13 Search Results for "Sridharan, Ramanujan"

Document
DOI: 10.4230/LIPIcs.ITCS.2024.64
Exponential-Time Approximation Schemes via Compression

Authors: Tanmay Inamdar, Madhumita Kundu, Pekka Parviainen, M. S. Ramanujan, and Saket Saurabh

Published in: LIPIcs, Volume 287, 15th Innovations in Theoretical Computer Science Conference (ITCS 2024)

Abstract
In this paper, we give a framework to design exponential-time approximation schemes for basic graph partitioning problems such as k-way cut, Multiway Cut, Steiner k-cut and Multicut, where the goal is to minimize the number of edges going across the parts. Our motivation to focus on approximation schemes for these problems comes from the fact that while it is possible to solve them exactly in 2^nn^{{𝒪}(1)} time (note that this is already faster than brute-forcing over all partitions or edge sets), it is not known whether one can do better. Using our framework, we design the first (1+ε)-approximation algorithms for the above problems that run in time 2^{f(ε)n} (for f(ε) < 1) for all these problems. As part of our framework, we present two compression procedures. The first of these is a "lossless" procedure, which is inspired by the seminal randomized contraction algorithm for Global Min-cut of Karger [SODA '93]. Here, we reduce the graph to an equivalent instance where the total number of edges is linearly bounded in the number of edges in an optimal solution of the original instance. Following this, we show how a careful combination of greedy choices and the best exact algorithm for the respective problems can exploit this structure and lead to our approximation schemes. Our first compression procedure bounds the number of edges linearly in the optimal solution, but this could still leave a dense graph as the solution size could be superlinear in the number of vertices. However, for several problems, it is known that they admit significantly faster algorithms on instances where solution size is linear in the number of vertices, in contrast to general instances. Hence, a natural question arises here. Could one reduce the solution size to linear in the number of vertices, at least in the case where we are willing to settle for a near-optimal solution, so that the aforementioned faster algorithms could be exploited? In the second compression procedure, using cut sparsifiers (this time, inspired by Benczúr and Karger [STOC '96]) we introduce "solution linearization" as a methodology to give an approximation-preserving reduction to the regime where solution size is linear in the number of vertices for certain cut problems. Using this, we obtain the first polynomial-space approximation schemes faster than 2^nn^{{𝒪}(1)} for Minimum bisection and Edge Bipartization. Along the way, we also design the first polynomial-space exact algorithms for these problems that run in time faster than 2^nn^{{𝒪}(1)}, in the regime where solution size is linear in the number of vertices. The use of randomized contraction and cut sparsifiers in the exponential-time setting is novel to the best of our knowledge and forms our conceptual contribution.
Cite as

Tanmay Inamdar, Madhumita Kundu, Pekka Parviainen, M. S. Ramanujan, and Saket Saurabh. Exponential-Time Approximation Schemes via Compression. In 15th Innovations in Theoretical Computer Science Conference (ITCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 287, pp. 64:1-64:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{inamdar_et_al:LIPIcs.ITCS.2024.64,
  author =	{Inamdar, Tanmay and Kundu, Madhumita and Parviainen, Pekka and Ramanujan, M. S. and Saurabh, Saket},
  title =	{{Exponential-Time Approximation Schemes via Compression}},
  booktitle =	{15th Innovations in Theoretical Computer Science Conference (ITCS 2024)},
  pages =	{64:1--64:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-309-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{287},
  editor =	{Guruswami, Venkatesan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2024.64},
  URN =		{urn:nbn:de:0030-drops-195920},
  doi =		{10.4230/LIPIcs.ITCS.2024.64},
  annote =	{Keywords: Exponential-Time Algorithms, Approximation Algorithms, Graph Algorithms, Cut Problems}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2023.28
FPT Approximations for Packing and Covering Problems Parameterized by Elimination Distance and Even Less

Authors: Tanmay Inamdar, Lawqueen Kanesh, Madhumita Kundu, M. S. Ramanujan, and Saket Saurabh

Published in: LIPIcs, Volume 284, 43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2023)

