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ALGORITHMICA
2008

Fixed-Parameter Complexity of Minimum Profile Problems

8 years 10 months ago
Fixed-Parameter Complexity of Minimum Profile Problems
The profile of a graph is an integer-valued parameter defined via vertex orderings; it is known that the profile of a graph equals the smallest number of edges of an interval supergraph. Since computing the profile of a graph is an NP-hard problem, we consider parameterized versions of the problem. Namely, we study the problem of deciding whether the profile of a connected graph of order n is at most n - 1 + k, considering k as the parameter; this is a parameterization above guaranteed value, since n - 1 is a tight lower bound for the profile. We present two fixed-parameter algorithms for this problem. The first algorithm is based on a forbidden subgraph characterization of interval graphs. The second algorithm is based on two simple kernelization rules which allow us to produce a kernel with linear number of vertices and edges. For showing the correctness of the second algorithm we need to establish structural properties of graphs with small profile which are of independent interest....
Gregory Gutin, Stefan Szeider, Anders Yeo
Added 08 Dec 2010
Updated 08 Dec 2010
Type Journal
Year 2008
Where ALGORITHMICA
Authors Gregory Gutin, Stefan Szeider, Anders Yeo
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