Related papers: Parameterized Algorithms for Computing MAD Trees
Phylogenetic trees and networks are leaf-labelled graphs used to model evolution. Display graphs are created by identifying common leaf labels in two or more phylogenetic trees or networks. The treewidth of such graphs is bounded as a…
We study the parameterized complexity of the directed variant of the classical {\sc Steiner Tree} problem on various classes of directed sparse graphs. While the parameterized complexity of {\sc Steiner Tree} parameterized by the number of…
We study the NP-hard problem of approximating a Minimum Routing Cost Spanning Tree in the message passing model with limited bandwidth (CONGEST model). In this problem one tries to find a spanning tree of a graph $G$ over $n$ nodes that…
Fixed parameter tractable algorithms for bounded treewidth are known to exist for a wide class of graph optimization problems. While most research in this area has been focused on exact algorithms, it is hard to find decompositions of…
We study the notion of local treewidth in sparse random graphs: the maximum treewidth over all $k$-vertex subgraphs of an $n$-vertex graph. When $k$ is not too large, we give nearly tight bounds for this local treewidth parameter; we also…
Algorithms for learning decision trees often include heuristic local-search operations such as (1) adjusting the threshold of a cut or (2) also exchanging the feature of that cut. We study minimizing the number of classification errors by…
We consider the problems ZERO EXTENSION and METRIC LABELLING under the paradigm of parameterized complexity. These are natural, well-studied problems with important applications, but have previously not received much attention from…
This paper investigates the complexity of finding secluded paths in graphs. We focus on the \textsc{Short Secluded Path} problem and a natural new variant we introduce, \textsc{Shortest Secluded Path}. Formally, given an undirected graph…
For the well-known Survivable Network Design Problem (SNDP) we are given an undirected graph $G$ with edge costs, a set $R$ of terminal vertices, and an integer demand $d_{s,t}$ for every terminal pair $s,t\in R$. The task is to compute a…
In the non-uniform sparsest cut problem, we are given a supply graph G and a demand graph D, both with the same set of nodes V. The goal is to find a cut of V that minimizes the ratio of the total capacity on the edges of G crossing the cut…
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,…
The Maximum Agreement Forest problem has been extensively studied in phylogenetics. Most previous work is on two binary phylogenetic trees. In this paper, we study a generalized version of the problem: the Maximum Agreement Forest problem…
We consider drawings of graphs in the plane in which vertices are assigned distinct points in the plane and edges are drawn as simple curves connecting the vertices and such that the edges intersect only at their common endpoints. There is…
In this paper, we consider different constrained partition problems for weighted trees and cactus graphs. We focus on the (l,u)-partition problem, which is the problem of partitioning a weighted graph into connected clusters such that each…
We consider the NP-hard problem of finding a spanning tree with a maximum number of internal vertices. This problem is a generalization of the famous Hamiltonian Path problem. Our dynamic-programming algorithms for general and…
Short spanning trees subject to additional constraints are important building blocks in various approximation algorithms. Especially in the context of the Traveling Salesman Problem (TSP), new techniques for finding spanning trees with…
The online dominating set problem is an online variant of the minimum dominating set problem, which is one of the most important NP-hard problems on graphs. This problem is defined as follows: Given an undirected graph $G = (V, E)$, in…
We consider the Shallow-Light Steiner Network problem from a fixed-parameter perspective. Given a graph $G$, a distance bound $L$, and $p$ pairs of vertices $(s_1,t_1),\cdots,(s_p,t_p)$, the objective is to find a minimum-cost subgraph $G'$…
Arising from structural graph theory, treewidth has become a focus of study in fixed-parameter tractable algorithms in various communities including combinatorics, integer-linear programming, and numerical analysis. Many NP-hard problems…
The problem of maximizing the $p$-th power of a $p$-norm over a halfspace-presented polytope in $\R^d$ is a convex maximization problem which plays a fundamental role in computational convexity. It has been shown in 1986 that this problem…