Abstract
For numerous graph problems in the realm of parameterized algorithms, using the size of a smallest deletion set (called a modulator) into well-understood graph families as parameterization has led to a long and successful line of research. Recently, however, there has been an extensive study of structural parameters that are potentially much smaller than the modulator size. In particular, recent papers [Jansen et al. STOC 2021; Agrawal et al. SODA 2022] have studied parameterization by the size of the modulator to a graph family ℋ(mod_ℋ(⋅)), elimination distance to ℋ(ed_ℋ(⋅)), and ℋ-treewidth (tw_ℋ(⋅)). These parameters are related by the fact that tw_ℋ lower bounds ed_ℋ, which in turn lower bounds mod_ℋ. While these new parameters have been successfully exploited to design fast exact algorithms their utility (especially that of ed_ℋ and tw_ℋ) in the context of approximation algorithms is mostly unexplored. The conceptual contribution of this paper is to present novel algorithmic meta-theorems that expand the impact of these structural parameters to the area of FPT Approximation, mirroring their utility in the design of exact FPT algorithms. Precisely, we show that if a covering or packing problem is definable in Monadic Second Order Logic and has a property called Finite Integer Index (FII), then the existence of an FPT Approximation Scheme (FPT-AS, i.e., (1±ε)-approximation) parameterized by mod_ℋ(⋅), ed_ℋ(⋅), and tw_ℋ(⋅) is in fact equivalent. As a consequence, we obtain FPT-ASes for a wide range of covering, packing, and domination problems on graphs with respect to these parameters. In the process, we show that several graph problems, that are W[1]-hard parameterized by mod_ℋ, admit FPT-ASes not only when parameterized by mod_ℋ, but even when parameterized by the potentially much smaller parameter tw_ℋ(⋅). In the spirit of [Agrawal et al. SODA 2022], our algorithmic results highlight a broader connection between these parameters in the world of approximation. As concrete exemplifications of our meta-theorems, we obtain FPT-ASes for well-studied graph problems such as Vertex Cover, Feedback Vertex Set, Cycle Packing and Dominating Set, parameterized by tw_ℋ(⋅) (and hence, also by mod_ℋ(⋅) or ed_ℋ(⋅)), where ℋ is any family of minor free graphs.
Cite as

Tanmay Inamdar, Lawqueen Kanesh, Madhumita Kundu, M. S. Ramanujan, and Saket Saurabh. FPT Approximations for Packing and Covering Problems Parameterized by Elimination Distance and Even Less. In 43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 284, pp. 28:1-28:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{inamdar_et_al:LIPIcs.FSTTCS.2023.28,
  author =	{Inamdar, Tanmay and Kanesh, Lawqueen and Kundu, Madhumita and Ramanujan, M. S. and Saurabh, Saket},
  title =	{{FPT Approximations for Packing and Covering Problems Parameterized by Elimination Distance and Even Less}},
  booktitle =	{43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2023)},
  pages =	{28:1--28:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-304-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{284},
  editor =	{Bouyer, Patricia and Srinivasan, Srikanth},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2023.28},
  URN =		{urn:nbn:de:0030-drops-194013},
  doi =		{10.4230/LIPIcs.FSTTCS.2023.28},
  annote =	{Keywords: FPT-AS, F-Deletion, Packing, Elimination Distance, Elimination Treewidth}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2023.45
Finding a Highly Connected Steiner Subgraph and its Applications

Authors: Eduard Eiben, Diptapriyo Majumdar, and M. S. Ramanujan

Published in: LIPIcs, Volume 272, 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)

Abstract
Given a (connected) undirected graph G, a set X ⊆ V(G) and integers k and p, the Steiner Subgraph Extension problem asks whether there exists a set S ⊇ X of at most k vertices such that G[S] is a p-edge-connected subgraph. This problem is a natural generalization of the well-studied Steiner Tree problem (set p = 1 and X to be the terminals). In this paper, we initiate the study of Steiner Subgraph Extension from the perspective of parameterized complexity and give a fixed-parameter algorithm (i.e., FPT algorithm) parameterized by k and p on graphs of bounded degeneracy (removing the assumption of bounded degeneracy results in W-hardness). Besides being an independent advance on the parameterized complexity of network design problems, our result has natural applications. In particular, we use our result to obtain new single-exponential FPT algorithms for several vertex-deletion problems studied in the literature, where the goal is to delete a smallest set of vertices such that: (i) the resulting graph belongs to a specified hereditary graph class, and (ii) the deleted set of vertices induces a p-edge-connected subgraph of the input graph.
Cite as

