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Documents authored by Jana, Satyabrata

Document
DOI: 10.4230/LIPIcs.IPEC.2024.4
On the Parameterized Complexity of Eulerian Strong Component Arc Deletion

Authors: Václav Blažej, Satyabrata Jana, M. S. Ramanujan, and Peter Strulo

Published in: LIPIcs, Volume 321, 19th International Symposium on Parameterized and Exact Computation (IPEC 2024)

Abstract
In this paper, we study the Eulerian Strong Component Arc Deletion problem, where the input is a directed multigraph and the goal is to delete the minimum number of arcs to ensure every strongly connected component of the resulting digraph is Eulerian. This problem is a natural extension of the Directed Feedback Arc Set problem and is also known to be motivated by certain scenarios arising in the study of housing markets. The complexity of the problem, when parameterized by solution size (i.e., size of the deletion set), has remained unresolved and has been highlighted in several papers. In this work, we answer this question by ruling out (subject to the usual complexity assumptions) a fixed-parameter tractable (FPT) algorithm for this parameter and conduct a broad analysis of the problem with respect to other natural parameterizations. We prove both positive and negative results. Among these, we demonstrate that the problem is also hard (W[1]-hard or even para-NP-hard) when parameterized by either treewidth or maximum degree alone. Complementing our lower bounds, we establish that the problem is in XP when parameterized by treewidth and FPT when parameterized either by both treewidth and maximum degree or by both treewidth and solution size. We show that these algorithms have near-optimal asymptotic dependence on the treewidth assuming the Exponential Time Hypothesis.
Cite as

Václav Blažej, Satyabrata Jana, M. S. Ramanujan, and Peter Strulo. On the Parameterized Complexity of Eulerian Strong Component Arc Deletion. In 19th International Symposium on Parameterized and Exact Computation (IPEC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 321, pp. 4:1-4:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{blazej_et_al:LIPIcs.IPEC.2024.4,
  author =	{Bla\v{z}ej, V\'{a}clav and Jana, Satyabrata and Ramanujan, M. S. and Strulo, Peter},
  title =	{{On the Parameterized Complexity of Eulerian Strong Component Arc Deletion}},
  booktitle =	{19th International Symposium on Parameterized and Exact Computation (IPEC 2024)},
  pages =	{4:1--4:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-353-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{321},
  editor =	{Bonnet, \'{E}douard and Rz\k{a}\.{z}ewski, Pawe{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2024.4},
  URN =		{urn:nbn:de:0030-drops-222306},
  doi =		{10.4230/LIPIcs.IPEC.2024.4},
  annote =	{Keywords: Parameterized complexity, Eulerian graphs, Treewidth}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2024.17
Subset Feedback Vertex Set in Tournaments as Fast as Without the Subset

Authors: Satyabrata Jana, Lawqueen Kanesh, Madhumita Kundu, and Saket Saurabh

Published in: LIPIcs, Volume 321, 19th International Symposium on Parameterized and Exact Computation (IPEC 2024)

Abstract
In the Feedback Vertex Set in Tournaments (FVST) problem, we are given a tournament T and a positive integer k. The objective is to determine whether there exists a vertex set X ⊆ V(T) of size at most k such that T-X is a directed acyclic graph. This problem is known to be equivalent to the problem of hitting all directed triangles, thereby using the best-known algorithm for the 3-Hitting Set problem results in an algorithm for FVST with a running time of 2.076^k ⋅ n^{𝒪(1)} [Wahlström, Ph.D. Thesis]. Kumar and Lokshtanov [STACS 2016] designed a more efficient algorithm with a running time of 1.6181^k ⋅ n^{𝒪(1)}. A generalization of FVST, called Subset-FVST, includes an additional subset S ⊆ V(T) in the input. The goal for Subset-FVST is to find a vertex set X ⊆ V(T) of size at most k such that T-X contains no directed cycles that pass through any vertex in S. This generalized problem can also be represented as a 3-Hitting Set problem, leading to a running time of 2.076^k ⋅ n^{𝒪(1)}. Bai and Xiao [Theoretical Computer Science 2023] improved this and obtained an algorithm with running time 2^{k + o(k)} ⋅ n^{𝒪(1)}. In our work, we extend the algorithm of Kumar and Lokshtanov [STACS 2016] to solve Subset-FVST, obtaining an algorithm with a running time {𝒪}(1.6181^k + n^{{𝒪}(1)}), matching the running time for FVST.
Cite as

