Approximately: Independence Implies Vertex Cover
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866910028117573632 |
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| author | Har-Peled, Sariel |
| author_facet | Har-Peled, Sariel |
| contents | $\newcommand{\eps}{\varepsilon}$
We observe that a $(1-\eps)$-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 $(1+\eps)$-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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_00840 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Approximately: Independence Implies Vertex Cover Har-Peled, Sariel Computational Geometry Data Structures and Algorithms $\newcommand{\eps}{\varepsilon}$ We observe that a $(1-\eps)$-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 $(1+\eps)$-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. |
| title | Approximately: Independence Implies Vertex Cover |
| topic | Computational Geometry Data Structures and Algorithms |
| url | https://arxiv.org/abs/2308.00840 |