Questions tagged [disjoint-paths]

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3
votes
1answer
121 views

Mutually exclusive replacement paths, an existing problem?

A replacement path is a simple path allocated to an edge $e \in G$ that connects the endpoints of $e$ in $G \setminus \{e\}$. The problem An undirected graph $G$ is given and the task is to allocate ...
7
votes
1answer
142 views

Label-disjoint paths in directed graphs

Checking if there are two edge-disjoint paths from $s$ to $t$ in a given undirected graph $G$ is in P via a standard solution based on maxflow. I am interested in the complexity of the following ...
10
votes
0answers
489 views

Simple path on dag with backward edges

What is the complexity of the following problem ($\in$ P? NP-hard?): Input: a directed acyclic graph $D=(V,E)$, a set of backward edges $E'\subset V\times V$, and two distinct nodes $s$ and $t$. ...
10
votes
1answer
625 views

Probability of generating a desired permutation by random swaps

I'm interested in the following problem. We're given as input a "target permutation" $\sigma\in S_n$, as well as an ordered list of indices $i_1,\ldots,i_m\in [n-1]$. Then, starting with the list $L=...
4
votes
1answer
255 views

For which values of $k$ is minimum length undirected $k$-disjoint-paths in $\mathcal{P}$?

In a related question, Saeed and Super8 have mentioned the Robertson-Seymour theory which enables us to find $k$ disjoint paths between pairs of vertices $\{s_i,t_i\}_{i=1}^k$ in poly time for fixed $...
2
votes
2answers
352 views

For which values of $k$ is the $k$-disjoint paths problem in $\mathcal{P}$?

The $k$-Vertex-Disjoint Paths Problem ($k$-$\text{DPP}$) is defined as follows: Input: A graph $G=(V,E)$ and $k$ pairs of vertices $(s_1,t_1),\ldots,(s_k,t_k)$. Question: Does there exist $k$-...