18 Search Results for "Kanesh, Lawqueen"

Document
DOI: 10.4230/LIPIcs.ITCS.2026.80
FPT Approximations for Connected Maximum Coverage

Authors: Tanmay Inamdar, Satyabrata Jana, Madhumita Kundu, Daniel Lokshtanov, Saket Saurabh, and Meirav Zehavi

Published in: LIPIcs, Volume 362, 17th Innovations in Theoretical Computer Science Conference (ITCS 2026)

Abstract
We revisit connectivity-constrained coverage through a unifying model, Partial Connected Red-Blue Dominating Set (PartialConRBDS). Given a bipartite graph G = (R∪ B,E) with red vertices R and blue vertices B, an auxiliary connectivity graph G_{conn} on R, and integers k,t, the task is to find a set S ⊆ R with |S| ≤ k such that G_{conn}[S] is connected and S dominates at least t blue vertices. This formulation captures connected variants of Maximum Coverage [Hochbaum-Rao, Inf. Proc. Lett., 2020; D'Angelo-Delfaraz, AAMAS 2025], Partial Vertex Cover, and Partial Dominating Set [Khuller et al., SODA 2014; Lamprou et al., TCS 2021] via standard encodings. Limits to parameterized tractability. PartialConRBDS is W[1]-hard parameterized by k even under strong restrictions: it remains hard when G_{conn} is a clique or a star and the incidence graph G is 3-degenerate, or when G is K_{2,2}-free. Inapproximability. For every ε > 0, there is no polynomial-time (1, 1-1/e+ε)-approximation unless 𝖯 = NP. Moreover, under ETH, no algorithm running in f(k)⋅ n^{o(k)} time achieves an g(k)-approximation for k for any computable function g(⋅), or for any ε > 0, a (1-1/e+ε)-approximation for t. Graphical special cases. Partial Connected Dominating Set is W[2]-hard parameterized by k and inherits the same ETH-based f(k)⋅ n^{o(k)} inapproximability bound as above; Partial Connected Vertex Cover is W[1]-hard parameterized by k. These hardness boundaries delineate a natural "sweet spot" for study: within appropriate structural restrictions on the incidence graph, one can still aim for fine-grained (FPT) approximations. Our algorithms. We solve PartialConRBDS exactly by reducing it to Relaxed Directed Steiner Out-Tree in time (2e)^t ⋅ n^{𝒪(1)}. For biclique-free incidences (i.e., when G excludes K_{d,d} as an induced subgraph), we obtain two complementary parameterized schemes: - An Efficient Parameterized Approximation Scheme (EPAS) running in time 2^{𝒪(k² d/ε)}⋅ n^{𝒪(1)} that either returns a connected solution of size at most k covering at least (1-ε)t blue vertices, or correctly reports that no connected size-k solution covers t; and - A Parameterized Approximation Scheme (PAS) running in time 2^{𝒪(kd(k²+log d))}⋅ n^{𝒪(1/ε)} that either returns a connected solution of size at most (1+ε)k covering at least t blue vertices, or correctly reports that no connected size-k solution covers t. Together, these results chart the boundary between hardness and FPT-approximability for connectivity-constrained coverage.
Cite as

Tanmay Inamdar, Satyabrata Jana, Madhumita Kundu, Daniel Lokshtanov, Saket Saurabh, and Meirav Zehavi. FPT Approximations for Connected Maximum Coverage. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 80:1-80:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{inamdar_et_al:LIPIcs.ITCS.2026.80,
  author =	{Inamdar, Tanmay and Jana, Satyabrata and Kundu, Madhumita and Lokshtanov, Daniel and Saurabh, Saket and Zehavi, Meirav},
  title =	{{FPT Approximations for Connected Maximum Coverage}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{80:1--80:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.80},
  URN =		{urn:nbn:de:0030-drops-253674},
  doi =		{10.4230/LIPIcs.ITCS.2026.80},
  annote =	{Keywords: Partial Dominating Set, Connectivity, Maximum Coverage, FPT Approximation, Fixed-parameter Tractability}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2025.43
A Finer View of the Parameterized Landscape of Labeled Graph Contractions

