Revising Johnson's table for the 21st century
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...
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| creator | de Figueiredo, Celina M. H de Melo, Alexsander A Sasaki, Diana Silva, Ana |
| description | 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. |
| doi_str_mv | 10.48550/arxiv.2104.14395 |
| format | Article |
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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
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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
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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.</abstract><doi>10.48550/arxiv.2104.14395</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Computer Science - Computational Complexity Mathematics - Combinatorics |
| title | Revising Johnson's table for the 21st century |
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