4 Search Results for "Banerjee, Niranka"

Document
DOI: 10.4230/LIPIcs.ISAAC.2025.29
Space-Efficient Depth-First Search via Augmented Succinct Graph Encodings

Authors: Michael Elberfeld, Frank Kammer, and Johannes Meintrup

Published in: LIPIcs, Volume 359, 36th International Symposium on Algorithms and Computation (ISAAC 2025)

Abstract
We call a graph G separable if a balanced separator can be computed for G of size O(n^ε) with ε < 1. Many real-world graphs are separable such as graphs of bounded genus, graphs of constant treewidth, and graphs excluding a fixed minor. In particular, the well-known planar graphs are separable. We present a succinct encoding of separable graphs G such that, after the encoding is computed, any number of depth-first searches (DFS) can be performed from any given start vertex, each in o(n) time and o(n) bits in the word RAM model. After the execution of a DFS, the succinct encoding of G is augmented such that the DFS tree is encoded inside the encoding while maintaining succinctness. Afterward, the encoding provides common DFS-related queries in constant time. These queries include queries such as lowest-common ancestor of two given vertices in the DFS tree or queries that output the lowpoint of a given vertex in the DFS tree. Furthermore, for planar graphs, we show that the succinct encoding can be computed in O(n) bits and expected linear time, and a compact variant can be constructed in O(n) time and bits. For other separable graph classes 𝒢 the runtime and space usage depends on the specific algorithms used to find balanced separators in graphs of 𝒢.
Cite as

Michael Elberfeld, Frank Kammer, and Johannes Meintrup. Space-Efficient Depth-First Search via Augmented Succinct Graph Encodings. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 29:1-29:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{elberfeld_et_al:LIPIcs.ISAAC.2025.29,
  author =	{Elberfeld, Michael and Kammer, Frank and Meintrup, Johannes},
  title =	{{Space-Efficient Depth-First Search via Augmented Succinct Graph Encodings}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{29:1--29:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-408-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{359},
  editor =	{Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.29},
  URN =		{urn:nbn:de:0030-drops-249379},
  doi =		{10.4230/LIPIcs.ISAAC.2025.29},
  annote =	{Keywords: Depth-First Search, Succinct, Space Efficient, Separable Graphs, Planar Graphs, Table Lookup, r-Division}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.29
The Tape Reconfiguration Problem and Its Consequences for Dominating Set Reconfiguration

Authors: Nicolas Bousquet, Quentin Deschamps, Arnaud Mary, Amer E. Mouawad, and Théo Pierron

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

Abstract
A dominating set of a graph G = (V,E) is a set of vertices D ⊆ V whose closed neighborhood is V, i.e., N[D] = V. We view a dominating set as a collection of tokens placed on the vertices of D. In the token sliding variant of the Dominating Set Reconfiguration problem (TS-DSR), we seek to transform a source dominating set into a target dominating set in G by sliding tokens along edges, and while maintaining a dominating set all along the transformation. TS-DSR is known to be PSPACE-complete even restricted to graphs of pathwidth w, for some non-explicit constant w and to be XL-complete parameterized by the size k of the solution. The first contribution of this article consists in using a novel approach to provide the first explicit constant for which the TS-DSR problem is PSPACE-complete, a question that was left open in the literature. From a parameterized complexity perspective, the token jumping variant of DSR, i.e., where tokens can jump to arbitrary vertices, is known to be FPT when parameterized by the size of the dominating sets on nowhere dense classes of graphs. But, in contrast, no non-trivial result was known about TS-DSR. We prove that DSR is actually much harder in the sliding model since it is XL-complete when restricted to bounded pathwidth graphs and even when parameterized by k plus the feedback vertex set number of the graph. This gives, for the first time, a difference of behavior between the complexity under token sliding and token jumping for some problem on graphs of bounded treewidth. All our results are obtained using a brand new method, based on the hardness of the so-called Tape Reconfiguration problem, a problem we believe to be of independent interest. We complement these hardness results with a positive result showing that DSR (parameterized by k) in the sliding model is FPT on planar graphs, also answering an open problem from the literature.
Cite as

Nicolas Bousquet, Quentin Deschamps, Arnaud Mary, Amer E. Mouawad, and Théo Pierron. The Tape Reconfiguration Problem and Its Consequences for Dominating Set Reconfiguration. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 29:1-29:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bousquet_et_al:LIPIcs.ESA.2025.29,
  author =	{Bousquet, Nicolas and Deschamps, Quentin and Mary, Arnaud and Mouawad, Amer E. and Pierron, Th\'{e}o},
  title =	{{The Tape Reconfiguration Problem and Its Consequences for Dominating Set Reconfiguration}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{29:1--29:15},
  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.2025.29},
  URN =		{urn:nbn:de:0030-drops-244974},
  doi =		{10.4230/LIPIcs.ESA.2025.29},
  annote =	{Keywords: combinatorial reconfiguration, parameterized complexity, structural graph parameters, treewidth, dominating set}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.41
Token Sliding Reconfiguration on DAGs

