18 Search Results for "Narayanaswamy, N. S."

Document
DOI: 10.4230/LIPIcs.IPEC.2025.26
Complexity of Local Search for CSPs Parameterized by Constraint Difference

Authors: Aditya Anand, Vincent Cohen-Addad, Tommaso D'Orsi, Anupam Gupta, Euiwoong Lee, Debmalya Panigrahi, and Sijin Peng

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

Abstract
In this paper, we study the parameterized complexity of local search, whose goal is to find a good nearby solution from the given current solution. Formally, given an optimization problem where the goal is to find the largest feasible subset S of a universe U, the new input consists of a current solution P (not necessarily feasible) as well as an ordinary input for the problem. Given the existence of a feasible solution S^*, the goal is to find a feasible solution as good as S^* in parameterized time f(k)⋅n^O(1), where k denotes the distance |PΔ S^*|. This model generalizes numerous classical parameterized optimization problems whose parameter k is the minimum number of elements removed from U to make it feasible, which corresponds to the case P = U. We apply this model to widely studied Constraint Satisfaction Problems (CSPs), where U is the set of constraints, and a subset U' of constraints is feasible if there is an assignment to the variables satisfying all constraints in U'. We give a complete characterization of the parameterized complexity of all boolean-alphabet symmetric CSPs, where the predicate’s acceptance depends on the number of true literals.
Cite as

Aditya Anand, Vincent Cohen-Addad, Tommaso D'Orsi, Anupam Gupta, Euiwoong Lee, Debmalya Panigrahi, and Sijin Peng. Complexity of Local Search for CSPs Parameterized by Constraint Difference. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 26:1-26:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{anand_et_al:LIPIcs.IPEC.2025.26,
  author =	{Anand, Aditya and Cohen-Addad, Vincent and D'Orsi, Tommaso and Gupta, Anupam and Lee, Euiwoong and Panigrahi, Debmalya and Peng, Sijin},
  title =	{{Complexity of Local Search for CSPs Parameterized by Constraint Difference}},
  booktitle =	{20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
  pages =	{26:1--26:17},
  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.2025.26},
  URN =		{urn:nbn:de:0030-drops-251586},
  doi =		{10.4230/LIPIcs.IPEC.2025.26},
  annote =	{Keywords: Constraint Satisfaction Problems, Parameterized Local Search, Optimization}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2025.48
Quadratic Kernel for Cliques or Trees Vertex Deletion

Authors: Soh Kumabe

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

Abstract
We consider Cliques or Trees Vertex Deletion, which is a hybrid of two fundamental parameterized problems: Cluster Vertex Deletion and Feedback Vertex Set. In this problem, we are given an undirected graph G and an integer k, and asked to find a vertex subset X of size at most k such that each connected component of G-X is either a clique or a tree. Jacob et al. (ISAAC, 2024) provided a kernel of O(k⁵) vertices for this problem, which was recently improved to O(k⁴) by Tsur (IPL, 2025). Our main result is a kernel of O(k²) vertices. This result closes the gap between the kernelization result for Feedback Vertex Set, which corresponds to the case where each connected component of G-X must be a tree. Although both cluster vertex deletion number and feedback vertex set number are well-studied structural parameters, little attention has been given to parameters that generalize both of them. In fact, the lowest common well-known generalization of them is clique-width, which is a highly general parameter. To fill the gap here, we initiate the study of the cliques or trees vertex deletion number as a structural parameter. We prove that Longest Cycle, which is a fundamental problem that does not admit o(n^k)-time algorithm unless ETH fails when k is the clique-width, becomes fixed-parameter tractable when parameterized by the cliques or trees vertex deletion number.
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Soh Kumabe. Quadratic Kernel for Cliques or Trees Vertex Deletion. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 48:1-48:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kumabe:LIPIcs.ISAAC.2025.48,
  author =	{Kumabe, Soh},
  title =	{{Quadratic Kernel for Cliques or Trees Vertex Deletion}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{48:1--48:15},
  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.2025.48},
  URN =		{urn:nbn:de:0030-drops-249568},
  doi =		{10.4230/LIPIcs.ISAAC.2025.48},
  annote =	{Keywords: Fixed-Parameter Tractability, Kernelization, Deletion to Scattered Graph Classes, Cluster Vertex Deletion, Feedback Vertex Set}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2025.38
Structural Parameters for Steiner Orientation

