A Framework for Approximation Schemes on Disk Graphs

Abstract

We initiate a systematic study of approximation schemes for fundamental optimization problems on disk graphs, a common generalization of both planar graphs and unit-disk graphs. Our main contribution is a general framework for designing efficient polynomial-time approximation schemes (EPTASes) for vertex-deletion problems on disk graphs, which results in EPTASes for many fundamental problems including Vertex Cover, Feedback Vertex Set, Small Cycle Hitting (in particular, Triangle Hitting), P k -Vertex Deletion for k ∈ {3, 4