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A multivariate analysis of the strict terminal connection problem
Journal of Computer and System Sciences ( IF 1.129 ) Pub Date : 2020-02-10 , DOI: 10.1016/j.jcss.2020.02.001
Alexsander A. Melo; Celina M.H. Figueiredo; Uéverton S. Souza

A strict connection tree of a graph G for a set W is a tree subgraph of G whose leaf set equals W. The Strict terminal connection problem (S-TCP) is a network design problem whose goal is to decide whether G admits a strict connection tree T for W with at most ℓ vertices of degree 2 and r vertices of degree at least 3. We establish a Poly vs. NP-c dichotomy for S-TCP with respect to ℓ and Δ(G). We prove that S-TCP parameterized by r is W[2]-hard even if ℓ is bounded by a constant; we provide a kernelization for S-TCP parameterized by ℓ, r and Δ(G), and we prove that such a version of the problem does not admit a polynomial kernel, unless NP⊆coNP/poly. Finally, we analyse S-TCP on split graphs and cographs.
更新日期:2020-02-10

 

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