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.
翻译:从计算角度来研究一个问题今天意味着什么?我们侧重于参数复杂性和D.S.Johnson的持续指南第16栏“格限制及其影响”,该栏在一份总表中提出了几个谜题,30个图表类别为行,11个问题为列。330个条目中有几个条目在35年后仍未被划入多面性或NP完整。我们通过证明问题仅限于非方向路径图时是NP-完整的,为施泰纳树柱提供了完全的二分法。我们根据NP-完整问题的参数复杂性所提供的颗粒性,对约翰逊的汇总表进行了修改。