Related papers: Open problems on Steiner trees and maximal distanc…
In the classical Steiner tree problem, given an undirected, connected graph $G=(V,E)$ with non-negative edge costs and a set of \emph{terminals} $T\subseteq V$, the objective is to find a minimum-cost tree $E' \subseteq E$ that spans the…
In this paper, we introduce the Fixed Topology Minimum-Length Tree with Neighborhood Problem, which aims to embed a rooted tree-shaped graph into a $d$-dimensional metric space while minimizing its total length provided that the nodes must…
We introduce a flow-dependent version of the quadratic Steiner tree problem in the plane. An instance of the problem on a set of embedded sources and a sink asks for a directed tree $T$ spanning these nodes and a bounded number of Steiner…
For an arbitrary tree we investigate the problems of constructing a maximum matching which minimizes or maximizes the cardinality of a maximum matching of the graph obtained from original one by its removal and present corresponding…
We study the complexity of geometric problems on spaces of low fractal dimension. It was recently shown by [Sidiropoulos & Sridhar, SoCG 2017] that several problems admit improved solutions when the input is a pointset in Euclidean space…
In algorithms for finite metric spaces, it is common to assume that the distance between two points can be computed in constant time, and complexity bounds are expressed only in terms of the number of points of the metric space. We…
We achieve a (randomized) polynomial-time approximation scheme (PTAS) for the Steiner Forest Problem in doubling metrics. Before our work, a PTAS is given only for the Euclidean plane in [FOCS 2008: Borradaile, Klein and Mathieu]. Our PTAS…
Given an undirected graph $G = (V, E)$ and a weight function $w:E \to \mathbb{R}$, the \textsc{Minimum Dominating Tree} problem asks to find a minimum weight sub-tree of $G$, $T = (U, F)$, such that every $v \in V \setminus U$ is adjacent…
Treedepth decomposition has several practical applications and can be used to speed up many parameterized algorithms. There are several works aiming to design a scalable algorithm to compute exact treedepth decompositions. Those include…
Minimum distance constraints (minDCs) appear in many geometric optimization problems. They pose major challenges for mixed-integer nonlinear programming (MINLP) due to their reverse-convexity. We develop new algorithms for tightening…
This paper addresses combinatorial optimization scheme for solving the multicriteria Steiner tree problem for communication network topology design (e.g., wireless mesh network). The solving scheme is based on several models: multicriteria…
Given a set $P$ of $n$ points in $\mathbb{R}^2$ and an input line $\gamma$ in $\mathbb{R}^2$, we present an algorithm that runs in optimal $\Theta(n\log n)$ time and $\Theta(n)$ space to solve a restricted version of the $1$-Steiner tree…
Calibrations are a possible tool to validate the minimality of a certain candidate. They have been introduced in the context of minimal surfaces and adapted to the case of Steiner problem in several variants. Our goal is to compare the…
We present two algorithms for computing the geodesic distance between phylogenetic trees in tree space, as introduced by Billera, Holmes, and Vogtmann (2001). We show that the possible combinatorial types of shortest paths between two trees…
We investigate the problem of designing a minimum cost flow network interconnecting n sources and a single sink, each with known locations and flows. The network may contain other unprescribed nodes, known as Steiner points. For concave…
We investigate minimal-perimeter configurations of two finite sets of points on the square lattice. This corresponds to a lattice version of the classical double-bubble problem. We give a detailed description of the fine geometry of…
We study optimization problems for partially hinged rectangular plates, modeling bridge roadways, in the presence of real and artificial obstacles. Real obstacles represent structural constraints to avoid, while artificial ones are…
The hop-constrained Steiner tree problem (HSTP) is a generalization of the classical Steiner tree problem. It asks for a minimum cost subtree that spans some specified nodes of a given graph, such that the number of edges between each node…
This paper formulates the problem of Extremum Seeking for optimization of cost functions defined on Riemannian manifolds. We extend the conventional extremum seeking algorithms for optimization problems in Euclidean spaces to optimization…
The Gilbert-Pollak Conjecture \citep{gilbert1968steiner}, also known as the Steiner Ratio Conjecture, states that for any finite point set in the Euclidean plane, the Steiner minimum tree has length at least $\sqrt{3}/2 \approx 0.866$ times…