Problems | Classic | Condition | ||
---|---|---|---|---|
Lower bound | Upper bound | Lower bound(s) | Upper bound(s) | |
Steiner Forest | 1.01 [19] | 2 [18] | \(C-\epsilon , k-\epsilon \) | 2C, k |
Directed Steiner Network | \(k^{1/4 - o(1)}\) [27] | \(k^{1/2+\epsilon }\) [21, 22] | \(C-\epsilon , k-\epsilon \) | \(C \cdot k^{1/2+\epsilon }, k\) |
Undirected Shortest Path | N/A | 1 | \(C-\epsilon \) | C |
Directed Shortest Path | N/A | 1 | \(C-\epsilon \) | C |
Steiner Tree | 1.01 [19] | 1.39 [17] | \(C-\epsilon \) | 1.39C |
Prize-Collecting Steiner Tree | 1.01 [19] | 1.97 [26] | \(C-\epsilon \) | 1.97C |