Related papers: Blocking optimal arborescences
Given a digraph $D=(V,A)$ and a positive integer $k$, an arc set $F\subseteq A$ is called a \textbf{$k$-arborescence} if it is the disjoint union of $k$ spanning arborescences. The problem of finding a minimum cost $k$-arborescence is known…
Given a digraph $D=(V,A)$ and a positive integer $k$, a subset $B\subseteq A$ is called a \textbf{$k$-union-arborescence}, if it is the disjoint union of $k$ spanning arborescences. When also arc-costs $c:A\to \mathbb{R}$ are given,…
The minimum-cost arborescence problem is a well-studied problem in the area of graph theory, with known polynomial-time algorithms for solving it. Previous literature introduced new variations on the original problem with different…
Minimum cost homomorphism problems can be viewed as a generalization of list homomorphism problems. They also extend two well-known graph colouring problems: the minimum colour sum problem and the optimum cost chromatic partition problem.…
Our input is a directed graph $G = (V,E)$ on $n$ vertices and $m$ edges with a designated root vertex $r$ and a function $cost: E \rightarrow \mathbb{R}_{\geq 0}$. The problem is to maintain a min-cost arborescence in $G$ in the presence of…
Color-constrained subgraph problems are those where we are given an edge-colored (directed or undirected) graph and the task is to find a specific type of subgraph, like a spanning tree, an arborescence, a single-source shortest path tree,…
In the matching interdiction problem, we are given an undirected graph with weights and interdiction costs on the edges and seek to remove a subset of the edges constrained to some budget, such that the weight of a maximum weight matching…
Inferring probabilistic networks from data is a notoriously difficult task. Under various goodness-of-fit measures, finding an optimal network is NP-hard, even if restricted to polytrees of bounded in-degree. Polynomial-time algorithms are…
We give polynomial time logarithmic approximation guarantees for the budget minimization, as well as for the profit maximization versions of minimum spanning tree interdiction. In this problem, the goal is to remove some edges of an…
A natural way to deal with multiple, partially conflicting objectives is turning all the objectives but one into budget constraints. Some classical polynomial-time optimization problems, such as spanning tree and forest, shortest path,…
We provide the directed counterpart of a slight extension of Katoh and Tanigawa's result on rooted-tree decompositions with matroid constraints. Our result characterises digraphs having a packing of arborescences with matroid constraints.…
We give almost-linear-time algorithms for approximating rooted minimum cut and maximum arborescence packing in directed graphs, two problems that are dual to each other [Edm73]. More specifically, for an $n$-vertex, $m$-edge directed graph…
Given an undirected graph with edge costs and node weights, the minimum bisection problem asks for a partition of the nodes into two parts of equal weight such that the sum of edge costs between the parts is minimized. We give a polynomial…
We consider a variant of the prize collecting Steiner tree problem in which we are given a \emph{directed graph} $D=(V,A)$, a monotone submodular prize function $p:2^V \rightarrow \mathbb{R}^+ \cup \{0\}$, a cost function $c:V \rightarrow…
Our input is a directed, rooted graph $G = (V \cup \{r\},E)$ where each vertex in $V$ has a partial order preference over its incoming edges. The preferences of a vertex extend naturally to preferences over arborescences rooted at $r$. We…
In the minimum spanning tree (MST) interdiction problem, we are given a graph $G=(V,E)$ with edge weights, and want to find some $X\subseteq E$ satisfying a knapsack constraint such that the MST weight in $(V,E\setminus X)$ is maximized.…
We give an algorithm for finding the arboricity of a weighted, undirected graph, defined as the minimum number of spanning forests that cover all edges of the graph, in $\sqrt{n} m^{1+o(1)}$ time. This improves on the previous best bound of…
We study the {\em min-cost chain-constrained spanning-tree} (abbreviated \mcst) problem: find a min-cost spanning tree in a graph subject to degree constraints on a nested family of node sets. We devise the {\em first} polytime algorithm…
Given two matroids $\mathcal{M}_{1} = (E, \mathcal{B}_{1})$ and $\mathcal{M}_{2} = (E, \mathcal{B}_{2})$ on a common ground set $E$ with base sets $\mathcal{B}_{1}$ and $\mathcal{B}_{2}$, some integer $k \in \mathbb{N}$, and two cost…
Given a graph $G = (V, E)$ and an integer $k$, the Minimum Membership Dominating Set problem asks to compute a set $S \subseteq V$ such that for each $v \in V$, $1 \leq |N[v] \cap S| \leq k$. The problem is known to be NP-complete even on…