An improved fixed-parameter algorithm for vertex cover
Information Processing Letters
Graph theory and its applications
Graph theory and its applications
A general method to speed up fixed-parameter-tractable algorithms
Information Processing Letters
Faster exact algorithms for hard problems: a parameterized point of view
Discrete Mathematics
Vertex cover: further observations and further improvements
Journal of Algorithms
Concrete Math
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Upper bounds for vertex cover further improved
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
Parameterized Complexity
The impact of parameterized complexity to interdisciplinary problem solving
The Multivariate Algorithmic Revolution and Beyond
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We introduce the problem PROFIT COVER which finds application in, among other areas, psychology of decision-making. A common assumption is that net value is a major determinant of human choice. PROFIT COVER incorporates the notion of net value in its definition. For a given graph G = (V, E) and an integer p 0, the goal is to determine PC 驴 V such that the profit, |E驴| - |PC|, is at least p, where E驴 are the by PC covered edges. We show that p-PROFIT COVER is a parameterization of VERTEX COVER. We present a fixed-parameter-tractable (fpt) algorithm for p-PROFIT COVER that runs in O(p|V| + 1.150964p). The algorithm generalizes to an fpt-algorithm of the same time complexity solving the problem p-EDGE WEIGHTED PROFIT COVER, where each edge e 驴 E has an integer weight w(e) 0, and the profit is determined by 驴e 驴 E驴 w(e) - |PC|. We combine our algorithm for p-PROFIT COVER with an fpt-algorithm for k-VERTEX COVER. We show that this results in a more efficient implementation to solve MINIMUM VERTEX COVER than each of the algorithms independently.