
Fast Distributed Approximation for TAP and 2EdgeConnectivity
The tree augmentation problem (TAP) is a fundamental network design prob...
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2nodeconnectivity network design
We consider network design problems in which we are given a graph G=(V,E...
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Node Connectivity Augmentation via Iterative Randomized Rounding
Many network design problems deal with the design of lowcost networks t...
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Improved Approximation for Tree Augmentation: Saving by Rewiring
The Tree Augmentation Problem (TAP) is a fundamental network design prob...
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Efficient constructions of convex combinations for 2edgeconnected subgraphs on fundamental classes
Finding the exact integrality gap α for the LP relaxation of the 2edge...
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An intelligent extension of Variable Neighbourhood Search for labelling graph problems
In this paper we describe an extension of the Variable Neighbourhood Sea...
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Tight bounds for popping algorithms
We sharpen runtime analysis for algorithms under the partial rejection ...
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Flexible Graph Connectivity: Approximating Network Design Problems Between 1 and 2connectivity
Graph connectivity and network design problems are among the most fundamental problems in combinatorial optimization. The minimum spanning tree problem, the two edgeconnected spanning subgraph problem (2ECSS) and the tree augmentation problem (TAP) are all examples of fundamental wellstudied network design tasks that postulate different initial states of the network and different assumptions on the reliability of network components. In this paper we motivate and study Flexible Graph Connectivity (FGC), a problem that mixes together both the modeling power and the complexities of all aforementioned problems and more. In a nutshell, FGC asks to design a connected network, while allowing to specify different reliability levels for individual edges. While this nonuniform nature of the problem makes it appealing from the modeling perspective, it also renders most existing algorithmic tools for dealing with network design problems unfit for approximating FGC. In this paper we develop a general algorithmic approach for approximating FGC that yields approximation algorithms with ratios that are very close to the best known bounds for many special cases, such as 2ECSS and TAP. Our algorithm and analysis combine various techniques including a weightscaling algorithm, a charging argument that uses a variant of exchange bijections between spanning trees and a factor revealing nonlinear optimization problem.
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