Approximately: Independence Implies Vertex Cover
Computational Geometry
2026-02-23 v3 Data Structures and Algorithms
Abstract
We observe that a -approximation algorithm to Independent Set, that works for any induced subgraph of the input graph, can be used, via a polynomial time reduction, to provide a -approximation to Vertex Cover. This basic observation was made before, see [BHR11]. As a consequence, we get a PTAS for VC for unweighted pseudo-disks, QQPTAS for VC for unweighted axis-aligned rectangles in the plane, and QPTAS for MWVC for weighted polygons in the plane. To the best of our knowledge all these results are new.
Cite
@article{arxiv.2308.00840,
title = {Approximately: Independence Implies Vertex Cover},
author = {Sariel Har-Peled},
journal= {arXiv preprint arXiv:2308.00840},
year = {2026}
}