Eduard Eiben, Diptapriyo Majumdar, and M. S. Ramanujan. Finding a Highly Connected Steiner Subgraph and its Applications. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 45:1-45:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{eiben_et_al:LIPIcs.MFCS.2023.45,
  author =	{Eiben, Eduard and Majumdar, Diptapriyo and Ramanujan, M. S.},
  title =	{{Finding a Highly Connected Steiner Subgraph and its Applications}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{45:1--45:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.45},
  URN =		{urn:nbn:de:0030-drops-185793},
  doi =		{10.4230/LIPIcs.MFCS.2023.45},
  annote =	{Keywords: Parameterized Complexity, Steiner Subgraph Extension, p-edge-connected graphs, Matroids, Representative Families}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2022.78
An Exact Algorithm for Knot-Free Vertex Deletion

Authors: M. S. Ramanujan, Abhishek Sahu, Saket Saurabh, and Shaily Verma

Published in: LIPIcs, Volume 241, 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)

Abstract
The study of the Knot-Free Vertex Deletion problem emerges from its application in the resolution of deadlocks called knots, detected in a classical distributed computation model, that is, the OR-model. A strongly connected subgraph Q of a digraph D with at least two vertices is said to be a knot if there is no arc (u,v) of D with u ∈ V(Q) and v ∉ V(Q) (no-out neighbors of the vertices in Q). Given a directed graph D, the Knot-Free Vertex Deletion (KFVD) problem asks to compute a minimum-size subset S ⊂ V(D) such that D[V⧵S] contains no knots. There is no exact algorithm known for the KFVD problem in the literature that is faster than the trivial O^⋆(2ⁿ) brute-force algorithm. In this paper, we obtain the first non-trivial upper bound for KFVD by designing an exact algorithm running in time 𝒪^⋆(1.576ⁿ), where n is the size of the vertex set in D.
Cite as

M. S. Ramanujan, Abhishek Sahu, Saket Saurabh, and Shaily Verma. An Exact Algorithm for Knot-Free Vertex Deletion. In 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 241, pp. 78:1-78:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{ramanujan_et_al:LIPIcs.MFCS.2022.78,
  author =	{Ramanujan, M. S. and Sahu, Abhishek and Saurabh, Saket and Verma, Shaily},
  title =	{{An Exact Algorithm for Knot-Free Vertex Deletion}},
  booktitle =	{47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)},
  pages =	{78:1--78:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-256-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{241},
  editor =	{Szeider, Stefan and Ganian, Robert and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2022.78},
  URN =		{urn:nbn:de:0030-drops-168769},
  doi =		{10.4230/LIPIcs.MFCS.2022.78},
  annote =	{Keywords: exact algorithm, knot-free graphs, branching algorithm}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2022.91
Backdoor Sets on Nowhere Dense SAT

Authors: Daniel Lokshtanov, Fahad Panolan, and M. S. Ramanujan

Published in: LIPIcs, Volume 229, 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)

