Related papers: Optimum adaptation of a Steiner network
The paper addresses design/building frameworks for some kinds of tree-like and hierarchical structures of systems. The following approaches are examined: (1) expert-based procedures, (2) hierarchical clustering; (3) spanning problems (e.g.,…
A directed network connecting a set A to a set B is a digraph containing an a-b path for each a in A and b in B. Vertices in the directed network not in A or B are called Steiner points. We show that in a finitely compact metric space in…
We introduce the problem of finding a spanning tree along with a partition of the tree edges into fewest number of feasible sets, where constraints on the edges define feasibility. The motivation comes from wireless networking, where we…
The Steiner Tree Problem (STP) in graphs is an important problem with various applications in many areas such as design of integrated circuits, evolution theory, networking, etc. In this paper, we propose an algorithm to solve the STP. The…
Given a graph $G = (V,E)$ and a subset $T \subseteq V$ of terminals, a \emph{Steiner tree} of $G$ is a tree that spans $T$. In the vertex-weighted Steiner tree (VST) problem, each vertex is assigned a non-negative weight, and the goal is to…
In \cite{siebert2019linear} the authors present a set of integer programs (IPs) for the Steiner tree problem, which can be used for both, the directed and the undirected setting of the problem. Each IP finds an optimal Steiner tree with a…
The goal for the Directed Steiner Tree problem is to find a minimum cost tree in a directed graph G=(V,E) that connects all terminals X to a given root r. It is well known that modulo a logarithmic factor it suffices to consider acyclic…
Given a set of $k$-colored points in the plane, we consider the problem of finding $k$ trees such that each tree connects all points of one color class, no two trees cross, and the total edge length of the trees is minimized. For $k=1$,…
This paper introduces an exact algorithm for the construction of a shortest curvature-constrained network interconnecting a given set of directed points in the plane and an iterative method for doing so in 3D space. Such a network will be…
In this paper, we consider Steiner forest and its generalizations, prize-collecting Steiner forest and k-Steiner forest, when the vertices of the input graph are points in the Euclidean plane and the lengths are Euclidean distances. First,…
Emerging optical and virtualization technologies enable the design of more flexible and demand-aware networked systems, in which resources can be optimized toward the actual workload they serve. For example, in a demand-aware datacenter…
We develop a general method of proving that certain star configurations in finit e-dimensional normed spaces are Steiner minimal trees. This method generalizes the results of Lawlor and Morgan (1994) that could only be applied to…
While much of network design focuses mostly on cost (number or weight of edges), node degrees have also played an important role. They have traditionally either appeared as an objective, to minimize the maximum degree (e.g., the Minimum…
In Connectivity Augmentation problems we are given a graph $H=(V,E_H)$ and an edge set $E$ on $V$, and seek a min-size edge set $J \subseteq E$ such that $H \cup J$ has larger edge/node connectivity than $H$. In the Edge-Connectivity…
Given a subset of active nodes in a network can we re- construct the cascade that has generated these observa- tions? This is a problem that has been studied in the literature, but here we focus in the case that tempo- ral information is…
The Steiner Multicycle problem consists of, given a complete graph, a weight function on its vertices, and a collection of pairwise disjoint non-unitary sets called terminal sets, finding a minimum weight collection of vertex-disjoint…
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…
Consider a compact $M \subset \mathbb{R}^d$ and $r > 0$. A maximal distance minimizer problem is to find a connected compact set $\Sigma$ of the minimal length, such that \[ \max_{y \in M} dist (y, \Sigma) \leq r. \] The inverse problem is…
We consider the problem of constructing optimal decision trees: given a collection of tests which can disambiguate between a set of $m$ possible diseases, each test having a cost, and the a-priori likelihood of the patient having any…
Network design under uncertainty arises in countless real-world settings and can be captured by the Stochastic Steiner Tree Problem (SSTP). Although there are a few approaches specifically tailored to this stochastic optimization problem,…