相关论文: A $2$-Approximation Algorithm for Flexible Graph C…
We present approximation algorithms for several network design problems in the model of Flexible Graph Connectivity (Adjiashvili, Hommelsheim and M\"uhlenthaler, "Flexible Graph Connectivity", Math. Program. pp. 1-33 (2021), and IPCO 2020:…
Graph connectivity and network design problems are among the most fundamental problems in combinatorial optimization. The minimum spanning tree problem, the two edge-connected spanning subgraph problem (2-ECSS) and the tree augmentation…
Flexible network design deals with building a network that guarantees some connectivity requirements between its vertices, even when some of its elements (like vertices or edges) fail. In particular, the set of edges (resp. vertices) of a…
Increasing the connectivity of a graph is a pivotal challenge in robust network design. The weighted connectivity augmentation problem is a common version of the problem that takes link costs into consideration. The problem is then to find…
We propose a simple and natural approximation algorithm for the problem of finding a 2-edge-connected spanning subgraph of minimum total edge cost in a graph. The algorithm maintains a spanning forest starting with an empty edge set. In…
The basic goal of survivable network design is to build cheap networks that guarantee the connectivity of certain pairs of nodes despite the failure of a few edges or nodes. A celebrated result by Jain [Combinatorica'01] provides a…
We present a $\frac53$-approximation algorithm for the matching augmentation problem (MAP): given a multi-graph with edges of cost either zero or one such that the edges of cost zero form a matching, find a 2-edge connected spanning…
We obtain a polynomial-time 17/12-approximation algorithm for the minimum-cost 2-vertex-connected spanning subgraph problem, restricted to graphs of minimum degree at least 3. Our algorithm uses the framework of ear-decompositions for…
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…
The Tree Augmentation Problem (TAP) is: given a connected graph $G=(V,{\cal E})$ and an edge set $E$ on $V$ find a minimum size subset of edges $F \subseteq E$ such that $(V,{\cal E} \cup F)$ is $2$-edge-connected. In the conference version…
We present a new approximation algorithm for the minimum 2-edge-connected spanning subgraph problem. Its approximation ratio is $\frac{4}{3}$, which matches the current best ratio. The approximation ratio of the algorithm is $\frac{6}{5}$…
Jaberi [7] presented approximation algorithms for the problem of computing a minimum size 2-vertex strongly biconnected subgraph in directed graphs. We have implemented approximation algorithms presented in [7] and we have tested the…
The $2$-admissibility of a graph is a promising measure to identify real-world networks which have an algorithmically favourable structure. In contrast to other related measures, like the weak/strong $2$-colouring numbers or the maximum…
We present improved approximation algorithms for some problems in the related areas of Capacitated Network Design and Flexible Graph Connectivity. In the Cap-$k$-ECSS problem, we are given a graph $G=(V,E)$ whose edges have non-negative…
We present a 6-approximation algorithm for the minimum-cost $k$-node connected spanning subgraph problem, assuming that the number of nodes is at least $k^3(k-1)+k$. We apply a combinatorial preprocessing, based on the Frank-Tardos…
Finding the most parsimonious tree inside a phylogenetic network with respect to a given character is an NP-hard combinatorial optimization problem that for many network topologies is essentially inapproximable. In contrast, if the network…
Given an edge weighted graph and a forest $F$, the $\textit{2-edge connectivity augmentation problem}$ is to pick a minimum weighted set of edges, $E'$, such that every connected component of $E'\cup F$ is 2-edge connected. Williamson et…
Connectivity augmentation problems are among the most elementary questions in Network Design. Many of these problems admit natural $2$-approximation algorithms, often through various classic techniques, whereas it remains open whether…
The $2$-Edge-Connected Spanning Subgraph problem (2-ECSS) is one of the most fundamental and well-studied problems in the context of network design. In the problem, we are given an undirected graph $G$, and the objective is to find a…
We describe a $\frac{3}{2}$-approximation algorithm for the Forest Augmentation Problem (\textsf{FAP}), which is a special case of the Weighted 2-Edge-Connected Spanning Subgraph Problem (\textsf{Weighted 2-ECSS}). This significantly…