24 Search Results for "Sridharan, Ramanujan"

Document
DOI: 10.4230/LIPIcs.SoCG.2026.49
Algorithms for Euclidean Distance Matrix Completion: Exploiting Proximity to Triviality

Authors: Fedor V. Fomin, Petr A. Golovach, M. S. Ramanujan, and Saket Saurabh

Published in: LIPIcs, Volume 367, 42nd International Symposium on Computational Geometry (SoCG 2026)

Abstract
In the d-Euclidean Distance Matrix Completion (d-EDMC) problem, one aims to determine whether a given partial matrix of pairwise distances can be extended to a full Euclidean distance matrix in d dimensions. This problem is a cornerstone of computational geometry with numerous applications. While classical work on this problem often focuses on exploiting connections to semidefinite programming typically leading to approximation algorithms, we focus on exact algorithms and propose a novel distance-from-triviality parameterization framework to obtain tractability results for d-EDMC. We identify key structural patterns in the input that capture entry density, including chordal substructures and coverability of specified entries by fully specified principal submatrices. We obtain: 1) The first fixed-parameter algorithm (FPT algorithm) for d-EDMC parameterized by d and the maximum number of unspecified entries per row/column. This is achieved through a novel compression algorithm that reduces a given instance to a submatrix on 𝒪(1) rows (for fixed values of the parameters). 2) The first FPT algorithm for d-EDMC parameterized by d and the minimum number of fully specified principal submatrices whose entries cover all specified entries of the given matrix. This result is also achieved through a compression algorithm. 3) A polynomial-time algorithm for d-EDMC when both d and the minimum fill-in of a natural graph representing the specified entries are fixed constants. This result is achieved by combining tools from distance geometry and algorithms from real algebraic geometry. Our work identifies interesting parallels between EDM completion and graph problems, with our algorithms exploiting techniques from both domains.
Cite as

Fedor V. Fomin, Petr A. Golovach, M. S. Ramanujan, and Saket Saurabh. Algorithms for Euclidean Distance Matrix Completion: Exploiting Proximity to Triviality. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 49:1-49:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{fomin_et_al:LIPIcs.SoCG.2026.49,
  author =	{Fomin, Fedor V. and Golovach, Petr A. and Ramanujan, M. S. and Saurabh, Saket},
  title =	{{Algorithms for Euclidean Distance Matrix Completion: Exploiting Proximity to Triviality}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{49:1--49:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-418-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{367},
  editor =	{Ahn, Hee-Kap and Hoffmann, Michael and Nayyeri, Amir},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.49},
  URN =		{urn:nbn:de:0030-drops-258552},
  doi =		{10.4230/LIPIcs.SoCG.2026.49},
  annote =	{Keywords: Parameterized Complexity, Euclidean Embedding, Polynomial Compression}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2025.16
Designing Compact ILPs via Fast Witness Verification

Authors: Michał Włodarczyk

Published in: LIPIcs, Volume 358, 20th International Symposium on Parameterized and Exact Computation (IPEC 2025)

Abstract
The standard formalization of preprocessing in parameterized complexity is given by kernelization. In this work, we depart from this paradigm and study a different type of preprocessing for problems without polynomial kernels, still aiming at producing instances that are easily solvable in practice. Specifically, we ask for which parameterized problems an instance (I,k) can be reduced in polynomial time to an integer linear program (ILP) with poly(k) constraints. We show that this property coincides with the parameterized complexity class WK[1], previously studied in the context of Turing kernelization lower bounds. In turn, the class WK[1] enjoys an elegant characterization in terms of witness verification protocols: a yes-instance should admit a witness of size poly(k) that can be verified in time poly(k). By combining known data structures with new ideas, we design such protocols for several problems, such as r-Way Cut, Vertex Multiway Cut, Steiner Tree, and Minimum Common String Partition, thus showing that they can be modeled by compact ILPs. We also present explicit ILP and MILP formulations for Weighted Vertex Cover on graphs with small (unweighted) vertex cover number. We believe that these results will provide a background for a systematic study of ILP-oriented preprocessing procedures for parameterized problems.
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Michał Włodarczyk. Designing Compact ILPs via Fast Witness Verification. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 16:1-16:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{wlodarczyk:LIPIcs.IPEC.2025.16,
  author =	{W{\l}odarczyk, Micha{\l}},
  title =	{{Designing Compact ILPs via Fast Witness Verification}},
  booktitle =	{20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
  pages =	{16:1--16:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-407-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{358},
  editor =	{Agrawal, Akanksha and van Leeuwen, Erik Jan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.16},
  URN =		{urn:nbn:de:0030-drops-251481},
  doi =		{10.4230/LIPIcs.IPEC.2025.16},
  annote =	{Keywords: integer programming, kernelization, nondeterminism, multiway cut}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2025.18
Bridging Treewidth and Clique-Width via Cograph-Modular-Treewidth

