Mapping the genome: some combinatorial problems arising in molecular biology
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Graph Searching and Interval Completion
SIAM Journal on Discrete Mathematics
The Linear Arrangement Problem Parameterized Above Guaranteed Value
Theory of Computing Systems
Interval completion with few edges
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Parameterizing above or below guaranteed values
Journal of Computer and System Sciences
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An ordering of a graph G=(V,E) is a one-to-one mapping α: V →{1,2,..., |V|}. The profile of an ordering α of G is prfα(G)=∑v∈V(α(v)– min {α(u): u ∈N[v]}); here N[v] denotes the closed neighborhood of v. The profile prf(G) of G is the minimum of prfα(G) over all orderings α of G. It is well-known that prf(G) equals the minimum number of edges in an interval graph H that contains G as a subgraph. We show by reduction to a problem kernel of linear size that deciding whether the profile of a connected graph G=(V,E) is at most |V|–1+k is fixed-parameter tractable with respect to the parameter k. Since |V|–1 is a tight lower bound for the profile of a connected graph G=(V,E), the parameterization above the guaranteed value |V|–1 is of particular interest.