Abstract
For a satisfiable CNF formula ϕ and an integer t, a weak backdoor set to treewidth-t is a set of variables such that there is an assignment to this set that reduces ϕ to a satisfiable formula that has an incidence graph of treewidth at most t. A natural research program in the work on fixed-parameter algorithms (FPT algorithms) for SAT is to delineate the tractability borders for the problem of detecting a small weak backdoor set to treewidth-t formulas. In this line of research, Gaspers and Szeider (ICALP 2012) showed that detecting a weak backdoor set of size at most k to treewidth-1 is W[2]-hard parameterized by k if the input is an arbitrary CNF formula. Fomin, Lokshtanov, Misra, Ramanujan and Saurabh (SODA 2015), showed that if the input is d-CNF, then detecting a weak backdoor set of size at most k to treewidth-t is fixed-parameter tractable (parameterized by k,t,d). These two results indicate that sparsity of the input plays a role in determining the parameterized complexity of detecting weak backdoor sets to treewidth-t. In this work, we take a major step towards characterizing the precise impact of sparsity on the parameterized complexity of this problem by obtaining algorithmic results for detecting small weak backdoor sets to treewidth-t for input formulas whose incidence graphs belong to a nowhere-dense graph class. Nowhere density provides a robust and well-understood notion of sparsity that is at the heart of several advances on model checking and structural graph theory. Moreover, nowhere-dense graph classes contain many well-studied graph classes such as bounded treewidth graphs, graphs that exclude a fixed (topological) minor and graphs of bounded expansion. Our main contribution is an algorithm that, given a formula ϕ whose incidence graph belongs to a fixed nowhere-dense graph class and an integer k, in time f(t,k)|ϕ|^O(1), either finds a satisfying assignment of ϕ, or concludes correctly that ϕ has no weak backdoor set of size at most k to treewidth-t. To obtain this algorithm, we develop a strategy that only relies on the fact that nowhere-dense graph classes are biclique-free. That is, for every nowhere-dense graph class, there is a p such that it is contained in the class of graphs that exclude K_{p,p} as a subgraph. This is a significant feature of our techniques since the class of biclique-free graphs also generalizes the class of graphs of bounded degeneracy, which are incomparable with nowhere-dense graph classes. As a result, our algorithm also generalizes the results of Fomin, Lokshtanov, Misra, Ramanujan and Saurabh (SODA 2015) for the special case of d-CNF formulas as input when d is fixed. This is because the incidence graphs of such formulas exclude K_{d+1,d+1} as a subgraph.
Cite as

Daniel Lokshtanov, Fahad Panolan, and M. S. Ramanujan. Backdoor Sets on Nowhere Dense SAT. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 91:1-91:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{lokshtanov_et_al:LIPIcs.ICALP.2022.91,
  author =	{Lokshtanov, Daniel and Panolan, Fahad and Ramanujan, M. S.},
  title =	{{Backdoor Sets on Nowhere Dense SAT}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{91:1--91:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-235-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{229},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.91},
  URN =		{urn:nbn:de:0030-drops-164323},
  doi =		{10.4230/LIPIcs.ICALP.2022.91},
  annote =	{Keywords: Fixed-parameter Tractability, Satisfiability, Backdoors, Treewidth}
}
Document
DOI: 10.4230/LIPIcs.ESA.2021.78
On Approximate Compressions for Connected Minor-Hitting Sets

Authors: M. S. Ramanujan

Published in: LIPIcs, Volume 204, 29th Annual European Symposium on Algorithms (ESA 2021)

Abstract
In the Connected ℱ-Deletion problem, ℱ is a fixed finite family of graphs and the objective is to compute a minimum set of vertices (or a vertex set of size at most k for some given k) such that (a) this set induces a connected subgraph of the given graph and (b) deleting this set results in a graph which excludes every F ∈ ℱ as a minor. In the area of kernelization, this problem is well known to exclude a polynomial kernel subject to standard complexity hypotheses even in very special cases such as ℱ = K₂, i.e., Connected Vertex Cover. In this work, we give a (2+ε)-approximate polynomial compression for the Connected ℱ-Deletion problem when ℱ contains at least one planar graph. This is the first approximate polynomial compression result for this generic problem. As a corollary, we obtain the first approximate polynomial compression result for the special case of Connected η-Treewidth Deletion.
Cite as

M. S. Ramanujan. On Approximate Compressions for Connected Minor-Hitting Sets. In 29th Annual European Symposium on Algorithms (ESA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 204, pp. 78:1-78:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{ramanujan:LIPIcs.ESA.2021.78,
  author =	{Ramanujan, M. S.},
  title =	{{On Approximate Compressions for Connected Minor-Hitting Sets}},
  booktitle =	{29th Annual European Symposium on Algorithms (ESA 2021)},
  pages =	{78:1--78:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-204-4},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{204},
  editor =	{Mutzel, Petra and Pagh, Rasmus 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.2021.78},
  URN =		{urn:nbn:de:0030-drops-146590},
  doi =		{10.4230/LIPIcs.ESA.2021.78},
  annote =	{Keywords: Parameterized Complexity, Kernelization, Approximation Algorithms}
}
Document
DOI: 10.4230/LIPIcs.STACS.2021.5
An FPT Algorithm for Elimination Distance to Bounded Degree Graphs

