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
Fixed-parameter complexity of minimum profile problems
IWPEC'06 Proceedings of the Second international conference on Parameterized and Exact Computation
Corrigendum. The Linear Arrangement Problem Parameterized Above Guaranteed Value
Theory of Computing Systems
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A linear arrangement (LA) is an assignment of distinct integers to the vertices of a graph. The cost of an LA is the sum of lengths of the edges of the graph, where the length of an edge is defined as the absolute value of the difference of the integers assigned to its ends. For many application one hopes to find an LA with small cost. However, it is a classical NP-complete problem to decide whether a given graph G admits an LA of cost bounded by a given integer. Since every edge of G contributes at least one to the cost of any LA, the problem becomes trivially fixed-parameter tractable (FPT) if parameterized by the upper bound of the cost. Fernau asked whether the problem remains FPT if parameterized by the upper bound of the cost minus the number of edges of the given graph; thus whether the problem is FPT "parameterized above guaranteed value." We answer this question positively by deriving an algorithm which decides in time O(m + n + 5.88k) whether a given graph with m edges and n vertices admits an LA of cost at most m + k (the algorithm computes such an LA if it exists). Our algorithm is based on a procedure which generates a problem kernel of linear size in linear time for a connected graph G. We also prove that more general parameterized LA problems stated by Serna and Thilikos are not FPT, unless P = NP.