback Vertex Set.
READ FULL TEXT
Comments
There are no comments yet.