Authors: Akanksha Agrawal, Lawqueen Kanesh, Fahad Panolan, M. S. Ramanujan, and Saket Saurabh

Published in: LIPIcs, Volume 187, 38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021)

Abstract
In the literature on parameterized graph problems, there has been an increased effort in recent years aimed at exploring novel notions of graph edit-distance that are more powerful than the size of a modulator to a specific graph class. In this line of research, Bulian and Dawar [Algorithmica, 2016] introduced the notion of elimination distance and showed that deciding whether a given graph has elimination distance at most k to any minor-closed class of graphs is fixed-parameter tractable parameterized by k [Algorithmica, 2017]. They showed that Graph Isomorphism parameterized by the elimination distance to bounded degree graphs is fixed-parameter tractable and asked whether determining the elimination distance to the class of bounded degree graphs is fixed-parameter tractable. Recently, Lindermayr et al. [MFCS 2020] obtained a fixed-parameter algorithm for this problem in the special case where the input is restricted to K₅-minor free graphs. In this paper, we answer the question of Bulian and Dawar in the affirmative for general graphs. In fact, we give a more general result capturing elimination distance to any graph class characterized by a finite set of graphs as forbidden induced subgraphs.
Cite as

Akanksha Agrawal, Lawqueen Kanesh, Fahad Panolan, M. S. Ramanujan, and Saket Saurabh. An FPT Algorithm for Elimination Distance to Bounded Degree Graphs. In 38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 187, pp. 5:1-5:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{agrawal_et_al:LIPIcs.STACS.2021.5,
  author =	{Agrawal, Akanksha and Kanesh, Lawqueen and Panolan, Fahad and Ramanujan, M. S. and Saurabh, Saket},
  title =	{{An FPT Algorithm for Elimination Distance to Bounded Degree Graphs}},
  booktitle =	{38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021)},
  pages =	{5:1--5:11},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-180-1},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{187},
  editor =	{Bl\"{a}ser, Markus and Monmege, Benjamin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2021.5},
  URN =		{urn:nbn:de:0030-drops-136507},
  doi =		{10.4230/LIPIcs.STACS.2021.5},
  annote =	{Keywords: Elimination Distance, Fixed-parameter Tractability, Graph Modification}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2020.1
On the Parameterized Complexity of Clique Elimination Distance

Authors: Akanksha Agrawal and M. S. Ramanujan

Published in: LIPIcs, Volume 180, 15th International Symposium on Parameterized and Exact Computation (IPEC 2020)

Abstract
Bulian and Dawar [Algorithmica, 2016] introduced the notion of elimination distance in an effort to define new tractable parameterizations for graph problems and showed that deciding whether a given graph has elimination distance at most k to any minor-closed class of graphs is fixed-parameter tractable parameterized by k [Algorithmica, 2017]. In this paper, we consider the problem of computing the elimination distance of a given graph to the class of cluster graphs and initiate the study of the parameterized complexity of a more general version - that of obtaining a modulator to such graphs. That is, we study the (η,Clq)-Elimination Deletion problem ((η,Clq)-ED Deletion) where, for a fixed η, one is given a graph G and k ∈ ℕ and the objective is to determine whether there is a set S ⊆ V(G) such that the graph G-S has elimination distance at most η to the class of cluster graphs. Our main result is a polynomial kernelization (parameterized by k) for this problem. As components in the proof of our main result, we develop a k^𝒪(η k + η²)n^𝒪(1)-time fixed-parameter algorithm for (η,Clq)-ED Deletion and a polynomial-time factor-min{𝒪(η⋅ opt⋅ log² n),opt^𝒪(1)} approximation algorithm for the same problem.
Cite as