Authors: Yashaswini Mathur and Prafullkumar Tale

Published in: LIPIcs, Volume 360, 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)

Abstract
We study the Labeled Contractibility problem, where the input consists of two vertex-labeled graphs G and H, and the goal is to determine whether H can be obtained from G via a sequence of edge contractions. Lafond and Marchand [WADS 2025] initiated the parameterized complexity study of this problem, showing it to be W[1]-hard when parameterized by the number k of allowed contractions. They also proved that the problem is fixed-parameter tractable when parameterized by the tree-width tw of G, via an application of Courcelle’s theorem resulting in a non-constructive algorithm. In this work, we present a constructive fixed-parameter algorithm for Labeled Contractibility with running time 2^{𝒪(tw²)} ⋅ |V(G)|^{𝒪(1)}. We also prove that unless the Exponential Time Hypothesis ({ETH}) fails, it does not admit an algorithm running in time 2^{o(tw²)} ⋅ |V(G)|^{𝒪(1)}. This result adds Labeled Contractibility to a small list of problems that admit such a lower bound and matching algorithm. We further strengthen existing hardness results by showing that the problem remains NP-complete even when both input graphs have bounded maximum degree. We also investigate parameterizations by (k + δ(G)) where δ(G) denotes the degeneracy of G, and rule out the existence of subexponential-time algorithms. This answers question raised in Lafond and Marchand [WADS 2025]. We additionally provide an improved FPT algorithm with better dependence on (k + δ(G)) than previously known. Finally, we analyze a brute-force algorithm for Labeled Contractibility with running time |V(H)|^{𝒪(|V(G)|)}, and show that this running time is optimal under {ETH}.
Cite as

Yashaswini Mathur and Prafullkumar Tale. A Finer View of the Parameterized Landscape of Labeled Graph Contractions. In 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 360, pp. 43:1-43:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{mathur_et_al:LIPIcs.FSTTCS.2025.43,
  author =	{Mathur, Yashaswini and Tale, Prafullkumar},
  title =	{{A Finer View of the Parameterized Landscape of Labeled Graph Contractions}},
  booktitle =	{45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)},
  pages =	{43:1--43:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-406-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{360},
  editor =	{Aiswarya, C. and Mehta, Ruta and Roy, Subhajit},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2025.43},
  URN =		{urn:nbn:de:0030-drops-251237},
  doi =		{10.4230/LIPIcs.FSTTCS.2025.43},
  annote =	{Keywords: Labeled Contraction, ETH Lower-bound, Treewidth, NP-hard}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.7
Graph Modification of Bounded Size to Minor-Closed Classes as Fast as Vertex Deletion

Authors: Laure Morelle, Ignasi Sau, and Dimitrios M. Thilikos

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
A replacement action is a function ℒ that maps each graph H to a collection of graphs of size at most |V(H)|. Given a graph class ℋ, we consider a general family of graph modification problems, called ℒ-Replacement to ℋ, where the input is a graph G and the question is whether it is possible to replace some induced subgraph H₁ of G on at most k vertices by a graph H₂ in ℒ(H₁) so that the resulting graph belongs to ℋ. ℒ-Replacement to ℋ can simulate many graph modification problems including vertex deletion, edge deletion/addition/edition/contraction, vertex identification, subgraph complementation, independent set deletion, (induced) matching deletion/contraction, etc. We present two algorithms. The first one solves ℒ-Replacement to ℋ in time 2^poly(k) ⋅ |V(G)|² for every minor-closed graph class ℋ, where poly is a polynomial whose degree depends on ℋ, under a mild technical condition on ℒ. This generalizes the results of Morelle, Sau, Stamoulis, and Thilikos [ICALP 2020, ICALP 2023] for the particular case of Vertex Deletion to ℋ within the same running time. Our second algorithm is an improvement of the first one when ℋ is the class of graphs embeddable in a surface of Euler genus at most g and runs in time 2^𝒪(k⁹) ⋅ |V(G)|², where the 𝒪(⋅) notation depends on g. To the best of our knowledge, these are the first parameterized algorithms with a reasonable parametric dependence for such a general family of graph modification problems to minor-closed classes.
Cite as

