Non-Uniform Robust Network Design in Planar Graphs

TL;DR

This paper develops approximation algorithms for bulk-robust network design in planar graphs, addressing non-uniform failure patterns with techniques that leverage planar embeddings and LP rounding.

Contribution

It extends existing methods to handle non-uniform failure scenarios in planar graphs using an augmentation framework and LP rounding based on planar embeddings.

Findings

Provides approximation algorithms for bulk-robust network design in planar graphs.

Establishes a connection to cut covering and dominating set problems in circle graphs.

Demonstrates potential adaptability of methods to other robust network design problems.

Abstract

Robust optimization is concerned with constructing solutions that remain feasible also when a limited number of resources is removed from the solution. Most studies of robust combinatorial optimization to date made the assumption that every resource is equally vulnerable, and that the set of scenarios is implicitly given by a single budget constraint. This paper studies a robustness model of a different kind. We focus on \textbf{bulk-robustness}, a model recently introduced~\cite{bulk} for addressing the need to model non-uniform failure patterns in systems. We significantly extend the techniques used in~\cite{bulk} to design approximation algorithm for bulk-robust network design problems in planar graphs. Our techniques use an augmentation framework, combined with linear programming (LP) rounding that depends on a planar embedding of the input graph. A connection to cut covering problems and the dominating set problem in circle graphs is established. Our methods use few of the specifics of bulk-robust optimization, hence it is conceivable that they can be adapted to solve other robust network design problems.