Related papers: Complexity of Splits Reconstruction for Low-Degree…
We study the limiting degree distribution of the vertex splitting model introduced in \cite{DDJS:2009}. This is a model of randomly growing ordered trees, where in each time step the tree is separated into two components by splitting a…
Vertex splitting replaces a vertex by two copies and partitions its incident edges amongst the copies. This problem has been studied as a graph editing operation to achieve desired properties with as few splits as possible, most often…
Parameterized complexity seeks to use input structure to obtain faster algorithms for NP-hard problems. This has been most successful for graphs of low treewidth: Many problems admit fast algorithms relative to treewidth and many of them…
In the classical partial vertex cover problem, we are given a graph $G$ and two positive integers $R$ and $L$. The goal is to check whether there is a subset $V'$ of $V$ of size at most $R$, such that $V'$ covers at least $L$ edges of $G$.…
Polytrees are a subclass of Bayesian networks that seek to capture the conditional dependencies between a set of $n$ variables as a directed forest and are motivated by their more efficient inference and improved interpretability. Since the…
Given an ordered partition $\Pi =\{P_1,P_2, ...,P_t\}$ of the vertex set $V$ of a connected graph $G=(V,E)$, the \emph{partition representation} of a vertex $v\in V$ with respect to the partition $\Pi$ is the vector…
We study the parameterized complexity of computing the tree-partition-width, a graph parameter equivalent to treewidth on graphs of bounded maximum degree. On one hand, we can obtain approximations of the tree-partition-width efficiently:…
We consider the problem of embedding the Steiner points of a Steiner tree with given topology into the rectilinear plane. Thereby, the length of the path between a distinguished terminal and each other terminal must not exceed given length…
Our goal is to visualize an additional data dimension of a tree with multifaceted data through superimposition on vertical strips, which we call columns. Specifically, we extend upward drawings of unordered rooted trees where vertices have…
r-gathering problem is a variant of facility location problems. In this problem, we are given a set of users and a set of facilities on same metric space. We open some of the facilities and assign each user to an open facility, so that at…
We consider problems of finding a maximum size/weight $t$-matching without forbidden subgraphs in an undirected graph $G$ with the maximum degree bounded by $t+1$, where $t$ is an integer greater than $2$. Depending on the variant forbidden…
Given a graph $G = (V,E)$, a threshold function $t~ :~ V \rightarrow \mathbb{N}$ and an integer $k$, we study the Harmless Set problem, where the goal is to find a subset of vertices $S \subseteq V$ of size at least $k$ such that every…
We investigate the complexity of finding a transformation from a given spanning tree in a graph to another given spanning tree in the same graph via a sequence of edge flips. The exchange property of the matroid bases immediately yields…
The tree-depth problem can be seen as finding an elimination tree of minimum height for a given input graph $G$. We introduce a bicriteria generalization in which additionally the width of the elimination tree needs to be bounded by some…
Two kinds of approximation algorithms exist for the k-BALANCED PARTITIONING problem: those that are fast but compute unsatisfying approximation ratios, and those that guarantee high quality ratios but are slow. In this paper we prove that…
We here investigate on the complexity of computing the \emph{tree-length} and the \emph{tree-breadth} of any graph $G$, that are respectively the best possible upper-bounds on the diameter and the radius of the bags in a tree decomposition…
We show that reconstructing a tree from order information on triples is NP-hard. This is in contrast to the case for ultra-metrics and for subtree information on quadruples which are both known to allow polynomial time reconstruction.
Constructing the maximum spanning tree $T$ of an edge-weighted connected graph $G$ is one of the important research topics in computer science and optimization, and the related research results have played an active role in practical…
Given a graph $G$ and an integer $b$, Bandwidth asks whether there exists a bijection $\pi$ from $V(G)$ to $\{1, \ldots, |V(G)|\}$ such that $\max_{\{u, v \} \in E(G)} | \pi(u) - \pi(v) | \leq b$. This is a classical NP-complete problem,…
We consider the minimum spanning tree (MST) problem under the restriction that for every vertex v, the edges of the tree that are adjacent to v satisfy a given family of constraints. A famous example thereof is the classical…