Authors: Tesshu Hanaka, Michael Lampis, Nikolaos Melissinos, Edouard Nemery, Hirotaka Ono, and Manolis Vasilakis

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

Abstract
We consider the Steiner Orientation problem, where we are given as input a mixed graph G = (V,E,A) and a set of k demand pairs (s_i,t_i), i ∈ [k]. The goal is to orient the undirected edges of G in a way that the resulting directed graph has a directed path from s_i to t_i for all i ∈ [k]. We adopt the point of view of structural parameterized complexity and investigate the complexity of Steiner Orientation for standard measures, such as treewidth. Our results indicate that Steiner Orientation is a surprisingly hard problem from this point of view. In particular, our main contributions are the following: 1) We show that Steiner Orientation is NP-complete on instances where the underlying graph has feedback vertex number 2, treewidth 2, pathwidth 3, and vertex integrity 6. 2) We present an XP algorithm parameterized by vertex cover number vc of complexity n^O(vc²). Furthermore, we show that this running time is essentially optimal by proving that a running time of n^o(vc²) would refute the ETH. 3) We consider parameterizations by the number of undirected or directed edges (|E| or |A|) and we observe that the trivial 2^|E| n^O(1)-time algorithm for the former parameter is optimal under the SETH. Complementing this, we show that the problem admits a 2^O(|A|) n^O(1)-time algorithm. In addition to the above, we consider the complexity of Steiner Orientation parameterized by tw+k (FPT), distance to clique (FPT), and vc+k (FPT with a polynomial kernel).
Cite as

Tesshu Hanaka, Michael Lampis, Nikolaos Melissinos, Edouard Nemery, Hirotaka Ono, and Manolis Vasilakis. Structural Parameters for Steiner Orientation. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 38:1-38:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{hanaka_et_al:LIPIcs.ISAAC.2025.38,
  author =	{Hanaka, Tesshu and Lampis, Michael and Melissinos, Nikolaos and Nemery, Edouard and Ono, Hirotaka and Vasilakis, Manolis},
  title =	{{Structural Parameters for Steiner Orientation}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{38:1--38:14},
  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.2025.38},
  URN =		{urn:nbn:de:0030-drops-249461},
  doi =		{10.4230/LIPIcs.ISAAC.2025.38},
  annote =	{Keywords: ETH, Steiner Orientation, Treewidth}
}
Document
DOI: 10.4230/LIPIcs.WADS.2025.35
Succinct Data Structures for Chordal Graph with Bounded Leafage or Vertex Leafage

Authors: Meng He and Kaiyu Wu

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

Abstract
We improve the recent succinct data structure result of Balakrishnan et al. for chordal graphs with bounded vertex leafage (SWAT 2024). A chordal graph is a widely studied graph class which can be characterized as the intersection graph of subtrees of a host tree, denoted as a tree representation of the chordal graph. The vertex leafage and leafage parameters of a chordal graph deal with the existence of a tree representation with a bounded number of leaves in either the subtrees representing the vertices or the host tree itself. We simplify the lower bound proof of Balakrishnan et al. which applied to only chordal graphs with bounded vertex leafage, and extend it to a lower bound proof for chordal graphs with bounded leafage as well. For both classes of graphs, the information-theoretic lower bound we (re-)obtain for k = o(n) is (k-1)nlog n - knlog k - o(knlog n) bits, where the leafage or vertex leafage of the graph is at most k = o(n). We further extend the range of the parameter k to Θ(n) as well. Then we give a succinct data structure using (k-1)nlog (n/k) + o(knlog n) bits to answer adjacent queries, which test the adjacency between pairs of vertices, in O((log k)/(log log n) + 1) time compared to the O(klog n) time of the data structure of Balakrishnan et al. For the neighborhood query which lists the neighbours of a given vertex, our query time is O((log n)/(log log n)) per neighbour compared to O(k²log n) per neighbour. We also extend the data structure ideas to obtain a succinct data structure for chordal graphs with bounded leafage k, answering an open question of Balakrishnan et al. Our succinct data structure, which uses (k-1)nlog (n/k) + o(knlog n) bits, has query time O(1) for the adjacent query and O(1) per neighbour for the neighborhood query. Using slightly more space (an additional (1+ε)nlog n bits for any ε > 0) allows distance queries, which compute the number of edges in the shortest path between two given vertices, to be answered in O(1) time as well.
Cite as

