Related papers: Parameterized Rural Postman Problem
Many well-known NP-hard algorithmic problems on directed graphs resist efficient parametrisations with most known width measures for directed graphs, such as directed treewidth, DAG-width, Kelly-width and many others. While these focus on…
We study the half-integral $k$-Directed Disjoint Paths Problem ($\tfrac12$kDDPP) in highly strongly connected digraphs. The integral kDDPP is NP-complete even when restricted to instances where $k=2$, and the input graph is $L$-strongly…
We study the algorithmic complexity of partitioning the vertex set of a given (di)graph into a small number of paths. The Path Partition problem (PP) has been studied extensively, as it includes Hamiltonian Path as a special case. The…
We introduce a novel approach of using important cuts which allowed us to design significantly faster fixed-parameter tractable (FPT) algorithms for the following routing problems: the Mixed Chinese Postman Problem parameterized by the…
In the Disjoint Shortest Paths problem one is given a graph $G$ and a set $\mathcal{T}=\{(s_1,t_1),\dots,(s_k,t_k)\}$ of $k$ vertex pairs. The question is whether there exist vertex-disjoint paths $P_1,\dots,P_k$ in $G$ so that each $P_i$…
In Path Set Packing, the input is an undirected graph $G$, a collection $\calp$ of simple paths in $G$, and a positive integer $k$. The problem is to decide whether there exist $k$ edge-disjoint paths in $\calp$. We study the parameterized…
We consider the k-outconnected directed Steiner tree problem (k-DST). Given a directed edge-weighted graph $G=(V,E,w)$, where $V=\{r\}\cup S \cup T$, and an integer $k$, the goal is to find a minimum cost subgraph of $G$ in which there are…
This paper considers a natural fault-tolerant shortest paths problem: for some constant integer $f$, given a directed weighted graph with no negative cycles and two fixed vertices $s$ and $t$, compute (either explicitly or implicitly) for…
Asymmetric Travelling Salesman Problem (ATSP) and its special case Directed Hamiltonicity are among the most fundamental problems in computer science. The dynamic programming algorithm running in time $O^*(2^n)$ developed almost 60 years…
In the Single Source Replacement Paths (SSRP) problem we are given a graph $G = (V, E)$, and a shortest paths tree $\widehat{K}$ rooted at a node $s$, and the goal is to output for every node $t \in V$ and for every edge $e$ in…
We show fixed-parameter tractability of the Directed Multicut problem with three terminal pairs (with a randomized algorithm). This problem, given a directed graph $G$, pairs of vertices (called terminals) $(s_1,t_1)$, $(s_2,t_2)$, and…
Abasi et al. (2014) and Gabizon et al. (2015) studied the following problems. In the $r$-Simple $k$-Path problem, given a digraph $G$ on $n$ vertices and integers $r,k$, decide whether $G$ has an $r$-simple $k$-path, which is a walk where…
We resolve positively a long standing open question regarding the fixed-parameter tractability of the parameterized Directed Feedback Vertex Set problem. In particular, we propose an algorithm which solves this problem in…
We introduce a new Steiner-type problem for directed graphs named \textsc{$q$-Root Steiner Tree}. Here one is given a directed graph $G=(V,A)$ and two subsets of its vertices, $R$ of size $q$ and $T$, and the task is to find a minimum size…
We consider parameterized verification problems for networks of timed automata (TAs) based on different communication primitives. To this end, we first consider disjunctive timed networks (DTNs), i.e., networks of TAs that communicate via…
We present a data structure that we call a Dynamic Representative Set. In its most basic form, it is given two parameters $0< k < n$ and allows us to maintain a representation of a family $\mathcal{F}$ of subsets of $\{1,\ldots,n\}$. It…
The $k$ disjoint shortest paths problem ($k$-DSPP) on a graph with $k$ source-sink pairs $(s_i, t_i)$ asks for the existence of $k$ pairwise edge- or vertex-disjoint shortest $s_i$-$t_i$-paths. It is known to be NP-complete if $k$ is part…
We introduce a general method for obtaining fixed-parameter algorithms for problems about finding paths in undirected graphs, where the length of the path could be unbounded in the parameter. The first application of our method is as…
In a directed graph $D$ on vertex set $v_1,\dots ,v_n$, a \emph{forward arc} is an arc $v_iv_j$ where $i<j$. A pair $v_i,v_j$ is \emph{forward connected} if there is a directed path from $v_i$ to $v_j$ consisting of forward arcs. In the…
In the Directed Disjoint Paths problem ($k$-DDP), we are given a digraph $k$ pairs of terminals, and the goal is to find $k$ pairwise vertex-disjoint paths connecting each pair of terminals. Bang-Jensen and Thomassen [SIAM J. Discrete Math.…