Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms 2019
DOI: 10.1137/1.9781611975482.104
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Losing Treewidth by Separating Subsets

Abstract: We study the problem of deleting the smallest set S of vertices (resp. edges) from a given graph G such that the induced subgraph (resp. subgraph) G \ S belongs to some class H. We consider the case where graphs in H have treewidth bounded by t, and give a general framework to obtain approximation algorithms for both vertex and edge-deletion settings from approximation algorithms for certain natural graph partitioning problems called k-Subset Vertex Separator and k-Subset Edge Separator, respectively.For the v… Show more

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Cited by 23 publications
(28 citation statements)
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“…3 However, it is not immediately clear if their approach can be extended to WPF-MFD. 4 Very recently, Gupta et al [22] have given O(log ) approximation algorithm for (unweighted) Planar F-Minor-Free Deletion, where is the maximum number of vertices in any planar graph in F.…”
Section: :6mentioning
confidence: 99%
“…3 However, it is not immediately clear if their approach can be extended to WPF-MFD. 4 Very recently, Gupta et al [22] have given O(log ) approximation algorithm for (unweighted) Planar F-Minor-Free Deletion, where is the maximum number of vertices in any planar graph in F.…”
Section: :6mentioning
confidence: 99%
“…Fomin et al [247] gave a randomized f (k)-approximation algorithm that runs in g(k) • nm for some computable functions f and g. The approximation ratio was improved by Gupta et al [255] that gave a deterministic O(log k)-approximation algorithm that runs in f (k)…”
Section: Treewidth and Planar Minor Deletionmentioning
confidence: 99%
“…Therefore, in order to solve H-MINOR DELETION, one can first solve TREEWIDTH k-DELETION to reduce the treewidth to k and then solve H-MINOR DELETION optimally using Courcelle's theorem [250]. Combined with the above algorithm for TREEWIDTH k-DELETION [255], this strategy yields an O(log k)-approximation algorithm that runs in f (|H|) • n O(1) time.…”
Section: Treewidth and Planar Minor Deletionmentioning
confidence: 99%
See 1 more Smart Citation
“…In fact, for every planar graph H, there is even a constant factor approximation algorithm for computing τ H (G). Indeed, a randomized constant factor approximation was first developed by Fomin, Lokshtanov, Misra, and Saurabh [21], and very recently a deterministic one was obtained by Gupta, Lee, Li, Manurangsi, and Włodarczyk [27].…”
Section: Approximation Algorithms For Packing and Covering Modelsmentioning
confidence: 99%