Meng He and Kaiyu Wu. Succinct Data Structures for Chordal Graph with Bounded Leafage or Vertex Leafage. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 35:1-35:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{he_et_al:LIPIcs.WADS.2025.35,
  author =	{He, Meng and Wu, Kaiyu},
  title =	{{Succinct Data Structures for Chordal Graph with Bounded Leafage or Vertex Leafage}},
  booktitle =	{19th International Symposium on Algorithms and Data Structures (WADS 2025)},
  pages =	{35:1--35:23},
  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.2025.35},
  URN =		{urn:nbn:de:0030-drops-242660},
  doi =		{10.4230/LIPIcs.WADS.2025.35},
  annote =	{Keywords: Chordal Graph, Leafage, Vertex Leafage, Succinct Data Structure}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.42
Broadcasting Under Structural Restrictions

Authors: Yudai Egami, Tatsuya Gima, Tesshu Hanaka, Yasuaki Kobayashi, Michael Lampis, Valia Mitsou, Edouard Nemery, Yota Otachi, Manolis Vasilakis, and Daniel Vaz

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

Abstract
In the Telephone Broadcast problem we are given a graph G = (V,E) with a designated source vertex s ∈ V. Our goal is to transmit a message, which is initially known only to s, to all vertices of the graph by using a process where in each round an informed vertex may transmit the message to one of its uninformed neighbors. The optimization objective is to minimize the number of rounds. Following up on several recent works, we investigate the structurally parameterized complexity of Telephone Broadcast. In particular, we first strengthen existing NP-hardness results by showing that the problem remains NP-complete on graphs of bounded tree-depth and also on cactus graphs which are one vertex deletion away from being path forests. Motivated by this (severe) hardness, we study several other parameterizations of the problem and obtain FPT algorithms parameterized by vertex integrity (generalizing a recent FPT algorithm parameterized by vertex cover by Fomin, Fraigniaud, and Golovach [TCS 2024]) and by distance to clique, as well as FPT approximation algorithms parameterized by clique-cover and cluster vertex deletion. Furthermore, we obtain structural results that relate the length of the optimal broadcast protocol of a graph G with its pathwidth and tree-depth. By presenting a substantial improvement over the best previously known bound for pathwidth (Aminian, Kamali, Seyed-Javadi, and Sumedha [ICALP 2025]) we exponentially improve the approximation ratio achievable in polynomial time on graphs of bounded pathwidth from 𝒪(4^pw) to 𝒪(pw).
Cite as

Yudai Egami, Tatsuya Gima, Tesshu Hanaka, Yasuaki Kobayashi, Michael Lampis, Valia Mitsou, Edouard Nemery, Yota Otachi, Manolis Vasilakis, and Daniel Vaz. Broadcasting Under Structural Restrictions. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 42:1-42:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{egami_et_al:LIPIcs.MFCS.2025.42,
  author =	{Egami, Yudai and Gima, Tatsuya and Hanaka, Tesshu and Kobayashi, Yasuaki and Lampis, Michael and Mitsou, Valia and Nemery, Edouard and Otachi, Yota and Vasilakis, Manolis and Vaz, Daniel},
  title =	{{Broadcasting Under Structural Restrictions}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{42:1--42:18},
  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.2025.42},
  URN =		{urn:nbn:de:0030-drops-241492},
  doi =		{10.4230/LIPIcs.MFCS.2025.42},
  annote =	{Keywords: Parameterized Complexity, Structural Graph Parameters, Telephone Broadcast}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.20
Kernelization in Almost Linear Time for Clustering into Bounded Vertex Cover Components

