Parametrized Tractability of Edge-Disjoint Paths on Directed Acyclic Graphs

dc.contributor.authorSlivkins, Aleksandrsen_US
dc.description.abstractGiven a graph and pairs $s_i t_i$ of terminals, the edge-disjoint paths problem is to determine whether there exist $s_i t_i$ paths that do not share any edges. We consider this problem on ditected acyclic graphs. It is known to be NP-complete and solvable in time $n^{O(k)}$ where $k$ is the number of paths. It has been a long-standing open question whether it is fixed-parameter tractable in $k$. We resolve this question in the negative: we show that the problem is $W[1]$-hard. In fact it remains $W[1]$-hard even if the demand graph consists of two sets of parallel edges. On a positive side, we give an $O(k! n)$ algorithm for the special case when $G$ is acyclic and $G+H$ is Eulerian, where $H$ is the demand graph. We generalize this result (1) to the case when $G+H$ is ``nearly" Eulerian, (2) to an analogous special case of the unsplittable flow problem. Finally, we consider a related NP-complete routing problem when only the first edge of each path cannot be shared, and prove that it is fixed-parameter tractable on directed graphs.en_US
dc.format.extent307076 bytes
dc.publisherCornell Universityen_US
dc.subjectcomputer scienceen_US
dc.subjecttechnical reporten_US
dc.titleParametrized Tractability of Edge-Disjoint Paths on Directed Acyclic Graphsen_US
dc.typetechnical reporten_US


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