
Towards constantfactor approximation for chordal / distancehereditary vertex deletion
For a family of graphs ℱ, Weighted ℱDeletion is the problem for which t...
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NodeWeighted Network Design in Planar and MinorClosed Families of Graphs
We consider nodeweighted survivable network design (SNDP) in planar gra...
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A Turing Kernelization Dichotomy for Structural Parameterizations of FMinorFree Deletion
For a fixed finite family of graphs F, the FMinorFree Deletion problem...
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Preprocessing for Outerplanar Vertex Deletion: An Elementary Kernel of Quartic Size
In the ℱMinorFree Deletion problem one is given an undirected graph G,...
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Polynomial Kernels for Hitting Forbidden Minors under Structural Parameterizations
We investigate polynomialtime preprocessing for the problem of hitting ...
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Tourneys and the Fast Generation and Obfuscation of Closed Knight's Tours
New algorithms for generating closed knight's tours are obtained by gene...
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Baker game and polynomialtime approximation schemes
Baker devised a technique to obtain approximation schemes for many optim...
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A Constantfactor Approximation for Weighted Bond Cover
The Weighted ℱVertex Deletion for a class F of graphs asks, weighted graph G, for a minimum weight vertex set S such that GS∈ F. The case when F is minorclosed and excludes some graph as a minor has received particular attention but a constantfactor approximation remained elusive for Weighted ℱVertex Deletion. Only three cases of minorclosed F are known to admit constantfactor approximations, namely Vertex Cover, Feedback Vertex Set and Diamond Hitting Set. We study the problem for the class F of θ_cminorfree graphs, under the equivalent setting of the Weighted cBond Cover problem, and present a constantfactor approximation algorithm using the primaldual method. For this, we leverage a structure theorem implicit in [Joret et al., SIDMA'14] which states the following: any graph G containing a θ_cminormodel either contains a large twoterminal protrusion, or contains a constantsize θ_cminormodel, or a collection of pairwise disjoint constantsized connected sets that can be contracted simultaneously to yield a dense graph. In the first case, we tame the graph by replacing the protrusion with a specialpurpose weighted gadget. For the second and third case, we provide a weighting scheme which guarantees a local approximation ratio. Besides making an important step in the quest of (dis)proving a constantfactor approximation for Weighted ℱVertex Deletion, our result may be useful as a template for algorithms for other minorclosed families.
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