Proves fine-grained nearly ETH-tight bounds for Courcelle's theorem depending on treewidth t and the number of first-order and second-order variables in each quantifier alternation block of the MSO formula.
11 Reinhard Diestel.Graph Theory, 4th Edition, volume 173 ofGraduate texts in mathematics
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Power network design variants of Steiner Tree are W[1]-hard parameterized by terminals, with XP algorithms for planar low-voltage cases and FPT results under a modified cost model.
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Fine-Grained Bounds for Courcelle's Theorem
Proves fine-grained nearly ETH-tight bounds for Courcelle's theorem depending on treewidth t and the number of first-order and second-order variables in each quantifier alternation block of the MSO formula.
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Parameterized Complexity of Power Network Design: Coordinating Cable Placement is Hard
Power network design variants of Steiner Tree are W[1]-hard parameterized by terminals, with XP algorithms for planar low-voltage cases and FPT results under a modified cost model.