Laure Morelle, Ignasi Sau, and Dimitrios M. Thilikos. Graph Modification of Bounded Size to Minor-Closed Classes as Fast as Vertex Deletion. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 7:1-7:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{morelle_et_al:LIPIcs.ESA.2025.7,
  author =	{Morelle, Laure and Sau, Ignasi and Thilikos, Dimitrios M.},
  title =	{{Graph Modification of Bounded Size to Minor-Closed Classes as Fast as Vertex Deletion}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{7:1--7:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian 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.2025.7},
  URN =		{urn:nbn:de:0030-drops-244751},
  doi =		{10.4230/LIPIcs.ESA.2025.7},
  annote =	{Keywords: Graph modification problems, Parameterized complexity, Graph minors, Flat Wall theorem, Irrelevant vertex technique, Algorithmic meta-theorem, Parametric dependence, Dynamic programming}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.13
Solving Partial Dominating Set and Related Problems Using Twin-Width

Authors: Jakub Balabán, Daniel Mock, and Peter Rossmanith

Published in: LIPIcs, Volume 345, 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)

Abstract
Partial vertex cover and partial dominating set are two well-investigated optimization problems. While they are W[1]-hard on general graphs, they have been shown to be fixed-parameter tractable on many sparse graph classes, including nowhere-dense classes. In this paper, we demonstrate that these problems are also fixed-parameter tractable with respect to the twin-width of a graph. Indeed, we establish a more general result: every graph property that can be expressed by a logical formula of the form ϕ≡∃ x₁⋯ ∃ x_k ∑_{α ∈ I} #y ψ_α(x₁,…,x_k,y) ≥ t, where ψ_α is a quantifier-free formula for each α ∈ I, t is an arbitrary number, and #y is a counting quantifier, can be evaluated in time f(d,k)n, where n is the number of vertices and d is the width of a contraction sequence that is part of the input. In addition to the aforementioned problems, this includes also connected partial dominating set and independent partial dominating set.
Cite as

Jakub Balabán, Daniel Mock, and Peter Rossmanith. Solving Partial Dominating Set and Related Problems Using Twin-Width. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 13:1-13:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{balaban_et_al:LIPIcs.MFCS.2025.13,
  author =	{Balab\'{a}n, Jakub and Mock, Daniel and Rossmanith, Peter},
  title =	{{Solving Partial Dominating Set and Related Problems Using Twin-Width}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{13:1--13:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-388-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{345},
  editor =	{Gawrychowski, Pawe{\l} and Mazowiecki, Filip and Skrzypczak, Micha{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2025.13},
  URN =		{urn:nbn:de:0030-drops-241203},
  doi =		{10.4230/LIPIcs.MFCS.2025.13},
  annote =	{Keywords: Partial Dominating Set, Partial Vertex Cover, meta-algorithm, counting logic, twin-width}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.90
Elimination Distance to Dominated Clusters

Authors: Nicole Schirrmacher, Sebastian Siebertz, and Alexandre Vigny

Published in: LIPIcs, Volume 345, 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)

Abstract
In the Dominated Cluster Deletion problem, we are given an undirected graph G and integers k and d and the question is to decide whether there exists a set of at most k vertices whose removal results in a graph in which each connected component has a dominating set of size at most d. In the Elimination Distance to Dominated Clusters problem, we are again given an undirected graph G and integers k and d and the question is to decide whether we can recursively delete vertices up to depth k such that each remaining connected component has a dominating set of size at most d. Bentert et al. [Bentert et al., MFCS 2024] recently provided an almost complete classification of the parameterized complexity of Dominated Cluster Deletion with respect to the parameters k, d, c, and Δ, where c and Δ are the degeneracy, and the maximum degree of the input graph, respectively. In particular, they provided a non-uniform algorithm with running time f(k,d)⋅ n^{𝒪(d)}. They left as an open problem whether the problem is fixed-parameter tractable with respect to the parameter k + d + c. We provide a uniform algorithm running in time f(k,d)⋅ n^{𝒪(d)} for both Dominated Cluster Deletion and Elimination Distance to Dominated Clusters. We furthermore show that both problems are FPT when parameterized by k+d+𝓁, where 𝓁 is the semi-ladder index of the input graph, a parameter that is upper bounded and may be much smaller than the degeneracy c, positively answering the open question of Bentert et al. We further complete the picture by providing an almost full classification for the parameterized complexity and kernelization complexity of Elimination Distance to Dominated Clusters. The one difficult base case that remains open is whether Treedepth (the case d = 0) is NP-hard on graphs of bounded maximum degree.
Cite as

