Emergent Mind
Abstract
We study the version of the $k$-disjoint paths problem where $k$ demand pairs $(s1,t1)$, $\dots$, $(sk,tk)$ are specified in the input and the paths in the solution are allowed to intersect, but such that no vertex is on more than $c$ paths. We show that on directed acyclic graphs the problem is solvable in time $n{O(d)}$ if we allow congestion $k-d$ for $k$ paths. Furthermore, we show that, under a suitable complexity theoretic assumption, the problem cannot be solved in time $f(k)n{o(d/\log d)}$ for any computable function $f$.
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