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Documents authored by Sandeep, R. B.

Document
DOI: 10.4230/LIPIcs.ESA.2020.72
Incompressibility of H-Free Edge Modification Problems: Towards a Dichotomy

Authors: Dániel Marx and R. B. Sandeep

Published in: LIPIcs, Volume 173, 28th Annual European Symposium on Algorithms (ESA 2020)

Abstract
Given a graph G and an integer k, the H-free Edge Editing problem is to find whether there exist at most k pairs of vertices in G such that changing the adjacency of the pairs in G results in a graph without any induced copy of H. The existence of polynomial kernels for H-free Edge Editing (that is, whether it is possible to reduce the size of the instance to k^O(1) in polynomial time) received significant attention in the parameterized complexity literature. Nontrivial polynomial kernels are known to exist for some graphs H with at most 4 vertices (e.g., path on 3 or 4 vertices, diamond, paw), but starting from 5 vertices, polynomial kernels are known only if H is either complete or empty. This suggests the conjecture that there is no other H with at least 5 vertices were H-free Edge Editing admits a polynomial kernel. Towards this goal, we obtain a set ℋ of nine 5-vertex graphs such that if for every H ∈ ℋ, H-free Edge Editing is incompressible and the complexity assumption NP ⊈ coNP/poly holds, then H-free Edge Editing is incompressible for every graph H with at least five vertices that is neither complete nor empty. That is, proving incompressibility for these nine graphs would give a complete classification of the kernelization complexity of H-free Edge Editing for every H with at least 5 vertices. We obtain similar result also for H-free Edge Deletion. Here the picture is more complicated due to the existence of another infinite family of graphs H where the problem is trivial (graphs with exactly one edge). We obtain a larger set ℋ of nineteen graphs whose incompressibility would give a complete classification of the kernelization complexity of H-free Edge Deletion for every graph H with at least 5 vertices. Analogous results follow also for the H-free Edge Completion problem by simple complementation.
Cite as

Dániel Marx and R. B. Sandeep. Incompressibility of H-Free Edge Modification Problems: Towards a Dichotomy. In 28th Annual European Symposium on Algorithms (ESA 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 173, pp. 72:1-72:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{marx_et_al:LIPIcs.ESA.2020.72,
  author =	{Marx, D\'{a}niel and Sandeep, R. B.},
  title =	{{Incompressibility of H-Free Edge Modification Problems: Towards a Dichotomy}},
  booktitle =	{28th Annual European Symposium on Algorithms (ESA 2020)},
  pages =	{72:1--72:25},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-162-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{173},
  editor =	{Grandoni, Fabrizio and Herman, Grzegorz and Sanders, Peter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2020.72},
  URN =		{urn:nbn:de:0030-drops-129383},
  doi =		{10.4230/LIPIcs.ESA.2020.72},
  annote =	{Keywords: incompressibility, edge modification problems, H-free graphs}
}
Document
DOI: 10.4230/LIPIcs.ESA.2018.10
A Polynomial Kernel for Diamond-Free Editing

Authors: Yixin Cao, Ashutosh Rai, R. B. Sandeep, and Junjie Ye

Published in: LIPIcs, Volume 112, 26th Annual European Symposium on Algorithms (ESA 2018)

Abstract
Given a fixed graph H, the H-free editing problem asks whether we can edit at most k edges to make a graph contain no induced copy of H. We obtain a polynomial kernel for this problem when H is a diamond. The incompressibility dichotomy for H being a 3-connected graph and the classical complexity dichotomy suggest that except for H being a complete/empty graph, H-free editing problems admit polynomial kernels only for a few small graphs H. Therefore, we believe that our result is an essential step toward a complete dichotomy on the compressibility of H-free editing. Additionally, we give a cubic-vertex kernel for the diamond-free edge deletion problem, which is far simpler than the previous kernel of the same size for the problem.
Cite as

Yixin Cao, Ashutosh Rai, R. B. Sandeep, and Junjie Ye. A Polynomial Kernel for Diamond-Free Editing. In 26th Annual European Symposium on Algorithms (ESA 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 112, pp. 10:1-10:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{cao_et_al:LIPIcs.ESA.2018.10,
  author =	{Cao, Yixin and Rai, Ashutosh and Sandeep, R. B. and Ye, Junjie},
  title =	{{A Polynomial Kernel for Diamond-Free Editing}},
  booktitle =	{26th Annual European Symposium on Algorithms (ESA 2018)},
  pages =	{10:1--10:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-081-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{112},
  editor =	{Azar, Yossi and Bast, Hannah and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2018.10},
  URN =		{urn:nbn:de:0030-drops-94732},
  doi =		{10.4230/LIPIcs.ESA.2018.10},
  annote =	{Keywords: Kernelization, Diamond-free, H-free editing, Graph modification problem}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2015.365
Parameterized Lower Bound and Improved Kernel for Diamond-free Edge Deletion

Authors: R. B. Sandeep and Naveen Sivadasan

Published in: LIPIcs, Volume 43, 10th International Symposium on Parameterized and Exact Computation (IPEC 2015)

Abstract
A diamond is a graph obtained by removing an edge from a complete graph on four vertices. A graph is diamond-free if it does not contain an induced diamond. The Diamond-free Edge Deletion problem asks to find whether there exist at most k edges in the input graph whose deletion results in a diamond-free graph. The problem was proved to be NP-complete and a polynomial kernel of O(k^4) vertices was found by Fellows et. al. (Discrete Optimization, 2011). In this paper, we give an improved kernel of O(k^3) vertices for Diamond-free Edge Deletion. We give an alternative proof of the NP-completeness of the problem and observe that it cannot be solved in time 2^{o(k)} * n^{O(1)}, unless the Exponential Time Hypothesis fails.
Cite as

R. B. Sandeep and Naveen Sivadasan. Parameterized Lower Bound and Improved Kernel for Diamond-free Edge Deletion. In 10th International Symposium on Parameterized and Exact Computation (IPEC 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 43, pp. 365-376, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{sandeep_et_al:LIPIcs.IPEC.2015.365,
  author =	{Sandeep, R. B. and Sivadasan, Naveen},
  title =	{{Parameterized Lower Bound and Improved Kernel for Diamond-free Edge Deletion}},
  booktitle =	{10th International Symposium on Parameterized and Exact Computation (IPEC 2015)},
  pages =	{365--376},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-92-7},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{43},
  editor =	{Husfeldt, Thore and Kanj, Iyad},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2015.365},
  URN =		{urn:nbn:de:0030-drops-55976},
  doi =		{10.4230/LIPIcs.IPEC.2015.365},
  annote =	{Keywords: edge deletion problems, polynomial kernelization}
}
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