Fiorini, Samuel, Joret, Gwenael ORCID: 0000-0002-7157-6694 and Schaudt, Oliver (2020). Improved approximation algorithms for hitting 3-vertex paths. Math. Program., 182 (1-2). S. 355 - 368. HEIDELBERG: SPRINGER HEIDELBERG. ISSN 1436-4646
Full text not available from this repository.Abstract
We study the problem of deleting a minimum cost set of vertices from a given vertex-weighted graph in such a way that the resulting graph has no induced path on three vertices. This problem is often calledcluster vertex deletionin the literature and admits a straightforward 3-approximation algorithm since it is a special case of the vertex cover problem on a 3-uniform hypergraph. Recently, You, Wang, and Cao described an efficient 5/2-approximation algorithm for the unweighted version of the problem. Our main result is a 9/4-approximation algorithm for arbitrary weights, using the local ratio technique. We further conjecture that the problem admits a 2-approximation algorithm and give some support for the conjecture. This is in sharp contrast with the fact that the similar problem of deleting vertices to eliminate all triangles in a graph is known to be UGC-hard to approximate to within a ratio better than 3, as proved by Guruswami and Lee.
Item Type: | Journal Article | ||||||||||||||||
Creators: |
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URN: | urn:nbn:de:hbz:38-328290 | ||||||||||||||||
DOI: | 10.1007/s10107-019-01395-y | ||||||||||||||||
Journal or Publication Title: | Math. Program. | ||||||||||||||||
Volume: | 182 | ||||||||||||||||
Number: | 1-2 | ||||||||||||||||
Page Range: | S. 355 - 368 | ||||||||||||||||
Date: | 2020 | ||||||||||||||||
Publisher: | SPRINGER HEIDELBERG | ||||||||||||||||
Place of Publication: | HEIDELBERG | ||||||||||||||||
ISSN: | 1436-4646 | ||||||||||||||||
Language: | English | ||||||||||||||||
Faculty: | Unspecified | ||||||||||||||||
Divisions: | Unspecified | ||||||||||||||||
Subjects: | no entry | ||||||||||||||||
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URI: | http://kups.ub.uni-koeln.de/id/eprint/32829 |
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