# A simple (2+ε)-approximation algorithm for Split Vertex Deletion

A split graph is a graph whose vertex set can be partitioned into a clique and a stable set. Given a graph G and weight function w: V(G) →ℚ_≥ 0, the Split Vertex Deletion (SVD) problem asks to find a minimum weight set of vertices X such that G-X is a split graph. It is easy to show that a graph is a split graph if and only it it does not contain a 4-cycle, 5-cycle, or a two edge matching as an induced subgraph. Therefore, SVD admits an easy 5-approximation algorithm. On the other hand, for every δ >0, SVD does not admit a (2-δ)-approximation algorithm, unless P=NP or the Unique Games Conjecture fails. For every ϵ >0, Lokshtanov, Misra, Panolan, Philip, and Saurabh recently gave a randomized (2+ϵ)-approximation algorithm for SVD. In this work we give an extremely simple deterministic (2+ϵ)-approximation algorithm for SVD.

## Authors

• 3 publications
• 15 publications
• 23 publications
• ### Improved approximation algorithms for hitting 3-vertex paths

We study the problem of deleting a minimum cost set of vertices from a g...
08/30/2018 ∙ by Samuel Fiorini, et al. ∙ 0

• ### Approximation algorithms on k- cycle covering and k- clique covering

Given a weighted graph G(V,E) with weight w: E→ Z^|E|_+. A k-cycle cove...
07/18/2018 ∙ by Zhongzheng Tang, et al. ∙ 0

• ### Faster branching algorithm for split to block vertex deletion

In the Split to Block Vertex Deletion (SBVD) problem the input is a spli...
06/24/2019 ∙ by Dekel Tsur, et al. ∙ 0

• ### Star Routing: Between Vehicle Routing and Vertex Cover

We consider an optimization problem posed by an actual newspaper company...
01/26/2019 ∙ by Diego Delle Donne, et al. ∙ 0

• ### A Tight Approximation Algorithm for the Cluster Vertex Deletion Problem

We give the first 2-approximation algorithm for the cluster vertex delet...
07/16/2020 ∙ by Manuel Aprile, et al. ∙ 0

• ### Tiny Transducer: A Highly-efficient Speech Recognition Model on Edge Devices

This paper proposes an extremely lightweight phone-based transducer mode...
01/18/2021 ∙ by Yuekai Zhang, et al. ∙ 0

• ### A note on the Split to Block Vertex Deletion problem

In the Split to Block Vertex Deletion (SBVD) problem the input is a spli...
06/24/2019 ∙ by Dekel Tsur, et al. ∙ 0

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