Revising Johnson's table for the 21st century
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Publication:2091799
DOI10.1016/J.DAM.2021.05.021zbMATH Open1502.05184arXiv2104.14395OpenAlexW3171927283MaRDI QIDQ2091799
Author name not available (Why is that?)
Publication date: 2 November 2022
Published in: (Search for Journal in Brave)
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.
Full work available at URL: https://arxiv.org/abs/2104.14395
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