Minimum Leaf Out-Branching Problems
AAIM '08 Proceedings of the 4th international conference on Algorithmic Aspects in Information and Management
Minimum leaf out-branching and related problems
Theoretical Computer Science
Note on Max Lin-2 above Average
Information Processing Letters
Note on maximal bisection above tight lower bound
Information Processing Letters
Betweenness parameterized above tight lower bound
Journal of Computer and System Sciences
Solving MAX-r-SAT above a tight lower bound
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
A probabilistic approach to problems parameterized above or below tight bounds
Journal of Computer and System Sciences
Journal of Computer and System Sciences
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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.