2020/09/23 by Matthew Drescher, Samuel Fiorini, Drescher, Matthew +3
Computer Science · #05C17 #05C69 #68W25 #Combinatorics (math.CO) #Complexity and Algorithms in Graphs #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning and Algorithms #Optimization and Search Problems
paper · pdf · doi:10.48550/arxiv.2009.11056
openalex publication_date 2020/09/23 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
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.