For any fixed constants k1 and k2 the weak 2-linkage problem with length bounds d(si,ti)+ki is in P; it is ETH-hard for c log^{1+ε}n bounds and remains NP-complete when one path must be shortest.
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The directed 2-linkage problem with length constraints
For any fixed constants k1 and k2 the weak 2-linkage problem with length bounds d(si,ti)+ki is in P; it is ETH-hard for c log^{1+ε}n bounds and remains NP-complete when one path must be shortest.