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

Published in: LIPIcs, Volume 358, 20th International Symposium on Parameterized and Exact Computation (IPEC 2025)

Abstract
Many classical graph problems - such as Max Cut, Chromatic Number, Edge Dominating Set, and Hamiltonian Cycle - are polynomial-time solvable on cographs, fixed-parameter tractable (FPT) when parameterized by treewidth, but W[1]-hard when parameterized by clique-width. In contrast, Graph Isomorphism is FPT parameterized by treewidth, but for clique-width it is known to be in XP; whether it is FPT or W[1]-hard is open. This reveals a sharp tractability gap between treewidth and clique-width. In this work, we propose a new structural graph parameter, 𝒞-modular-treewidth, which lies between treewidth and clique-width. The parameter leverages modular decomposition and restricts modules to induce graphs from a fixed class 𝒞 (e.g., cographs or edgeless graphs). By exploiting true and false twins - a hallmark of cograph-like structure - our parameter allows the design of efficient algorithms for several hard problems beyond the reach of treewidth-based methods. In this work, we show that 𝒞-modular-treewidth enables efficient solutions under suitable choices of 𝒞, opening a new pathway in the parameterized complexity landscape between treewidth and clique-width. In particular we show that - When parameterized by cograph-modular-treewidth, Isomorphism admits an FPT algorithm, whereas Chromatic Number remains W[1]-hard. - When parameterized by independent-modular-treewidth, Hamiltonian Cycle and Edge Dominating Set remain W[1]-hard.
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Václav Blažej, Satyabrata Jana, M. S. Ramanujan, and Peter Strulo. Bridging Treewidth and Clique-Width via Cograph-Modular-Treewidth. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 18:1-18:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{blazej_et_al:LIPIcs.IPEC.2025.18,
  author =	{Bla\v{z}ej, V\'{a}clav and Jana, Satyabrata and Ramanujan, M. S. and Strulo, Peter},
  title =	{{Bridging Treewidth and Clique-Width via Cograph-Modular-Treewidth}},
  booktitle =	{20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
  pages =	{18:1--18:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-407-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{358},
  editor =	{Agrawal, Akanksha and van Leeuwen, Erik Jan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.18},
  URN =		{urn:nbn:de:0030-drops-251507},
  doi =		{10.4230/LIPIcs.IPEC.2025.18},
  annote =	{Keywords: Treewidth, Clique-width, Cograph, FPT, W\lbrack1\rbrack-hard}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.15
Linear Layouts Revisited: Stacks, Queues, and Exact Algorithms

Authors: Thomas Depian, Simon D. Fink, Robert Ganian, and Vaishali Surianarayanan

