What does it mean today to study a problem from a computational point of view? We focus on parameterized complexity and on Column 16 “Graph Restrictions and Their Effect” of D.S. Johnson’s Ongoing guide, where several puzzles were proposed in a summary table with 30 graph classes as rows and 11 problems as columns. Several of the 330 entries remain unclassified into Polynomial or NP-complete after 35 years. We provide a full dichotomy for the Steiner Tree column by proving that the problem is NP-complete when restricted to Undirected Path graphs. We revise Johnson’s summary table according to the granularity provided by the parameterized complexity for NP-complete problems.
Revising Johnson's Table for the 21st century / Celina M.H.de Figueiredo; Alexsander A.de Melo; Diana Sasaki; FERREIRA DA SILVA A. - In: DISCRETE APPLIED MATHEMATICS. - ISSN 0166-218X. - STAMPA. - 323:(2022), pp. 184-200. [10.1016/j.dam.2021.05.021]
Revising Johnson's Table for the 21st century
FERREIRA DA SILVA A
2022
Abstract
What does it mean today to study a problem from a computational point of view? We focus on parameterized complexity and on Column 16 “Graph Restrictions and Their Effect” of D.S. Johnson’s Ongoing guide, where several puzzles were proposed in a summary table with 30 graph classes as rows and 11 problems as columns. Several of the 330 entries remain unclassified into Polynomial or NP-complete after 35 years. We provide a full dichotomy for the Steiner Tree column by proving that the problem is NP-complete when restricted to Undirected Path graphs. We revise Johnson’s summary table according to the granularity provided by the parameterized complexity for NP-complete problems.File | Dimensione | Formato | |
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