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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 $w: V(G) to mathbb{Q}_{geq 0}$, 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 $delta >0$, SVD does not admit a $(2-delta)$-approximation algorithm, unless P=NP or the Unique Games Conjecture fails. For every $epsilon >0$, Lokshtanov, Misra, Panolan, Philip, and Saurabh recently gave a randomized $(2+epsilon)$-approximation algorithm for SVD. In this work we give an extremely simple deterministic $(2+epsilon)$-approximation algorithm for SVD.
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 th
We present a local algorithm (constant-time distributed algorithm) for finding a 3-approximate vertex cover in bounded-degree graphs. The algorithm is deterministic, and no auxiliary information besides port numbering is required.
A cactus is a connected graph that does not contain $K_4 - e$ as a minor. Given a graph $G = (V, E)$ and integer $k ge 0$, Cactus Vertex Deletion (also known as Diamond Hitting Set) is the problem of deciding whether $G$ has a vertex set of size at m
One of the most fundamental results in combinatorial optimization is the polynomial-time 3/2-approximation algorithm for the metric traveling salesman problem. It was presented by Christofides in 1976 and is well known as the Christofides algorithm.
This paper introduces a novel algorithmic solution for the approximation of a given multivariate function by a nomographic function that is composed of a one-dimensional continuous and monotone outer function and a sum of univariate continuous inner