A simple 7/3-approximation algorithm for feedback vertex set in tournaments

Aprile, Manuel; Drescher, Matthew; Fiorini, Samuel; Huynh, Tony

doi:10.48550/arxiv.2008.08779

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2022

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“…Lokshtanov, Misra, Mukherjee, Panolan, Philip, and Saurabh [18] recently gave a randomized 2-approximation algorithm, but no deterministic (polynomial-time) 2-approximation algorithm is known. For FVST, one round of the Sherali-Adams hierarchy actually provides a 7/3-approximation [3]. This is in contrast with Theorem 3.…”

Section: Other Related Workmentioning

confidence: 80%

A tight approximation algorithm for the cluster vertex deletion problem

et al. 2022

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We give the first 2-approximation algorithm for the cluster vertex deletion problem. This is tight, since approximating the problem within any constant factor smaller than 2 is UGC-hard. Our algorithm combines the previous approaches, based on the local ratio technique and the management of true twins, with a novel construction of a "good" cost function on the vertices at distance at most 2 from any vertex of the input graph.As an additional contribution, we also study cluster vertex deletion from the polyhedral perspective, where we prove almost matching upper and lower bounds on how well linear programming relaxations can approximate the problem.

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Section: Other Related Workmentioning

confidence: 80%