# Markus S. Dregi

• 2013 IEEE 54th Annual Symposium on Foundations of…
• 2013
We give an algorithm that for an input n-vertex graph G and integer k &gt; 0, in time O(c<sup>k</sup>n) either outputs that the tree width of G is larger than k, or gives a tree decomposition of G of width at most 5k + 4. This is the first algorithm providing a constant factor approximation for tree width which runs in time single-exponential in k and(More)
• SIAM J. Comput.
• 2016
We give an algorithm that for an input n-vertex graph G and integer k > 0, in time O(cn) either outputs that the treewidth of G is larger than k, or gives a tree decomposition of G of width at most 5k + 4. This is the first algorithm providing a constant factor approximation for treewidth which runs in time single-exponential in k and linear in n. Treewidth(More)
We study the computational complexity of the graph modification problems Threshold Editing and Chain Editing, adding and deleting as few edges as possible to transform the input into a threshold (or chain) graph. In this article, we show that both problems are NP-hard, resolving a conjecture by Natanzon, Shamir, and Sharan (Discrete Applied Mathematics,(More)
We prove that for every positive integer r and for every graph class G of bounded expansion, the r-Dominating Set problem admits a linear kernel on graphs from G. Moreover, when G is only assumed to be nowhere dense, then we give an almost linear kernel on G for the classic Dominating Set problem, i.e., for the case r = 1. These results generalize a line of(More)
• Algorithmica
• 2014
The Weighted Vertex Integrity (wVI) problem takes as input an n-vertex graph G, a weight function $$w:V(G)\rightarrow {\mathbb {N}}$$ w : V ( G ) → N , and an integer p. The task is to decide if there exists a set $$X\subseteq V(G)$$ X ⊆ V ( G ) such that the weight of X plus the weight of a heaviest component of $$G-X$$ G - X is at most p. Among other(More)
• ICALP
• 2014
The bandwidth of a n-vertex graph G is the smallest integer b such that there exists a bijective function f : V (G) → {1, ..., n}, called a layout of G, such that for every edge uv ∈ E(G), |f(u)− f(v)| ≤ b. In the Bandwidth problem we are given as input a graph G and integer b, and asked whether the bandwidth of G is at most b. We present two results(More)
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