Akanksha Agrawal and M. S. Ramanujan. On the Parameterized Complexity of Clique Elimination Distance. In 15th International Symposium on Parameterized and Exact Computation (IPEC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 180, pp. 1:1-1:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{agrawal_et_al:LIPIcs.IPEC.2020.1,
  author =	{Agrawal, Akanksha and Ramanujan, M. S.},
  title =	{{On the Parameterized Complexity of Clique Elimination Distance}},
  booktitle =	{15th International Symposium on Parameterized and Exact Computation (IPEC 2020)},
  pages =	{1:1--1:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-172-6},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{180},
  editor =	{Cao, Yixin and Pilipczuk, Marcin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2020.1},
  URN =		{urn:nbn:de:0030-drops-133043},
  doi =		{10.4230/LIPIcs.IPEC.2020.1},
  annote =	{Keywords: Elimination Distance, Cluster Graphs, Kernelization}
}
Document
DOI: 10.4230/LIPIcs.ESA.2020.50
On the Complexity of Recovering Incidence Matrices

Authors: Fedor V. Fomin, Petr Golovach, Pranabendu Misra, and M. S. Ramanujan

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

Abstract
The incidence matrix of a graph is a fundamental object naturally appearing in many applications, involving graphs such as social networks, communication networks, or transportation networks. Often, the data collected about the incidence relations can have some slight noise. In this paper, we initiate the study of the computational complexity of recovering incidence matrices of graphs from a binary matrix: given a binary matrix M which can be written as the superposition of two binary matrices L and S, where S is the incidence matrix of a graph from a specified graph class, and L is a matrix (i) of small rank or, (ii) of small (Hamming) weight. Further, identify all those graphs whose incidence matrices form part of such a superposition. Here, L represents the noise in the input matrix M. Another motivation for this problem comes from the Matroid Minors project of Geelen, Gerards and Whittle, where perturbed graphic and co-graphic matroids play a prominent role. There, it is expected that a perturbed binary matroid (or its dual) is presented as L+S where L is a low rank matrix and S is the incidence matrix of a graph. Here, we address the complexity of constructing such a decomposition. When L is of small rank, we show that the problem is NP-complete, but it can be decided in time (mn)^O(r), where m,n are dimensions of M and r is an upper-bound on the rank of L. When L is of small weight, then the problem is solvable in polynomial time (mn)^O(1). Furthermore, in many applications it is desirable to have the list of all possible solutions for further analysis. We show that our algorithms naturally extend to enumeration algorithms for the above two problems with delay (mn)^O(r) and (mn)^O(1), respectively, between consecutive outputs.
Cite as

Fedor V. Fomin, Petr Golovach, Pranabendu Misra, and M. S. Ramanujan. On the Complexity of Recovering Incidence Matrices. In 28th Annual European Symposium on Algorithms (ESA 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 173, pp. 50:1-50:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{fomin_et_al:LIPIcs.ESA.2020.50,
  author =	{Fomin, Fedor V. and Golovach, Petr and Misra, Pranabendu and Ramanujan, M. S.},
  title =	{{On the Complexity of Recovering Incidence Matrices}},
  booktitle =	{28th Annual European Symposium on Algorithms (ESA 2020)},
  pages =	{50:1--50:13},
  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.2020.50},
  URN =		{urn:nbn:de:0030-drops-129164},
  doi =		{10.4230/LIPIcs.ESA.2020.50},
  annote =	{Keywords: Graph Incidence Matrix, Matrix Recovery, Enumeration Algorithm}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2020.75
On the Parameterized Complexity of Deletion to ℋ-Free Strong Components

Authors: Rian Neogi, M. S. Ramanujan, Saket Saurabh, and Roohani Sharma

Published in: LIPIcs, Volume 170, 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)

Abstract
Directed Feedback Vertex Set (DFVS) is a fundamental computational problem that has received extensive attention in parameterized complexity. In this paper, we initiate the study of a wide generalization, the ℋ-SCC Deletion problem. Here, one is given a digraph D, an integer k and the objective is to decide whether there is a vertex set of size at most k whose deletion leaves a digraph where every strong component excludes graphs in the fixed finite family ℋ as (not necessarily induced) subgraphs. When ℋ comprises only the digraph with a single arc, then this problem is precisely DFVS. Our main result is a proof that this problem is fixed-parameter tractable parameterized by the size of the deletion set if ℋ only contains rooted graphs or if ℋ contains at least one directed path. Along with generalizing the fixed-parameter tractability result for DFVS, our result also generalizes the recent results of Göke et al. [CIAC 2019] for the 1-Out-Regular Vertex Deletion and Bounded Size Strong Component Vertex Deletion problems. Moreover, we design algorithms for the two above mentioned problems, whose running times are better and match with the best bounds for DFVS, without using the heavy machinery of shadow removal as is done by Göke et al. [CIAC 2019].
Cite as