Nicole Schirrmacher, Sebastian Siebertz, and Alexandre Vigny. Elimination Distance to Dominated Clusters. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 90:1-90:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{schirrmacher_et_al:LIPIcs.MFCS.2025.90,
  author =	{Schirrmacher, Nicole and Siebertz, Sebastian and Vigny, Alexandre},
  title =	{{Elimination Distance to Dominated Clusters}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{90:1--90:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-388-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{345},
  editor =	{Gawrychowski, Pawe{\l} and Mazowiecki, Filip and Skrzypczak, Micha{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2025.90},
  URN =		{urn:nbn:de:0030-drops-241978},
  doi =		{10.4230/LIPIcs.MFCS.2025.90},
  annote =	{Keywords: Graph theory, Fixed-parameter algorithms, Dominated cluster, Elimination distance}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2025.15
Exponential-Time Approximation (Schemes) for Vertex-Ordering Problems

Authors: Matthias Bentert, Fedor V. Fomin, Tanmay Inamdar, and Saket Saurabh

Published in: LIPIcs, Volume 325, 16th Innovations in Theoretical Computer Science Conference (ITCS 2025)

Abstract
In this paper, we begin the exploration of vertex-ordering problems through the lens of exponential-time approximation algorithms. In particular, we ask the following question: Can we simultaneously beat the running times of the fastest known (exponential-time) exact algorithms and the best known approximation factors that can be achieved in polynomial time? Following the recent research initiated by Esmer et al. (ESA 2022, IPEC 2023, SODA 2024) on vertex-subset problems, and by Inamdar et al. (ITCS 2024) on graph-partitioning problems, we focus on vertex-ordering problems. In particular, we give positive results for Feedback Arc Set, Optimal Linear Arrangement, Cutwidth, and Pathwidth. Most of our algorithms build upon a novel "balanced-cut" approach - which is our main conceptual contribution. This allows us to solve various problems in very general settings allowing for directed and arc-weighted input graphs. Our main technical contribution is a (1+ε)-approximation for any ε > 0 for (weighted) Feedback Arc Set in O^*((2-δ_ε)^n) time, where δ_ε > 0 is a constant only depending on ε.
Cite as

Matthias Bentert, Fedor V. Fomin, Tanmay Inamdar, and Saket Saurabh. Exponential-Time Approximation (Schemes) for Vertex-Ordering Problems. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 15:1-15:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bentert_et_al:LIPIcs.ITCS.2025.15,
  author =	{Bentert, Matthias and Fomin, Fedor V. and Inamdar, Tanmay and Saurabh, Saket},
  title =	{{Exponential-Time Approximation (Schemes) for Vertex-Ordering Problems}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{15:1--15:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-361-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{325},
  editor =	{Meka, Raghu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2025.15},
  URN =		{urn:nbn:de:0030-drops-226431},
  doi =		{10.4230/LIPIcs.ITCS.2025.15},
  annote =	{Keywords: Feedback Arc Set, Cutwidth, Optimal Linear Arrangement, Pathwidth}
}
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.STACS.2024.44
Decremental Sensitivity Oracles for Covering and Packing Minors

Authors: Lawqueen Kanesh, Fahad Panolan, M. S. Ramanujan, and Peter Strulo

Published in: LIPIcs, Volume 289, 41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024)