Authors: Jona Dirks and Alexandre Vigny

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

Abstract
Given a graph G and two independent sets of same size, the Independent Set Reconfiguration Problem under token sliding asks whether one can, in a step by step manner, transform the first independent set into the second one. In each step we must preserve the condition of independence. Further, referring to solution vertices as tokens, we are only permitted to slide a token along an edge. Until the recent work of Ito et al. [Ito et al. MFCS 2022] this problem was only considered on undirected graphs. In this work, we study reconfiguration under token sliding focusing on DAGs. We present a complete dichotomy of intractability in regard to the depth of the DAG, by proving that this problem is NP-complete for DAGs of depth 3 and W[1]-hard for depth 4 when parameterized by the number of tokens k, and that these bounds are tight. Further, we prove that it is fixed parameter tractable on DAGs parameterized by the combination of treewidth and k. We show that this result applies to undirected graphs, when the number of times a token can visit a vertex is restricted.
Cite as

Jona Dirks and Alexandre Vigny. Token Sliding Reconfiguration on DAGs. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 41:1-41:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{dirks_et_al:LIPIcs.MFCS.2025.41,
  author =	{Dirks, Jona and Vigny, Alexandre},
  title =	{{Token Sliding Reconfiguration on DAGs}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{41:1--41:17},
  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.2025.41},
  URN =		{urn:nbn:de:0030-drops-241486},
  doi =		{10.4230/LIPIcs.MFCS.2025.41},
  annote =	{Keywords: Graph theory, FPT algorithms, Reconfiguration, Independent Sets}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2020.10
Optimal Output Sensitive Fault Tolerant Cuts

Authors: Niranka Banerjee, Venkatesh Raman, and Saket Saurabh

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

Abstract
In this paper we consider two classic cut-problems, Global Min-Cut and Min k-Cut, via the lens of fault tolerant network design. In particular, given a graph G on n vertices, and a positive integer f, our objective is to compute an upper bound on the size of the sparsest subgraph H of G that preserves edge connectivity of G (denoted by λ(G)) in the case of Global Min-Cut, and λ(G,k) (denotes the minimum number of edges whose removal would partition the graph into at least k connected components) in the case of Min k-Cut, upon failure of any f edges of G. The subgraph H corresponding to Global Min-Cut and Min k-Cut is called f-FTCS and f-FT-k-CS, respectively. We obtain the following results about the sizes of f-FTCS and f-FT-k-CS. - There exists an f-FTCS with (n-1)(f+λ(G)) edges. We complement this upper bound with a matching lower bound, by constructing an infinite family of graphs where any f-FTCS must have at least ((n-λ(G)-1)(λ(G)+f-1))/2+(n-λ(G)-1)+/λ(G)(λ(G)+1))/2 edges. - There exists an f-FT-k-CS with min{(2f+λ(G,k)-(k-1))(n-1), (f+λ(G,k))(n-k)+𝓁} edges. We complement this upper bound with a lower bound, by constructing an infinite family of graphs where any f-FT-k-CS must have at least ((n-λ(G,k)-1)(λ(G,k)+f-k+1))/2)+n-λ(G,k)+k-3+((λ(G,k)-k+3)(λ(G,k)-k+2))/2 edges. Our upper bounds exploit the structural properties of k-connectivity certificates. On the other hand, for our lower bounds we construct an infinite family of graphs, such that for any graph in the family any f-FTCS (or f-FT-k-CS) must contain all its edges. We also add that our upper bounds are constructive. That is, there exist polynomial time algorithms that construct H with the aforementioned number of edges.
Cite as

Niranka Banerjee, Venkatesh Raman, and Saket Saurabh. Optimal Output Sensitive Fault Tolerant Cuts. 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. 10:1-10:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{banerjee_et_al:LIPIcs.FSTTCS.2020.10,
  author =	{Banerjee, Niranka and Raman, Venkatesh and Saurabh, Saket},
  title =	{{Optimal Output Sensitive Fault Tolerant Cuts}},
  booktitle =	{40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020)},
  pages =	{10:1--10:19},
  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.2020.10},
  URN =		{urn:nbn:de:0030-drops-132515},
  doi =		{10.4230/LIPIcs.FSTTCS.2020.10},
  annote =	{Keywords: Fault tolerant, minimum cuts, upper bound, lower bound}
}
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