Related papers: Structural Parameterization of Steiner Tree Packin…
Given a set $P$ of $n$ points with their pairwise distances, the traveling salesman problem (TSP) asks for a shortest tour that visits each point exactly once. A TSP instance is rectilinear when the points lie in the plane and the distance…
Some biological experiments show that the tubular structures of Physarum polycephalum are often analogous to those of Steiner trees. Therefore, the emerging Physarum-inspired Algorithms (PAs) have the potential of computing Steiner trees.…
Let G=(V,E) be a connected graph, where V and E represent, respectively, the node-set and the edge-set. Besides, let Q \subseteq V be a set of terminal nodes, and r \in Q be the root node of the graph. Given a weight c_{ij} \in \mathbb{N}…
A stable cutset in a graph $G$ is a set $S\subseteq V(G)$ such that vertices of $S$ are pairwise non-adjacent and such that $G-S$ is disconnected, i.e., it is both stable (or independent) set and a cutset (or separator). Unlike general…
We study the classical problem of computing geometric thickness, i.e., finding a straight-line drawing of an input graph and a partition of its edges into as few parts as possible so that each part is crossing-free. Since the problem is…
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 a new Steiner tree problem, called vertex-cover-weighted Steiner tree problem. This problem defines the weight of a Steiner tree as the minimum weight of vertex covers in the tree, and seeks a minimum-weight Steiner tree in a…
The Vehicle Routing Problem (VRP) is a popular generalization of the Traveling Salesperson Problem. Instead of one salesperson traversing the entire weighted, undirected graph $G$, there are $k$ vehicles available to jointly cover the set…
Network design problems aim to compute low-cost structures such as routes, trees and subgraphs. Often, it is natural and desirable to require that these structures have small hop length or hop diameter. Unfortunately, optimization problems…
Branchwidth determines how graphs, and more generally, arbitrary connectivity (basically symmetric and submodular) functions could be decomposed into a tree-like structure by specific cuts. We develop a general framework for designing…
We associate a graph with a 1-safe Petri net and study the parameterized complexity of various problems with parameters derived from the graph. With treewidth as the parameter, we give W[1]-hardness results for many problems about 1-safe…
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…
The Planar Steiner Tree problem is one of the most fundamental NP-complete problems as it models many network design problems. Recall that an instance of this problem consists of a graph with edge weights, and a subset of vertices (often…
Parallel parameterized complexity theory studies how fixed-parameter tractable (fpt) problems can be solved in parallel. Previous theoretical work focused on parallel algorithms that are very fast in principle, but did not take into account…
We propose an algorithm whose input are parameters $k$ and $r$ and a hypergraph $H$ of rank at most $r$. The algorithm either returns a tree decomposition of $H$ of generalized hypertree width at most $4k$ or 'NO'. In the latter case, it is…
In this article, we study the Euclidean minimum spanning tree problem in an imprecise setup. The problem is known as the \emph{Minimum Spanning Tree Problem with Neighborhoods} in the literature. We study the problem where the neighborhoods…
Given a graph G, a matching is a subset of edges of G that do not share an endpoint. A matching M is uniquely restricted if the subgraph induced by the endpoints of the edges of M has exactly one perfect matching. Given a graph G and a…
We consider a variant of treewidth that we call clique-partitioned treewidth in which each bag is partitioned into cliques. This is motivated by the recent development of FPT-algorithms based on similar parameters for various problems. With…
In this paper, we consider the Uniform Cost-Distance Steiner Tree Problem in metric spaces, a generalization of the well-known Steiner tree problem. Cost-distance Steiner trees minimize the sum of the total length and the weighted path…
The Spanning Tree Congestion (STC) problem is the following NP-hard problem: given a graph $G$, construct a spanning tree $T$ of $G$ minimizing its maximum edge congestion where the congestion of an edge $e\in T$ is the number of edges $uv$…