Abstract
In the valley-free path model, a path in a given directed graph is valid if it consists of a sequence of forward edges followed by a sequence of backward edges. This model is motivated by routing policies of autonomous systems in the Internet. We give a $2$-approximation algorithm for the problem of computing a maximumn number of edge- or vertex-disjoint valid paths between two given vertices $s$ and $t$, and we show that no better approximation ratio is possible unless $P=NP$. Furthermore, we give a $2$-approximation algorithm for the problem of computing a minimum vertex cut that separates $s$ and $t$ with respect to all valid paths and prove that the problem is APX-hard. The corresponding problem for edge cuts is shown to be polynomial-time solvable. For the multiway variant of the cut problem, we give a $4$-approximation algorithm. We present additional results for acyclic graphs
Citation
Thomas Erlebach. Alexander Hall. Alessandro Panconesi. Danic Vukadinović. "Cuts and Disjoint Paths in the Valley-Free Path Model." Internet Math. 3 (3) 333 - 360, 2006.
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