Satyabrata Jana, Lawqueen Kanesh, Madhumita Kundu, and Saket Saurabh. Subset Feedback Vertex Set in Tournaments as Fast as Without the Subset. In 19th International Symposium on Parameterized and Exact Computation (IPEC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 321, pp. 17:1-17:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{jana_et_al:LIPIcs.IPEC.2024.17,
  author =	{Jana, Satyabrata and Kanesh, Lawqueen and Kundu, Madhumita and Saurabh, Saket},
  title =	{{Subset Feedback Vertex Set in Tournaments as Fast as Without the Subset}},
  booktitle =	{19th International Symposium on Parameterized and Exact Computation (IPEC 2024)},
  pages =	{17:1--17:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-353-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{321},
  editor =	{Bonnet, \'{E}douard and Rz\k{a}\.{z}ewski, Pawe{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2024.17},
  URN =		{urn:nbn:de:0030-drops-222438},
  doi =		{10.4230/LIPIcs.IPEC.2024.17},
  annote =	{Keywords: Parameterized algorithms, Feedback vertex set, Tournaments, Fixed parameter tractable, Graph partitions}
}
Document
DOI: 10.4230/LIPIcs.ESA.2024.17
Cuts in Graphs with Matroid Constraints

Authors: Aritra Banik, Fedor V. Fomin, Petr A. Golovach, Tanmay Inamdar, Satyabrata Jana, and Saket Saurabh

Published in: LIPIcs, Volume 308, 32nd Annual European Symposium on Algorithms (ESA 2024)

Abstract
Vertex (s, t)-Cut and Vertex Multiway Cut are two fundamental graph separation problems in algorithmic graph theory. We study matroidal generalizations of these problems, where in addition to the usual input, we are given a representation R ∈ 𝔽^{r × n} of a linear matroid ℳ = (V(G), ℐ) of rank r in the input, and the goal is to determine whether there exists a vertex subset S ⊆ V(G) that has the required cut properties, as well as is independent in the matroid ℳ. We refer to these problems as Independent Vertex (s, t){-cut}, and Independent Multiway Cut, respectively. We show that these problems are fixed-parameter tractable (FPT) when parameterized by the solution size (which can be assumed to be equal to the rank of the matroid ℳ). These results are obtained by exploiting the recent technique of flow augmentation [Kim et al. STOC '22], combined with a dynamic programming algorithm on flow-paths á la [Feige and Mahdian, STOC '06] that maintains a representative family of solutions w.r.t. the given matroid [Marx, TCS '06; Fomin et al., JACM]. As a corollary, we also obtain FPT algorithms for the independent version of Odd Cycle Transversal. Further, our results can be generalized to other variants of the problems, e.g., weighted versions, or edge-deletion versions.
Cite as

Aritra Banik, Fedor V. Fomin, Petr A. Golovach, Tanmay Inamdar, Satyabrata Jana, and Saket Saurabh. Cuts in Graphs with Matroid Constraints. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 17:1-17:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{banik_et_al:LIPIcs.ESA.2024.17,
  author =	{Banik, Aritra and Fomin, Fedor V. and Golovach, Petr A. and Inamdar, Tanmay and Jana, Satyabrata and Saurabh, Saket},
  title =	{{Cuts in Graphs with Matroid Constraints}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{17:1--17:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-338-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{308},
  editor =	{Chan, Timothy and Fischer, Johannes and Iacono, John and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2024.17},
  URN =		{urn:nbn:de:0030-drops-210887},
  doi =		{10.4230/LIPIcs.ESA.2024.17},
  annote =	{Keywords: s-t-cut, multiway Cut, matroid, odd cycle transversal, feedback vertex set, fixed-parameter tractability}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2023.5
Difference Determines the Degree: Structural Kernelizations of Component Order Connectivity

