eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2022-09-15
50:1
50:16
10.4230/LIPIcs.APPROX/RANDOM.2022.50
article
Some Results on Approximability of Minimum Sum Vertex Cover
Stanković, Aleksa
1
https://orcid.org/0000-0002-8416-8665
Department of Mathematics, KTH Royal Institute of Technology, Stockholm, Sweden
We study the Minimum Sum Vertex Cover problem, which asks for an ordering of vertices in a graph that minimizes the total cover time of edges. In particular, n vertices of the graph are visited according to an ordering, and for each edge this induces the first time it is covered. The goal of the problem is to find the ordering which minimizes the sum of the cover times over all edges in the graph.
In this work we give the first explicit hardness of approximation result for Minimum Sum Vertex Cover. In particular, assuming the Unique Games Conjecture, we show that the Minimum Sum Vertex Cover problem cannot be approximated within 1.014. The best approximation ratio for Minimum Sum Vertex Cover as of now is 16/9, due to a recent work of Bansal, Batra, Farhadi, and Tetali.
We also revisit an approximation algorithm for regular graphs outlined in the work of Feige, Lovász, and Tetali, and show that Minimum Sum Vertex Cover can be approximated within 1.225 on regular graphs.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol245-approx-random2022/LIPIcs.APPROX-RANDOM.2022.50/LIPIcs.APPROX-RANDOM.2022.50.pdf
Hardness of approximation
approximability
approximation algorithms
Label Cover
Unique Games Conjecture
Vertex Cover