Abstract
In this paper, we present the first decremental fixed-parameter sensitivity oracles for a number of basic covering and packing problems on graphs. In particular, we obtain the first decremental sensitivity oracles for Vertex Planarization (delete k vertices to make the graph planar) and Cycle Packing (pack k vertex-disjoint cycles in the given graph). That is, we give a sensitivity oracle that preprocesses the given graph in time f(k,𝓁)n^{{O}(1)} such that, when given a set of 𝓁 edge deletions, the data structure decides in time f(k,𝓁) whether the updated graph is a positive instance of the problem. These results are obtained as a corollary of our central result, which is the first decremental sensitivity oracle for Topological Minor Deletion (cover all topological minors in the input graph that belong to a specified set, using k vertices). Though our methodology closely follows the literature, we are able to produce the first explicit bounds on the preprocessing and query times for several problems. We also initiate the study of fixed-parameter sensitivity oracles with so-called structural parameterizations and give sufficient conditions for the existence of fixed-parameter sensitivity oracles where the parameter is just the treewidth of the graph. In contrast, all existing literature on this topic and the aforementioned results in this paper assume a bound on the solution size (a weaker parameter than treewidth for many problems). As corollaries, we obtain decremental sensitivity oracles for well-studied problems such as Vertex Cover and Dominating Set when only the treewidth of the input graph is bounded. A feature of our methodology behind these results is that we are able to obtain query times independent of treewidth.
Cite as

Lawqueen Kanesh, Fahad Panolan, M. S. Ramanujan, and Peter Strulo. Decremental Sensitivity Oracles for Covering and Packing Minors. In 41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 289, pp. 44:1-44:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{kanesh_et_al:LIPIcs.STACS.2024.44,
  author =	{Kanesh, Lawqueen and Panolan, Fahad and Ramanujan, M. S. and Strulo, Peter},
  title =	{{Decremental Sensitivity Oracles for Covering and Packing Minors}},
  booktitle =	{41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024)},
  pages =	{44:1--44:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-311-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{289},
  editor =	{Beyersdorff, Olaf and Kant\'{e}, Mamadou Moustapha and Kupferman, Orna and Lokshtanov, Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2024.44},
  URN =		{urn:nbn:de:0030-drops-197544},
  doi =		{10.4230/LIPIcs.STACS.2024.44},
  annote =	{Keywords: Sensitivity oracles, Data Structures, FPT algorithms}
}
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.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.2023.55
Fixed-Parameter Algorithms for Fair Hitting Set Problems

Authors: Tanmay Inamdar, Lawqueen Kanesh, Madhumita Kundu, Nidhi Purohit, and Saket Saurabh

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

Abstract
Selection of a group of representatives satisfying certain fairness constraints, is a commonly occurring scenario. Motivated by this, we initiate a systematic algorithmic study of a fair version of Hitting Set. In the classical Hitting Set problem, the input is a universe 𝒰, a family ℱ of subsets of 𝒰, and a non-negative integer k. The goal is to determine whether there exists a subset S ⊆ 𝒰 of size k that hits (i.e., intersects) every set in ℱ. Inspired by several recent works, we formulate a fair version of this problem, as follows. The input additionally contains a family ℬ of subsets of 𝒰, where each subset in ℬ can be thought of as the group of elements of the same type. We want to find a set S ⊆ 𝒰 of size k that (i) hits all sets of ℱ, and (ii) does not contain too many elements of each type. We call this problem Fair Hitting Set, and chart out its tractability boundary from both classical as well as multivariate perspective. Our results use a multitude of techniques from parameterized complexity including classical to advanced tools, such as, methods of representative sets for matroids, FO model checking, and a generalization of best known kernels for Hitting Set.
Cite as

Tanmay Inamdar, Lawqueen Kanesh, Madhumita Kundu, Nidhi Purohit, and Saket Saurabh. Fixed-Parameter Algorithms for Fair Hitting Set Problems. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 55:1-55:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{inamdar_et_al:LIPIcs.MFCS.2023.55,
  author =	{Inamdar, Tanmay and Kanesh, Lawqueen and Kundu, Madhumita and Purohit, Nidhi and Saurabh, Saket},
  title =	{{Fixed-Parameter Algorithms for Fair Hitting Set Problems}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{55:1--55:14},
  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.2023.55},
  URN =		{urn:nbn:de:0030-drops-185897},
  doi =		{10.4230/LIPIcs.MFCS.2023.55},
  annote =	{Keywords: Fairness, Parameterized Algorithms, Hitting Set}
}
Document
DOI: 10.4230/LIPIcs.STACS.2022.39
Further Exploiting c-Closure for FPT Algorithms and Kernels for Domination Problems

