Abstract
Measure & Conquer is an approach helpful for designing branching algorithms. A key point in the approach is how to design the measure. Given a graph \(G=(V,E)\) and an integer k, the Bounded Degree-one Deletion problem asks for if there exists a subset D of at most k vertices such that the degree of any vertex in \(G[V\setminus D]\) is upper bounded by one. Combining the parameter with a potential as the measure in Measure & Conquer, where the potential is a lower bound of the decrement of the parameter, we design a branching algorithm running in polynomial space and \(O(1.882^k+|V||E|)\) time, which improves the current best parameterized complexity \(O^*(2^k)\) of the problem.
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Wu, B.Y. (2015). A Measure and Conquer Approach for the Parameterized Bounded Degree-One Vertex Deletion. In: Xu, D., Du, D., Du, D. (eds) Computing and Combinatorics. COCOON 2015. Lecture Notes in Computer Science(), vol 9198. Springer, Cham. https://doi.org/10.1007/978-3-319-21398-9_37
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DOI: https://doi.org/10.1007/978-3-319-21398-9_37
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