From: Tree diet: reducing the treewidth to unlock FPT algorithms in RNA bioinformatics
Parameter | Source treewidth | Target treewidth | Difference | ||
---|---|---|---|---|---|
Problem | tw | \(tw'\) | \(d=tw-tw'\) | ||
Graph-Diet | FPT | Para-NP-hard | Para-NP-harda | ||
via MSO | \(tw'=2\) | \(d=1\) | |||
Theorem 1 | EDP(\(K_4\)) [30] | Theorem 3 | |||
Tree-Diet | XP | FPT open | Para-NP-hard \(tw'=1\) Theorem 3 | Para-NP-hard | |
\(O^*((6\Delta )^{tw})\) | \(d=1\) | ||||
Theorem 7 | Theorem 5 | ||||
Binary-Tree-Diet | FPT | W[1]-hard Theorem 5 | XP open | ||
Path-Diet | \(O^*(12^{tw})\) | XP | |||
Theorem 7 | \(O^*(tw^d)\) | ||||
Theorem 8 |