Related papers: Optimal algorithm for computing Steiner 3-eccentri…
In this work we consider the Metric Steiner Forest problem in the sublinear time model. Given a set $V$ of $n$ points in a metric space where distances are provided by means of query access to an $n\times n$ distance matrix, along with a…
Embeddings of graphs into distributions of trees that preserve distances in expectation are a cornerstone of many optimization algorithms. Unfortunately, online or dynamic algorithms which use these embeddings seem inherently randomized and…
We give an algorithm for finding the arboricity of a weighted, undirected graph, defined as the minimum number of spanning forests that cover all edges of the graph, in $\sqrt{n} m^{1+o(1)}$ time. This improves on the previous best bound of…
Given a complete graph $G=(V,E)$, with nonnegative edge costs, two subsets $R \subset V$ and $R^{\prime} \subset R$, a partition $\mathcal{R}=\{R_1,R_2,\ldots,R_k\}$ of $R$, $R_i \cap R_j=\phi$, $i \neq j$ and…
We introduce a temporal Steiner network problem in which a graph, as well as changes to its edges and/or vertices over a set of discrete times, are given as input; the goal is to find a minimal subgraph satisfying a set of $k$…
Steiner Tree Packing (STP) is a notoriously hard problem in classical complexity theory, which is of practical relevance to VLSI circuit design. Previous research has approached this problem by providing heuristic or approximate algorithms.…
Prize-Collecting Steiner Tree (PCST) is a generalization of the Steiner Tree problem, a fundamental problem in computer science. In the classic Steiner Tree problem, we aim to connect a set of vertices known as terminals using the…
The Steiner Forest problem, also known as the Generalized Steiner Tree problem, is a fundamental optimization problem on edge-weighted graphs where, given a set of vertex pairs, the goal is to select a minimum-cost subgraph such that each…
The $S$-Steiner tree packing problem provides mathematical foundations for optimizing multi-path information transmission, particularly in designing fault-tolerant parallelized routing architectures for massive-scale network…
A tree $t$-spanner of a graph $G$ is a spanning tree of $G$ such that the distance between pairs of vertices in the tree is at most $t$ times their distance in $G$. Deciding tree $t$-spanner admissible graphs has been proved to be tractable…
Estimating similarity between vertices is a fundamental issue in network analysis across various domains, such as social networks and biological networks. Methods based on common neighbors and structural contexts have received much…
We consider the eccentric graph of a graph $G$, denoted by $ecc(G)$, which has the same vertex set as $G$, and two vertices in the eccentric graph are adjacent iff their distance in $G$ is equal to the eccentricity of one of them. In this…
Steiner Tree Problem (STP) in graphs aims to find a tree of minimum weight in the graph that connects a given set of vertices. It is a classic NP-hard combinatorial optimization problem and has many real-world applications (e.g., VLSI chip…
In this paper we study the Steiner tree problem over a dynamic set of terminals. We consider the model where we are given an $n$-vertex graph $G=(V,E,w)$ with positive real edge weights, and our goal is to maintain a tree which is a good…
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…
Wiener index, defined as the sum of distances between all unordered pairs of vertices, is one of the most popular molecular descriptors. It is well known that among 2-vertex connected graphs on $n\ge 3$ vertices, the cycle $C_n$ attains the…
For a simple graph $G$, the $3$-distance graph, $D_3(G)$, is a graph with the vertex set $V(G)$ and two vertices are adjacent if and only if their distance is $3$ in the graph $G$. For a connected graph $G$, we provide some conditions for…
The \emph{eccentricity} of a vertex $u$ in a graph $G$, denoted by $e_G(u)$, is the maximum distance from $u$ to other vertices in $G$. We study extremal problems for the average eccentricity and the first and second Zagreb eccentricity…
In this work, I collect and discuss a series of open questions in one-dimensional geometric optimization in Euclidean spaces. The focus is on two classes of problems: maximal distance minimizers and Steiner trees. Maximal distance…
In this paper we propose and study a new complexity model for approximation algorithms. The main motivation are practical problems over large data sets that need to be solved many times for different scenarios, e.g., many multicast trees…