DeepAI AI Chat
Log In Sign Up

Approximating (p,2) flexible graph connectivity via the primal-dual method

09/22/2022
by   Ishan Bansal, et al.
University of Waterloo
cornell university
0

We consider the Flexible Graph Connectivity model (denoted FGC) introduced by Adjiashvili, Hommelsheim and Mühlenthaler (IPCO 2020, Mathematical Programming 2021), and its generalization, (p,q)-FGC, where p ≥ 1 and q ≥ 0 are integers, introduced by Boyd et al. (FSTTCS 2021). In the (p,q)-FGC model, we have an undirected connected graph G=(V,E), non-negative costs c on the edges, and a partition (𝒮, 𝒰) of E into a set of safe edges 𝒮 and a set of unsafe edges 𝒰. A subset F ⊆ E of edges is called feasible if for any set F'⊆𝒰 with |F'| ≤ q, the subgraph (V, F ∖ F') is p-edge connected. The goal is to find a feasible edge-set of minimum cost. For the special case of (p,q)-FGC when q = 2, we give an O(1) approximation algorithm, thus improving on the logarithmic approximation ratio of Boyd et al. (FSTTCS 2021). Our algorithm is based on the primal-dual method for covering an uncrossable family, due to Williamson et al. (Combinatorica 1995). We conclude by studying weakly uncrossable families, which are a generalization of the well-known notion of an uncrossable family.

READ FULL TEXT

page 1

page 2

page 3

page 4

02/27/2022

Approximation Algorithms for Flexible Graph Connectivity

We present approximation algorithms for several network design problems ...
11/17/2022

Extensions of the (p,q)-Flexible-Graph-Connectivity model

We present approximation algorithms for network design problems in some ...
07/22/2020

An Improved Approximation Algorithm for the Matching Augmentation Problem

We present a 5/3-approximation algorithm for the matching augmentation p...
10/19/2017

A Primal-Dual based Distributed Approximation Algorithm for Prize Collecting Steiner Tree

Constructing a steiner tree of a graph is a fundamental problem in many ...
09/21/2020

On rooted k-connectivity problems in quasi-bipartite digraphs

We consider the directed Rooted Subset k-Edge-Connectivity problem: give...
08/14/2018

A Simple Primal-Dual Approximation Algorithm for 2-Edge-Connected Spanning Subgraphs

We propose a very simple and natural approximation algorithm for the pro...
04/08/2018

Multi-Level Steiner Trees

In the classical Steiner tree problem, one is given an undirected, conne...