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

Abstract
In spite of the extensive study of stack and queue layouts, many fundamental questions remain open concerning the complexity-theoretic frontiers for computing stack and queue layouts. A stack (resp. queue) layout places vertices along a line and assigns edges to pages so that no two edges on the same page are crossing (resp. nested). We provide three new algorithms which together substantially expand our understanding of these problems: 1) A fixed-parameter algorithm for computing minimum-page stack and queue layouts w.r.t. the vertex integrity of an n-vertex graph G. This result is motivated by an open question in the literature and generalizes the previous algorithms parameterizing by the vertex cover number of G. The proof relies on a newly developed Ramsey pruning technique. Vertex integrity intuitively measures the vertex deletion distance to a subgraph with only small connected components. 2) An n^𝒪(q 𝓁) algorithm for computing 𝓁-page stack and queue layouts of page width at most q. This is the first algorithm avoiding a double-exponential dependency on the parameters. The page width of a layout measures the maximum number of edges one needs to cross on any page to reach the outer face. 3) A 2^𝒪(n) algorithm for computing 1-page queue layouts. This improves upon the previously fastest n^𝒪(n) algorithm and can be seen as a counterpart to the recent subexponential algorithm for computing 2-page stack layouts [ICALP'24], but relies on an entirely different technique.
Cite as

Thomas Depian, Simon D. Fink, Robert Ganian, and Vaishali Surianarayanan. Linear Layouts Revisited: Stacks, Queues, and Exact Algorithms. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 15:1-15:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{depian_et_al:LIPIcs.ESA.2025.15,
  author =	{Depian, Thomas and Fink, Simon D. and Ganian, Robert and Surianarayanan, Vaishali},
  title =	{{Linear Layouts Revisited: Stacks, Queues, and Exact Algorithms}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{15:1--15:18},
  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.2025.15},
  URN =		{urn:nbn:de:0030-drops-244835},
  doi =		{10.4230/LIPIcs.ESA.2025.15},
  annote =	{Keywords: stack layouts, queue layouts, parameterized algorithms, vertex integrity, Ramsey theory}
}
Document
DOI: 10.4230/LIPIcs.WADS.2025.20
Routing Few Robots in a Crowded Network

Authors: Argyrios Deligkas, Eduard Eiben, Robert Ganian, Iyad Kanj, Dominik Leko, and M. S. Ramanujan

Published in: LIPIcs, Volume 349, 19th International Symposium on Algorithms and Data Structures (WADS 2025)

Abstract
In Graph Coordinated Motion Planning, we are given a graph G some of whose vertices are occupied by robots, and we are asked to route k marked robots to their destinations while avoiding collisions and without exceeding a given budget 𝓁 on the number of robot moves. We continue the recent investigation of the problem [ICALP 2024], focusing on the parameter k that captures the task of routing a small number of robots in a possibly crowded graph. We prove that the problem is W[1]-hard parameterized by 𝓁 even for k = 1, but fixed-parameter tractable parameterized by k plus the treedepth of G. We complement the latter algorithm with an NP-hardness reduction which shows that both parameters are necessary to achieve tractability.
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Argyrios Deligkas, Eduard Eiben, Robert Ganian, Iyad Kanj, Dominik Leko, and M. S. Ramanujan. Routing Few Robots in a Crowded Network. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 20:1-20:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{deligkas_et_al:LIPIcs.WADS.2025.20,
  author =	{Deligkas, Argyrios and Eiben, Eduard and Ganian, Robert and Kanj, Iyad and Leko, Dominik and Ramanujan, M. S.},
  title =	{{Routing Few Robots in a Crowded Network}},
  booktitle =	{19th International Symposium on Algorithms and Data Structures (WADS 2025)},
  pages =	{20:1--20:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-398-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{349},
  editor =	{Morin, Pat and Oh, Eunjin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.20},
  URN =		{urn:nbn:de:0030-drops-242516},
  doi =		{10.4230/LIPIcs.WADS.2025.20},
  annote =	{Keywords: graph coordinated motion planning, parameterized complexity, treedepth}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.12
All-Subsets Important Separators with Applications to Sample Sets, Balanced Separators and Vertex Sparsifiers in Directed Graphs