Authors: Sriram Bhyravarapu, Satyabrata Jana, Saket Saurabh, and Roohani Sharma

Published in: LIPIcs, Volume 285, 18th International Symposium on Parameterized and Exact Computation (IPEC 2023)

Abstract
We consider the question of polynomial kernelization of a generalization of the classical Vertex Cover problem parameterized by a parameter that is provably smaller than the solution size. In particular, we focus on the c-Component Order Connectivity problem (c-COC) where given an undirected graph G and a non-negative integer t, the objective is to test whether there exists a set S of size at most t such that every component of G-S contains at most c vertices. Such a set S is called a c-coc set. It is known that c-COC admits a kernel with {O}(ct) vertices. Observe that for c = 1, this corresponds to the Vertex Cover problem. We study the c-Component Order Connectivity problem parameterized by the size of a d-coc set (c-COC/d-COC), where c,d ∈ ℕ with c ≤ d. In particular, the input is an undirected graph G, a positive integer t and a set M of at most k vertices of G, such that the size of each connected component in G - M is at most d. The question is to find a set S of vertices of size at most t, such that the size of each connected component in G - S is at most c. In this paper, we give a kernel for c-COC/d-COC with O(k^{d-c+1}) vertices and O(k^{d-c+2}) edges. Our result exhibits that the difference in d and c, and not their absolute values, determines the exact degree of the polynomial in the kernel size. When c = d = 1, the c-COC/d-COC problem is exactly the Vertex Cover problem parameterized by the solution size, which has a kernel with O(k) vertices and O(k²) edges, and this is asymptotically tight [Dell & Melkebeek, JACM 2014]. We also show that the dependence of d-c in the exponent of the kernel size cannot be avoided under reasonable complexity assumptions.
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Sriram Bhyravarapu, Satyabrata Jana, Saket Saurabh, and Roohani Sharma. Difference Determines the Degree: Structural Kernelizations of Component Order Connectivity. In 18th International Symposium on Parameterized and Exact Computation (IPEC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 285, pp. 5:1-5:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{bhyravarapu_et_al:LIPIcs.IPEC.2023.5,
  author =	{Bhyravarapu, Sriram and Jana, Satyabrata and Saurabh, Saket and Sharma, Roohani},
  title =	{{Difference Determines the Degree: Structural Kernelizations of Component Order Connectivity}},
  booktitle =	{18th International Symposium on Parameterized and Exact Computation (IPEC 2023)},
  pages =	{5:1--5:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-305-8},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{285},
  editor =	{Misra, Neeldhara and Wahlstr\"{o}m, Magnus},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2023.5},
  URN =		{urn:nbn:de:0030-drops-194241},
  doi =		{10.4230/LIPIcs.IPEC.2023.5},
  annote =	{Keywords: Kernelization, Component Order Connectivity, Vertex Cover, Structural Parameterizations}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2023.56
Parameterized Approximation Scheme for Feedback Vertex Set

Authors: Satyabrata Jana, Daniel Lokshtanov, Soumen Mandal, Ashutosh Rai, and Saket Saurabh

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

Abstract
Feedback Vertex Set (FVS) is one of the most studied vertex deletion problems in the field of graph algorithms. In the decision version of the problem, given a graph G and an integer k, the question is whether there exists a set S of at most k vertices in G such that G-S is acyclic. It is one of the first few problems which were shown to be NP-complete, and has been extensively studied from the viewpoint of approximation and parameterized algorithms. The best-known polynomial time approximation algorithm for FVS is a 2-factor approximation, while the best known deterministic and randomized FPT algorithms run in time 𝒪^*(3.460^k) and 𝒪^*(2.7^k) respectively. In this paper, we contribute to the newly established area of parameterized approximation, by studying FVS in this paradigm. In particular, we combine the approaches of parameterized and approximation algorithms for the study of FVS, and achieve an approximation guarantee with a factor better than 2 in randomized FPT running time, that improves over the best known parameterized algorithm for FVS. We give three simple randomized (1+ε) approximation algorithms for FVS, running in times 𝒪^*(2^{εk}⋅ 2.7^{(1-ε)k}), 𝒪^*(({(4/(1+ε))^{(1+ε)}}⋅{(ε/3)^ε})^k), and 𝒪^*(4^{(1-ε)k}) respectively for every ε ∈ (0,1). Combining these three algorithms, we obtain a factor (1+ε) approximation algorithm for FVS, which has better running time than the best-known (randomized) FPT algorithm for every ε ∈ (0, 1). This is the first attempt to look at a parameterized approximation of FVS to the best of our knowledge. Our algorithms are very simple, and they rely on some well-known reduction rules used for arriving at FPT algorithms for FVS.
Cite as

