Approximating Minimum-Cost k-Node Connected Subgraphs via Independence-Free Graphs

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 algorithm for $k$-outconnectivity, to transform any input into an instance such that the iterative rounding method gives a 2-approximation guarantee. This is the first constant-factor approximation algorithm even in the asymptotic setting of the problem, that is, the restriction to instances where the number of nodes is lower bounded by a function of $k$.Comment: 20 pages, 1 figure, 28 reference

Algorithms and Hardness Results for Compressing Graphs with Distance Constraints

Graphs have been widely utilized in network design and other applications. A natural question is, can we keep as few edges of the original graph as possible, but still make sure that the vertices are connected within certain distance constraints. In this thesis, we will consider different versions of graph compression problems, including graph spanners, approximate distance oracles, and Steiner networks. Since these problems are all NP-hard problems, we will mostly focus on designing approximation algorithms and proving inapproximability results

LIPIcs, Volume 274, ESA 2023, Complete Volume

LIPIcs, Volume 274, ESA 2023, Complete Volum