Authors: Lawqueen Kanesh, Jayakrishnan Madathil, Sanjukta Roy, Abhishek Sahu, and Saket Saurabh

Published in: LIPIcs, Volume 219, 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)

Abstract
For a positive integer c, a graph G is said to be c-closed if every pair of non-adjacent vertices in G have at most c-1 neighbours in common. The closure of a graph G, denoted by cl(G), is the least positive integer c for which G is c-closed. The class of c-closed graphs was introduced by Fox et al. [ICALP `18 and SICOMP `20]. Koana et al. [ESA `20] started the study of using cl(G) as an additional structural parameter to design kernels for problems that are W-hard under standard parameterizations. In particular, they studied problems such as Independent Set, Induced Matching, Irredundant Set and (Threshold) Dominating Set, and showed that each of these problems admits a polynomial kernel, either w.r.t. the parameter k+c or w.r.t. the parameter k for each fixed value of c. Here, k is the solution size and c = cl(G). The work of Koana et al. left several questions open, one of which was whether the Perfect Code problem admits a fixed-parameter tractable (FPT) algorithm and a polynomial kernel on c-closed graphs. In this paper, among other results, we answer this question in the affirmative. Inspired by the FPT algorithm for Perfect Code, we further explore two more domination problems on the graphs of bounded closure. The other problems that we study are Connected Dominating Set and Partial Dominating Set. We show that Perfect Code and Connected Dominating Set are fixed-parameter tractable w.r.t. the parameter k+cl(G), whereas Partial Dominating Set, parameterized by k is W[1]-hard even when cl(G) = 2. We also show that for each fixed c, Perfect Code admits a polynomial kernel on the class of c-closed graphs. And we observe that Connected Dominating Set has no polynomial kernel even on 2-closed graphs, unless NP ⊆ co-NP/poly.
Cite as

Lawqueen Kanesh, Jayakrishnan Madathil, Sanjukta Roy, Abhishek Sahu, and Saket Saurabh. Further Exploiting c-Closure for FPT Algorithms and Kernels for Domination Problems. In 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 219, pp. 39:1-39:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{kanesh_et_al:LIPIcs.STACS.2022.39,
  author =	{Kanesh, Lawqueen and Madathil, Jayakrishnan and Roy, Sanjukta and Sahu, Abhishek and Saurabh, Saket},
  title =	{{Further Exploiting c-Closure for FPT Algorithms and Kernels for Domination Problems}},
  booktitle =	{39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)},
  pages =	{39:1--39:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-222-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{219},
  editor =	{Berenbrink, Petra and Monmege, Benjamin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2022.39},
  URN =		{urn:nbn:de:0030-drops-158494},
  doi =		{10.4230/LIPIcs.STACS.2022.39},
  annote =	{Keywords: c-closed graphs, domination problems, perfect code, connected dominating set, fixed-parameter tractable, polynomial kernel}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2021.23
A Polynomial Kernel for Bipartite Permutation Vertex Deletion

Authors: Lawqueen Kanesh, Jayakrishnan Madathil, Abhishek Sahu, Saket Saurabh, and Shaily Verma

Published in: LIPIcs, Volume 214, 16th International Symposium on Parameterized and Exact Computation (IPEC 2021)