Satyabrata Jana, Daniel Lokshtanov, Soumen Mandal, Ashutosh Rai, and Saket Saurabh. Parameterized Approximation Scheme for Feedback Vertex Set. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 56:1-56:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{jana_et_al:LIPIcs.MFCS.2023.56,
  author =	{Jana, Satyabrata and Lokshtanov, Daniel and Mandal, Soumen and Rai, Ashutosh and Saurabh, Saket},
  title =	{{Parameterized Approximation Scheme for Feedback Vertex Set}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{56:1--56:15},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.56},
  URN =		{urn:nbn:de:0030-drops-185902},
  doi =		{10.4230/LIPIcs.MFCS.2023.56},
  annote =	{Keywords: Feedback Vertex Set, Parameterized Approximation}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2022.2
Parameterized Complexity of Perfectly Matched Sets

Authors: Akanksha Agrawal, Sutanay Bhattacharjee, Satyabrata Jana, and Abhishek Sahu

Published in: LIPIcs, Volume 249, 17th International Symposium on Parameterized and Exact Computation (IPEC 2022)

Abstract
For an undirected graph G, a pair of vertex disjoint subsets (A, B) is a pair of perfectly matched sets if each vertex in A (resp. B) has exactly one neighbor in B (resp. A). In the above, the size of the pair is |A| (= |B|). Given a graph G and a positive integer k, the Perfectly Matched Sets problem asks whether there exists a pair of perfectly matched sets of size at least k in G. This problem is known to be NP-hard on planar graphs and W[1]-hard on general graphs, when parameterized by k. However, little is known about the parameterized complexity of the problem in restricted graph classes. In this work, we study the problem parameterized by k, and design FPT algorithms for: i) apex-minor-free graphs running in time 2^O(√k)⋅ n^O(1), and ii) K_{b,b}-free graphs. We obtain a linear kernel for planar graphs and k^𝒪(d)-sized kernel for d-degenerate graphs. It is known that the problem is W[1]-hard on chordal graphs, in fact on split graphs, parameterized by k. We complement this hardness result by designing a polynomial-time algorithm for interval graphs.
Cite as

Akanksha Agrawal, Sutanay Bhattacharjee, Satyabrata Jana, and Abhishek Sahu. Parameterized Complexity of Perfectly Matched Sets. In 17th International Symposium on Parameterized and Exact Computation (IPEC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 249, pp. 2:1-2:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{agrawal_et_al:LIPIcs.IPEC.2022.2,
  author =	{Agrawal, Akanksha and Bhattacharjee, Sutanay and Jana, Satyabrata and Sahu, Abhishek},
  title =	{{Parameterized Complexity of Perfectly Matched Sets}},
  booktitle =	{17th International Symposium on Parameterized and Exact Computation (IPEC 2022)},
  pages =	{2:1--2:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-260-0},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{249},
  editor =	{Dell, Holger and Nederlof, Jesper},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2022.2},
  URN =		{urn:nbn:de:0030-drops-173580},
  doi =		{10.4230/LIPIcs.IPEC.2022.2},
  annote =	{Keywords: Perfectly Matched Sets, Parameterized Complexity, Apex-minor-free graphs, d-degenerate graphs, Planar graphs, Interval Graphs}
}
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