Polynomial Turing Compressions for Some Graph Problems Parameterized by Modular-Width

01/12/2022

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by   Weidong Luo, et al.

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In this paper we investigate the parameterized complexity for NP-hard graph problems parameterized by a structural parameter modular-width. We develop a recipe that is able to simplify the process of obtaining polynomial Turing compressions for a class of graph problems parameterized by modular-width. Moreover, we prove that several problems, which include chromatic number, independent set, Hamiltonian cycle, etc. have polynomial Turing compressions parameterized by modular-width. In addition, under the assumption that P ≠ NP, we provide tight kernels for a few problems such as Steiner tree parameterized by modular-width. Meanwhile, we demonstrate that some problems, which includes dominating set, odd cycle transversal, connected vertex cover, etc. are fixed-parameter tractable parameterized by modular-width.