Authors: Aditya Anand, Euiwoong Lee, Jason Li, and Thatchaphol Saranurak

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract
Given a directed graph G with n vertices and m edges, a parameter k and two disjoint subsets S,T ⊆ V(G), we show that the number of all-subsets important separators, which is the number of A-B important vertex separators of size at most k over all A ⊆ S and B ⊆ T, is at most β(|S|, |T|, k) = 4^k binom(|S|, ≤ k) binom(|T|, ≤ 2k), where binom(x, ≤ c) = ∑_{i = 1}^c binom(x,i), and that they can be enumerated in time 𝒪(β(|S|,|T|,k)k²(m+n)). This is a generalization of the folklore result stating that the number of A-B important separators for two fixed sets A and B is at most 4^k (first implicitly shown by Chen, Liu and Lu Algorithmica '09). From this result, we obtain the following applications: 1) We give a construction for detection sets and sample sets in directed graphs, generalizing the results of Kleinberg (Internet Mathematics' 03) and Feige and Mahdian (STOC' 06) to directed graphs. 2) Via our new sample sets, we give the first FPT algorithm for finding balanced separators in directed graphs parameterized by k, the size of the separator. Our algorithm runs in time 2^{𝒪(k)} ⋅ (m + n). 3) Additionally, we show a 𝒪(√{log k}) approximation algorithm for finding balanced separators in directed graphs in polynomial time. This improves the best known approximation guarantee of 𝒪(√{log n}) and matches the known guarantee in undirected graphs by Feige, Hajiaghayi and Lee (SICOMP' 08). 4) Finally, using our algorithm for listing all-subsets important separators, we give a deterministic construction of vertex cut sparsifiers in directed graphs when we are interested in preserving min-cuts of size upto c between bipartitions of the terminal set. Our algorithm constructs a sparsifier of size 𝒪(binom(t, ≤ 3c)2^{𝒪(c)}) and runs in time 𝒪(binom(t, ≤ 3c) 2^{𝒪(c)}(m + n)), where t is the number of terminals, and the sparsifier additionally preserves the set of important separators of size at most c between bipartitions of the terminals.
Cite as

Aditya Anand, Euiwoong Lee, Jason Li, and Thatchaphol Saranurak. All-Subsets Important Separators with Applications to Sample Sets, Balanced Separators and Vertex Sparsifiers in Directed Graphs. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 12:1-12:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{anand_et_al:LIPIcs.ICALP.2025.12,
  author =	{Anand, Aditya and Lee, Euiwoong and Li, Jason and Saranurak, Thatchaphol},
  title =	{{All-Subsets Important Separators with Applications to Sample Sets, Balanced Separators and Vertex Sparsifiers in Directed Graphs}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{12:1--12:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.12},
  URN =		{urn:nbn:de:0030-drops-233892},
  doi =		{10.4230/LIPIcs.ICALP.2025.12},
  annote =	{Keywords: directed graphs, important separators, sample sets, balanced separators}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2025.15
When Distances Lie: Euclidean Embeddings in the Presence of Outliers and Distance Violations

Authors: Matthias Bentert, Fedor V. Fomin, Petr A. Golovach, M. S. Ramanujan, and Saket Saurabh

Published in: LIPIcs, Volume 332, 41st International Symposium on Computational Geometry (SoCG 2025)

Abstract
Distance geometry explores the properties of distance spaces that can be exactly represented as the pairwise Euclidean distances between points in ℝ^d (d ≥ 1), or equivalently, distance spaces that can be isometrically embedded in ℝ^d. In this work, we investigate whether a distance space can be isometrically embedded in ℝ^d after applying a limited number of modifications. Specifically, we focus on two types of modifications: outlier deletion (removing points) and distance modification (adjusting distances between points). The central problem, Euclidean Embedding Editing, asks whether an input distance space on n points can be transformed, using at most k modifications, into a space that is isometrically embeddable in ℝ^d. We present several fixed-parameter tractable (FPT) and approximation algorithms for this problem. Our first result is an algorithm that solves Euclidean Embedding Editing in time (dk)^𝒪(d+k) + n^𝒪(1). The core subroutine of this algorithm, which is of independent interest, is a polynomial-time method for compressing the input distance space into an equivalent instance of Euclidean Embedding Editing with 𝒪((dk)²) points. For the special but important case of Euclidean Embedding Editing where only outlier deletions are allowed, we improve the parameter dependence of the FPT algorithm and obtain a running time of min{(d+3)^k, 2^{d+k}} ⋅ n^𝒪(1). Additionally, we provide an FPT-approximation algorithm for this problem, which outputs a set of at most 2 ⋅ Opt outliers in time 2^d ⋅ n^{𝒪(1)}. This 2-approximation algorithm improves upon the previous (3+ε)-approximation algorithm by Sidiropoulos, Wang, and Wang [SODA '17]. Furthermore, we complement our algorithms with hardness results motivating our choice of parameterizations.
Cite as

