Related papers: A simplified 1.5-approximation algorithm for augme…
Given a $k$-vertex-connected graph $G$ and a set $S$ of extra edges (links), the goal of the $k$-vertex-connectivity augmentation problem is to find a set $S' \subseteq S$ of minimum size such that adding $S'$ to $G$ makes it…
The Matching Augmentation Problem (MAP) has recently received significant attention as an important step towards better approximation algorithms for finding cheap $2$-edge connected subgraphs. This has culminated in a…
We present a $\frac74$ 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 consider the matching augmentation problem (MAP), where a matching of a graph needs to be extended into a $2$-edge-connected spanning subgraph by adding the minimum number of edges to it. We present a polynomial-time algorithm with an…
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…
In the Tree Augmentation problem we are given a tree $T=(V,F)$ and a set $E \subseteq V \times V$ of edges with positive integer costs $\{c_e:e \in E\}$. The goal is to augment $T$ by a minimum cost edge set $J \subseteq E$ such that $T…
For a connected graph, a {\em minimum vertex separator} is a minimum set of vertices whose removal creates at least two connected components. The vertex connectivity of the graph refers to the size of the minimum vertex separator and a…
We prove new results for approximating the graphic TSP and some related problems. We obtain polynomial-time algorithms with improved approximation guarantees. For the graphic TSP itself, we improve the approximation ratio to 7/5. For a…
We consider network design problems in which we are given a graph and seek a min-size $2$-connected subgraph that satisfies a prescribed property. $\bullet$ In the 1-Connectivity Augmentation problem the goal is to augment a connected graph…
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…
The Weighted Tree Augmentation problem (WTAP) is a fundamental problem in network design. In this paper, we consider this problem in the online setting. We are given an $n$-vertex spanning tree $T$ and an additional set $L$ of edges (called…
In the $Activation$ $k$ $Disjoint$ $st$-$Paths$ ($Activation$ $k$-$DP$) problem we are given a graph $G=(V,E)$ with activation costs $\{c_{uv}^u,c_{uv}^v\}$ for every edge $uv \in E$, a source-sink pair $s,t \in V$, and an integer $k$. The…
We consider the following two variants of the Capacitated $k$-Edge Connected Subgraph} (Cap-k-ECS) problem. Near Min-Cuts Cover: Given a graph $G=(V,E)$ with edge costs and $E_0 \subseteq E$, find a min-cost edge set $J \subseteq E…
In the k-edge-connected spanning subgraph problem we are given a graph (V, E) and costs for each edge, and want to find a minimum-cost subset F of E such that (V, F) is k-edge-connected. We show there is a constant eps > 0 so that for all k…
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 $\frac{6}{5}$…
We study the unweighted Tree Augmentation Problem (TAP) via the Lasserre (Sum of Squares) system. We prove an approximation guarantee of ($1.8+\epsilon$) relative to an SDP relaxation, which matches the combinatorial approximation guarantee…
A subset $T \subseteq V$ of terminals is $k$-connected to a root $s$ in a directed/undirected graph $J$ if $J$ has $k$ internally-disjoint $vs$-paths for every $v \in T$; $T$ is $k$-connected in $J$ if $T$ is $k$-connected to every $s \in…
We study budget constrained network upgradeable problems. We are given an undirected edge weighted graph $G=(V,E)$ where the weight an edge $e \in E$ can be upgraded for a cost $c(e)$. Given a budget $B$ for improvement, the goal is to find…
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:…
Finding a smallest subgraph that is k-edge-connected, or augmenting a k-edge-connected graph with a smallest subset of given candidate edges to become (k+1)-edge-connected, are among the most fundamental Network Design problems. They are…