
Constant Factor Approximation for Tracking Paths and Fault Tolerant Feedback Vertex Set
Consider a vertexweighted graph G with a source s and a target t. Track...
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A Constantfactor Approximation for Weighted Bond Cover
The Weighted ℱVertex Deletion for a class F of graphs asks, weighted gr...
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On the Parallel Parameterized Complexity of the Graph Isomorphism Problem
In this paper, we study the parallel and the space complexity of the gra...
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A Tight Approximation Algorithm for the Cluster Vertex Deletion Problem
We give the first 2approximation algorithm for the cluster vertex delet...
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Designing Practical PTASes for Minimum Feedback Vertex Set in Planar Graphs
We present two algorithms for the minimum feedback vertex set problem in...
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The KCentre Problem for Necklaces
In graph theory, the objective of the kcentre problem is to find a set ...
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SemiRandom Graphs with Planted Sparse Vertex Cuts: Algorithms for Exact and Approximate Recovery
The problem of computing the vertex expansion of a graph is an NPhard p...
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Towards constantfactor approximation for chordal / distancehereditary vertex deletion
For a family of graphs ℱ, Weighted ℱDeletion is the problem for which the input is a vertex weighted graph G=(V,E) and the goal is to delete S⊆ V with minimum weight such that G∖ S∈ℱ. Designing a constantfactor approximation algorithm for large subclasses of perfect graphs has been an interesting research direction. Block graphs, 3leaf power graphs, and interval graphs are known to admit constantfactor approximation algorithms, but the question is open for chordal graphs and distancehereditary graphs. In this paper, we add one more class to this list by presenting a constantfactor approximation algorithm when F is the intersection of chordal graphs and distancehereditary graphs. They are known as ptolemaic graphs and form a superset of both block graphs and 3leaf power graphs above. Our proof presents new properties and algorithmic results on interclique digraphs as well as an approximation algorithm for a variant of Feedback Vertex Set that exploits this relationship (named Feedback Vertex Set with Precedence Constraints), each of which may be of independent interest.
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