Matthias Bentert, Fedor V. Fomin, Petr A. Golovach, M. S. Ramanujan, and Saket Saurabh. When Distances Lie: Euclidean Embeddings in the Presence of Outliers and Distance Violations. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 15:1-15:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bentert_et_al:LIPIcs.SoCG.2025.15,
  author =	{Bentert, Matthias and Fomin, Fedor V. and Golovach, Petr A. and Ramanujan, M. S. and Saurabh, Saket},
  title =	{{When Distances Lie: Euclidean Embeddings in the Presence of Outliers and Distance Violations}},
  booktitle =	{41st International Symposium on Computational Geometry (SoCG 2025)},
  pages =	{15:1--15:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-370-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{332},
  editor =	{Aichholzer, Oswin and Wang, Haitao},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2025.15},
  URN =		{urn:nbn:de:0030-drops-231672},
  doi =		{10.4230/LIPIcs.SoCG.2025.15},
  annote =	{Keywords: Parameterized Complexity, Euclidean Embedding, FPT-approximation}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2025.44
A Minor-Testing Approach for Coordinated Motion Planning with Sliding Robots

Authors: Eduard Eiben, Robert Ganian, Iyad Kanj, and M. S. Ramanujan

Published in: LIPIcs, Volume 332, 41st International Symposium on Computational Geometry (SoCG 2025)

Abstract
We study a variant of the Coordinated Motion Planning problem on undirected graphs, referred to herein as the Coordinated Sliding-Motion Planning (CSMP) problem. In this variant, we are given an undirected graph G, k robots R₁,… ,R_k positioned on distinct vertices of G, p ≤ k distinct destination vertices for robots R₁,… ,R_p, and 𝓁 ∈ ℕ. The problem is to decide if there is a serial schedule of at most 𝓁 moves (i.e., of makespan 𝓁) such that at the end of the schedule each robot with a destination reaches it, where a robot’s move is a free path (unoccupied by any robots) from its current position to an unoccupied vertex. The problem is known to be NP-hard even on full grids. It has been studied in several contexts, including coin movement and reconfiguration problems, with respect to feasibility, complexity, and approximation. Geometric variants of the problem, in which congruent geometric-shape robots (e.g., unit disk/squares) slide or translate in the Euclidean plane, have also been studied extensively. We investigate the parameterized complexity of CSMP with respect to two parameters: the number k of robots and the makespan 𝓁. As our first result, we present a fixed-parameter algorithm for CSMP parameterized by k. For our second result, we present a fixed-parameter algorithm parameterized by 𝓁 for the special case of CSMP in which only a single robot has a destination and the graph is planar. A crucial new ingredient for both of our results is that the solution admits a succinct representation as a small labeled topological minor of the input graph.
Cite as

Eduard Eiben, Robert Ganian, Iyad Kanj, and M. S. Ramanujan. A Minor-Testing Approach for Coordinated Motion Planning with Sliding Robots. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 44:1-44:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{eiben_et_al:LIPIcs.SoCG.2025.44,
  author =	{Eiben, Eduard and Ganian, Robert and Kanj, Iyad and Ramanujan, M. S.},
  title =	{{A Minor-Testing Approach for Coordinated Motion Planning with Sliding Robots}},
  booktitle =	{41st International Symposium on Computational Geometry (SoCG 2025)},
  pages =	{44:1--44:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-370-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{332},
  editor =	{Aichholzer, Oswin and Wang, Haitao},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2025.44},
  URN =		{urn:nbn:de:0030-drops-231966},
  doi =		{10.4230/LIPIcs.SoCG.2025.44},
  annote =	{Keywords: coordinated motion planning on graphs, parameterized complexity, topological minor testing, planar graphs}
}
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.2024.7
On Controlling Knockout Tournaments Without Perfect Information