Rian Neogi, M. S. Ramanujan, Saket Saurabh, and Roohani Sharma. On the Parameterized Complexity of Deletion to ℋ-Free Strong Components. In 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 170, pp. 75:1-75:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{neogi_et_al:LIPIcs.MFCS.2020.75,
  author =	{Neogi, Rian and Ramanujan, M. S. and Saurabh, Saket and Sharma, Roohani},
  title =	{{On the Parameterized Complexity of Deletion to ℋ-Free Strong Components}},
  booktitle =	{45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)},
  pages =	{75:1--75:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-159-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{170},
  editor =	{Esparza, Javier and Kr\'{a}l', Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2020.75},
  URN =		{urn:nbn:de:0030-drops-127444},
  doi =		{10.4230/LIPIcs.MFCS.2020.75},
  annote =	{Keywords: Directed Cut Problems, Fixed-parameter Tractability, DFVS}
}
Document
DOI: 10.4230/LIPIcs.ESA.2019.77
An Approximate Kernel for Connected Feedback Vertex Set

Authors: M. S. Ramanujan

Published in: LIPIcs, Volume 144, 27th Annual European Symposium on Algorithms (ESA 2019)

Abstract
The Feedback Vertex Set problem is a fundamental computational problem which has been the subject of intensive study in various domains of algorithmics. In this problem, one is given an undirected graph G and an integer k as input. The objective is to determine whether at most k vertices can be deleted from G such that the resulting graph is acyclic. The study of preprocessing algorithms for this problem has a long and rich history, culminating in the quadratic kernelization of Thomasse [SODA 2010]. However, it is known that when the solution is required to induce a connected subgraph (such a set is called a connected feedback vertex set), a polynomial kernelization is unlikely to exist and the problem is NP-hard to approximate below a factor of 2 (assuming the Unique Games Conjecture). In this paper, we show that if one is interested in only preserving approximate solutions (even of quality arbitrarily close to the optimum), then there is a drastic improvement in our ability to preprocess this problem. Specifically, we prove that for every fixed 0<epsilon<1, graph G, and k in N, the following holds: There is a polynomial time computable graph G' of size k^O(1) such that for every c >= 1, any c-approximate connected feedback vertex set of G' of size at most k is a c * (1+epsilon)-approximate connected feedback vertex set of G. Our result adds to the set of approximate kernelization algorithms introduced by Lokshtanov et al. [STOC 2017]. As a consequence of our main result, we show that Connected Feedback Vertex Set can be approximated within a factor min{OPT^O(1),n^(1-delta)} in polynomial time for some delta>0.
Cite as

M. S. Ramanujan. An Approximate Kernel for Connected Feedback Vertex Set. In 27th Annual European Symposium on Algorithms (ESA 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 144, pp. 77:1-77:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{ramanujan:LIPIcs.ESA.2019.77,
  author =	{Ramanujan, M. S.},
  title =	{{An Approximate Kernel for Connected Feedback Vertex Set}},
  booktitle =	{27th Annual European Symposium on Algorithms (ESA 2019)},
  pages =	{77:1--77:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-124-5},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{144},
  editor =	{Bender, Michael A. and Svensson, Ola 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.2019.77},
  URN =		{urn:nbn:de:0030-drops-111989},
  doi =		{10.4230/LIPIcs.ESA.2019.77},
  annote =	{Keywords: Parameterized Complexity, Kernelization, Approximation Algorithms}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2017.36
On Structural Parameterizations of the Edge Disjoint Paths Problem

Authors: Robert Ganian, Sebastian Ordyniak, and Ramanujan Sridharan

Published in: LIPIcs, Volume 92, 28th International Symposium on Algorithms and Computation (ISAAC 2017)