Abstract
In a permutation graph, vertices represent the elements of a permutation, and edges represent pairs of elements that are reversed by the permutation. In the Permutation Vertex Deletion problem, given an undirected graph G and an integer k, the objective is to test whether there exists a vertex subset S ⊆ V(G) such that |S| ≤ k and G-S is a permutation graph. The parameterized complexity of Permutation Vertex Deletion is a well-known open problem. Bożyk et al. [IPEC 2020] initiated a study towards this problem by requiring that G-S be a bipartite permutation graph (a permutation graph that is bipartite). They called this the Bipartite Permutation Vertex Deletion (BPVD) problem. They showed that the problem admits a factor 9-approximation algorithm as well as a fixed parameter tractable (FPT) algorithm running in time 𝒪(9^k |V(G)|⁹). And they posed the question {whether BPVD admits a polynomial kernel.} We resolve this question in the affirmative by designing a polynomial kernel for BPVD. In particular, we obtain the following: Given an instance (G,k) of BPVD, in polynomial time we obtain an equivalent instance (G',k') of BPVD such that k' ≤ k, and |V(G')|+|E(G')| ≤ k^{𝒪(1)}.
Cite as

Lawqueen Kanesh, Jayakrishnan Madathil, Abhishek Sahu, Saket Saurabh, and Shaily Verma. A Polynomial Kernel for Bipartite Permutation Vertex Deletion. In 16th International Symposium on Parameterized and Exact Computation (IPEC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 214, pp. 23:1-23:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{kanesh_et_al:LIPIcs.IPEC.2021.23,
  author =	{Kanesh, Lawqueen and Madathil, Jayakrishnan and Sahu, Abhishek and Saurabh, Saket and Verma, Shaily},
  title =	{{A Polynomial Kernel for Bipartite Permutation Vertex Deletion}},
  booktitle =	{16th International Symposium on Parameterized and Exact Computation (IPEC 2021)},
  pages =	{23:1--23:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-216-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{214},
  editor =	{Golovach, Petr A. and Zehavi, Meirav},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2021.23},
  URN =		{urn:nbn:de:0030-drops-154065},
  doi =		{10.4230/LIPIcs.IPEC.2021.23},
  annote =	{Keywords: kernelization, bipartite permutation graph, bicliques}
}
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.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.FSTTCS.2020.18
Parameterized Complexity of Feedback Vertex Sets on Hypergraphs

Authors: Pratibha Choudhary, Lawqueen Kanesh, Daniel Lokshtanov, Fahad Panolan, and Saket Saurabh

Published in: LIPIcs, Volume 182, 40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020)

Abstract
A feedback vertex set in a hypergraph H is a set of vertices S such that deleting S from H results in an acyclic hypergraph. Here, deleting a vertex means removing the vertex and all incident hyperedges, and a hypergraph is acyclic if its vertex-edge incidence graph is acyclic. We study the (parameterized complexity of) the Hypergraph Feedback Vertex Set (HFVS) problem: given as input a hypergraph H and an integer k, determine whether H has a feedback vertex set of size at most k. It is easy to see that this problem generalizes the classic Feedback Vertex Set (FVS) problem on graphs. Remarkably, despite the central role of FVS in parameterized algorithms and complexity, the parameterized complexity of a generalization of FVS to hypergraphs has not been studied previously. In this paper, we fill this void. Our main results are as follows - HFVS is W[2]-hard (as opposed to FVS, which is fixed parameter tractable). - If the input hypergraph is restricted to a linear hypergraph (no two hyperedges intersect in more than one vertex), HFVS admits a randomized algorithm with running time 2^{𝒪(k³log k)}n^{𝒪(1)}. - If the input hypergraph is restricted to a d-hypergraph (hyperedges have cardinality at most d), then HFVS admits a deterministic algorithm with running time d^{𝒪(k)}n^{𝒪(1)}. The algorithm for linear hypergraphs combines ideas from the randomized algorithm for FVS by Becker et al. [J. Artif. Intell. Res., 2000] with the branching algorithm for Point Line Cover by Langerman and Morin [Discrete & Computational Geometry, 2005].
Cite as