Authors: Václav Blažej, Sushmita Gupta, M. S. Ramanujan, and Peter Strulo

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

Abstract
Over the last decade, extensive research has been conducted on the algorithmic aspects of designing single-elimination (SE) tournaments. Addressing natural questions of algorithmic tractability, we identify key properties of input instances that enable the tournament designer to efficiently schedule the tournament in a way that maximizes the chances of a preferred player winning. Much of the prior algorithmic work on this topic focuses on the perfect (complete and deterministic) information scenario, especially in the context of fixed-parameter algorithm design. Our contributions constitute the first fixed-parameter tractability results applicable to more general settings of SE tournament design with potential imperfect information.
Cite as

Václav Blažej, Sushmita Gupta, M. S. Ramanujan, and Peter Strulo. On Controlling Knockout Tournaments Without Perfect Information. In 19th International Symposium on Parameterized and Exact Computation (IPEC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 321, pp. 7:1-7:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{blazej_et_al:LIPIcs.IPEC.2024.7,
  author =	{Bla\v{z}ej, V\'{a}clav and Gupta, Sushmita and Ramanujan, M. S. and Strulo, Peter},
  title =	{{On Controlling Knockout Tournaments Without Perfect Information}},
  booktitle =	{19th International Symposium on Parameterized and Exact Computation (IPEC 2024)},
  pages =	{7:1--7:15},
  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.2024.7},
  URN =		{urn:nbn:de:0030-drops-222337},
  doi =		{10.4230/LIPIcs.IPEC.2024.7},
  annote =	{Keywords: Parameterized algorithms, Tournament design, Imperfect information}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.53
Parameterized Algorithms for Coordinated Motion Planning: Minimizing Energy

Authors: Argyrios Deligkas, Eduard Eiben, Robert Ganian, Iyad Kanj, and M. S. Ramanujan

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
We study the parameterized complexity of a generalization of the coordinated motion planning problem on graphs, where the goal is to route a specified subset of a given set of k robots to their destinations with the aim of minimizing the total energy (i.e., the total length traveled). We develop novel techniques to push beyond previously-established results that were restricted to solid grids. We design a fixed-parameter additive approximation algorithm for this problem parameterized by k alone. This result, which is of independent interest, allows us to prove the following two results pertaining to well-studied coordinated motion planning problems: (1) A fixed-parameter algorithm, parameterized by k, for routing a single robot to its destination while avoiding the other robots, which is related to the famous Rush-Hour Puzzle; and (2) a fixed-parameter algorithm, parameterized by k plus the treewidth of the input graph, for the standard Coordinated Motion Planning (CMP) problem in which we need to route all the k robots to their destinations. The latter of these results implies, among others, the fixed-parameter tractability of CMP parameterized by k on graphs of bounded outerplanarity, which include bounded-height subgrids. We complement the above results with a lower bound which rules out the fixed-parameter tractability for CMP when parameterized by the total energy. This contrasts the recently-obtained tractability of the problem on solid grids under the same parameterization. As our final result, we strengthen the aforementioned fixed-parameter tractability to hold not only on solid grids but all graphs of bounded local treewidth - a class including, among others, all graphs of bounded genus.
Cite as

Argyrios Deligkas, Eduard Eiben, Robert Ganian, Iyad Kanj, and M. S. Ramanujan. Parameterized Algorithms for Coordinated Motion Planning: Minimizing Energy. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 53:1-53:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{deligkas_et_al:LIPIcs.ICALP.2024.53,
  author =	{Deligkas, Argyrios and Eiben, Eduard and Ganian, Robert and Kanj, Iyad and Ramanujan, M. S.},
  title =	{{Parameterized Algorithms for Coordinated Motion Planning: Minimizing Energy}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{53:1--53:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.53},
  URN =		{urn:nbn:de:0030-drops-201968},
  doi =		{10.4230/LIPIcs.ICALP.2024.53},
  annote =	{Keywords: coordinated motion planning, multi-agent path finding, parameterized complexity}
}
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.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.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.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.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}
}
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