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Two Approaches to Approximation Algorithms for Vertex Deletion Problems

par Drescher, Matthew
Président du jury Cardinal, Jean
Promoteur Fiorini, Samuel
Publication Non publié, 2021-11-15

Thèse de doctorat

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Résumé :

We give a 2-approximation algorithm for Cluster Vertex Deletion. This tight result matches the hardness lower bound. We obtain a new deterministic 7/3-approximation algorithm for Feedback Vertex Set in Tournaments. This result is based on the LP given by just one round of Sherali-Adams. We find a new, simpler deterministic (2 + epsilon)-approximation algorithm for Split Vertex Deletion. We give a 2-approximation algorithm for Claw-Free Vertex Deletion in triangle-free graphs. In the case of general graphs we prove that it is UGC-hard to obtain an approximation ratio lower than 3.