2021/04/29 by de Figueiredo, Celina M. H., de Melo, Alexsander A., Sasaki, Diana +1
#Combinatorics (math.CO) #Computational Complexity (cs.CC) #FOS: Computer and information sciences #FOS: Mathematics
paper · doi:10.48550/arxiv.2104.14395
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.