Abstract
In this paper we revisit the classical Edge Disjoint Paths (EDP) problem, where one is given an undirected graph G and a set of terminal pairs P and asks whether G contains a set of pairwise edge-disjoint paths connecting every terminal pair in P. Our focus lies on structural parameterizations for the problem that allow for efficient (polynomial-time or fpt) algorithms. As our first result, we answer an open question stated in Fleszar, Mnich, and Spoerhase (2016), by showing that the problem can be solved in polynomial time if the input graph has a feedback vertex set of size one. We also show that EDP parameterized by the treewidth and the maximum degree of the input graph is fixed-parameter tractable. Having developed two novel algorithms for EDP using structural restrictions on the input graph, we then turn our attention towards the augmented graph, i.e., the graph obtained from the input graph after adding one edge between every terminal pair. In constrast to the input graph, where EDP is known to remain NP-hard even for treewidth two, a result by Zhou et al. (2000) shows that EDP can be solved in non-uniform polynomial time if the augmented graph has constant treewidth; we note that the possible improvement of this result to an fpt-algorithm has remained open since then. We show that this is highly unlikely by establishing the W[1]-hardness of the problem parameterized by the treewidth (and even feedback vertex set) of the augmented graph. Finally, we develop an fpt-algorithm for EDP by exploiting a novel structural parameter of the augmented graph.
Cite as

Robert Ganian, Sebastian Ordyniak, and Ramanujan Sridharan. On Structural Parameterizations of the Edge Disjoint Paths Problem. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 36:1-36:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{ganian_et_al:LIPIcs.ISAAC.2017.36,
  author =	{Ganian, Robert and Ordyniak, Sebastian and Sridharan, Ramanujan},
  title =	{{On Structural Parameterizations of the Edge Disjoint Paths Problem}},
  booktitle =	{28th International Symposium on Algorithms and Computation (ISAAC 2017)},
  pages =	{36:1--36:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-054-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{92},
  editor =	{Okamoto, Yoshio and Tokuyama, Takeshi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.36},
  URN =		{urn:nbn:de:0030-drops-82555},
  doi =		{10.4230/LIPIcs.ISAAC.2017.36},
  annote =	{Keywords: edge disjoint path problem, feedback vertex set, treewidth, fracture number, parameterized complexity}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2016.23
Backdoors for Linear Temporal Logic

Authors: Arne Meier, Sebastian Ordyniak, Ramanujan Sridharan, and Irena Schindler

Published in: LIPIcs, Volume 63, 11th International Symposium on Parameterized and Exact Computation (IPEC 2016)

Abstract
In the present paper, we introduce the backdoor set approach into the field of temporal logic for the global fragment of linear temporal logic. We study the parameterized complexity of the satisfiability problem parameterized by the size of the backdoor. We distinguish between backdoor detection and evaluation of backdoors into the fragments of Horn and Krom formulas. Here we classify the operator fragments of globally-operators for past/future/always, and the combination of them. Detection is shown to be fixed-parameter tractable (FPT) whereas the complexity of evaluation behaves differently. We show that for Krom formulas the problem is paraNP-complete. For Horn formulas, the complexity is shown to be either fixed parameter tractable or paraNP-complete depending on the considered operator fragment.
Cite as

Arne Meier, Sebastian Ordyniak, Ramanujan Sridharan, and Irena Schindler. Backdoors for Linear Temporal Logic. In 11th International Symposium on Parameterized and Exact Computation (IPEC 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 63, pp. 23:1-23:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{meier_et_al:LIPIcs.IPEC.2016.23,
  author =	{Meier, Arne and Ordyniak, Sebastian and Sridharan, Ramanujan and Schindler, Irena},
  title =	{{Backdoors for Linear Temporal Logic}},
  booktitle =	{11th International Symposium on Parameterized and Exact Computation (IPEC 2016)},
  pages =	{23:1--23:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-023-1},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{63},
  editor =	{Guo, Jiong and Hermelin, Danny},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2016.23},
  URN =		{urn:nbn:de:0030-drops-69462},
  doi =		{10.4230/LIPIcs.IPEC.2016.23},
  annote =	{Keywords: Linear Temporal Logic, Parameterized Complexity, Backdoor Sets}
}
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