Pratibha Choudhary, Lawqueen Kanesh, Daniel Lokshtanov, Fahad Panolan, and Saket Saurabh. Parameterized Complexity of Feedback Vertex Sets on Hypergraphs. In 40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 182, pp. 18:1-18:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{choudhary_et_al:LIPIcs.FSTTCS.2020.18,
  author =	{Choudhary, Pratibha and Kanesh, Lawqueen and Lokshtanov, Daniel and Panolan, Fahad and Saurabh, Saket},
  title =	{{Parameterized Complexity of Feedback Vertex Sets on Hypergraphs}},
  booktitle =	{40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020)},
  pages =	{18:1--18:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-174-0},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{182},
  editor =	{Saxena, Nitin and Simon, Sunil},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2020.18},
  URN =		{urn:nbn:de:0030-drops-132596},
  doi =		{10.4230/LIPIcs.FSTTCS.2020.18},
  annote =	{Keywords: feedback vertex sets, hypergraphs, FPT, randomized algorithms}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2019.18
Exact and Approximate Digraph Bandwidth

Authors: Pallavi Jain, Lawqueen Kanesh, William Lochet, Saket Saurabh, and Roohani Sharma

Published in: LIPIcs, Volume 150, 39th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2019)

Abstract
In this paper, we introduce a directed variant of the classical Bandwidth problem and study it from the view-point of moderately exponential time algorithms, both exactly and approximately. Motivated by the definitions of the directed variants of the classical Cutwidth and Pathwidth problems, we define Digraph Bandwidth as follows. Given a digraph D and an ordering sigma of its vertices, the digraph bandwidth of sigma with respect to D is equal to the maximum value of sigma(v)-sigma(u) over all arcs (u,v) of D going forward along sigma (that is, when sigma(u) < sigma (v)). The Digraph Bandwidth problem takes as input a digraph D and asks to output an ordering with the minimum digraph bandwidth. The undirected Bandwidth easily reduces to Digraph Bandwidth and thus, it immediately implies that Directed Bandwidth is {NP-hard}. While an O^*(n!) time algorithm for the problem is trivial, the goal of this paper is to design algorithms for Digraph Bandwidth which have running times of the form 2^O(n). In particular, we obtain the following results. Here, n and m denote the number of vertices and arcs of the input digraph D, respectively. - Digraph Bandwidth can be solved in O^*(3^n * 2^m) time. This result implies a 2^O(n) time algorithm on sparse graphs, such as graphs of bounded average degree. - Let G be the underlying undirected graph of the input digraph. If the treewidth of G is at most t, then Digraph Bandwidth can be solved in time O^*(2^(n + (t+2) log n)). This result implies a 2^(n+O(sqrt(n) log n)) algorithm for directed planar graphs and, in general, for the class of digraphs whose underlying undirected graph excludes some fixed graph H as a minor. - Digraph Bandwidth can be solved in min{O^*(4^n * b^n), O^*(4^n * 2^(b log b log n))} time, where b denotes the optimal digraph bandwidth of D. This allow us to deduce a 2^O(n) algorithm in many cases, for example when b <= n/(log^2n). - Finally, we give a (Single) Exponential Time Approximation Scheme for Digraph Bandwidth. In particular, we show that for any fixed real epsilon > 0, we can find an ordering whose digraph bandwidth is at most (1+epsilon) times the optimal digraph bandwidth, in time O^*(4^n * (ceil[4/epsilon])^n).
Cite as

Pallavi Jain, Lawqueen Kanesh, William Lochet, Saket Saurabh, and Roohani Sharma. Exact and Approximate Digraph Bandwidth. In 39th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 150, pp. 18:1-18:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{jain_et_al:LIPIcs.FSTTCS.2019.18,
  author =	{Jain, Pallavi and Kanesh, Lawqueen and Lochet, William and Saurabh, Saket and Sharma, Roohani},
  title =	{{Exact and Approximate Digraph Bandwidth}},
  booktitle =	{39th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2019)},
  pages =	{18:1--18:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-131-3},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{150},
  editor =	{Chattopadhyay, Arkadev and Gastin, Paul},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2019.18},
  URN =		{urn:nbn:de:0030-drops-115802},
  doi =		{10.4230/LIPIcs.FSTTCS.2019.18},
  annote =	{Keywords: directed bandwidth, digraph bandwidth, approximation scheme, exact exponential algorithms}
}
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