Authors: Sriram Bhyravarapu, Pritesh Kumar, Madhumita Kundu, Shivesh K. Roy, Sahiba, and Saket Saurabh

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

Abstract
Motivated by the growing interest in graph clustering and the framework proposed during the Dagstuhl Seminar 23331, we consider a natural specialization of this general approach (as also suggested during the seminar). The seminar introduced a broad perspective on clustering, where the goal is to partition a graph into connected components (or "clusters") that satisfy simple structural integrity constraints - not necessarily limited to cliques. In our work, we focus on the case where each cluster is required to have bounded vertex cover number. Specifically, a connected component C satisfies this condition if there exists a set S ⊆ V(C) with |S| ≤ d such that C - S is an independent set. We study this within the framework of the {Vertex Deletion to d-Vertex Cover Components} ({Vertex Deletion to d-VCC}) problem: given a graph G and an integer k, the task is to determine whether there exists a vertex set S ⊆ V(G) of size at most k such that every connected component of G - S has vertex cover number at most d. We also examine the edge-deletion variant, {Edge Deletion to d-Vertex Cover Components} ({Edge Deletion to d-VCC}), where the goal is to delete at most k edges so that each connected component of the resulting graph has vertex cover number at most d. We obtain following results. 1) {Vertex Deletion to d-VCC} admits a kernel with {𝒪}(d⁶k³) vertices and {𝒪}(d⁹k⁴) edges. 2) {Edge Deletion to d-VCC}, admits a kernel with {𝒪}(d⁴k) vertices and {𝒪}(d⁵k) edges. Both of our kernelization algorithms run in time 𝒪(1.253^d ⋅ (kd)^{𝒪(1)} ⋅ n log n). It is important to note that, unless the Exponential Time Hypothesis (ETH) fails, the dependence on d cannot be improved to 2^{o(d)}, as the case k = 0 reduces to solving the classical Vertex Cover problem, which is known to require 2^{Ω(d)} time under ETH. A key ingredient in our kernelization algorithms is a structural result about the hereditary graph class 𝒢_d, consisting of graphs in which every connected component has vertex cover number at most d. We show that 𝒢_d admits a finite obstruction set (with respect to the induced subgraph relation) of size 2^{𝒪(d²)}, where each obstruction graph has at most 3d + 2 vertices. This combinatorial result may be of independent interest.
Cite as

Sriram Bhyravarapu, Pritesh Kumar, Madhumita Kundu, Shivesh K. Roy, Sahiba, and Saket Saurabh. Kernelization in Almost Linear Time for Clustering into Bounded Vertex Cover Components. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 20:1-20:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bhyravarapu_et_al:LIPIcs.MFCS.2025.20,
  author =	{Bhyravarapu, Sriram and Kumar, Pritesh and Kundu, Madhumita and Roy, Shivesh K. and Sahiba and Saurabh, Saket},
  title =	{{Kernelization in Almost Linear Time for Clustering into Bounded Vertex Cover Components}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{20:1--20:18},
  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.2025.20},
  URN =		{urn:nbn:de:0030-drops-241276},
  doi =		{10.4230/LIPIcs.MFCS.2025.20},
  annote =	{Keywords: Parameterized complexity, Polynomial Kernels, Vertex Cover, Finite Forbidden Characterization}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.65
Parameterized Spanning Tree Congestion

Authors: Michael Lampis, Valia Mitsou, Edouard Nemery, Yota Otachi, Manolis Vasilakis, and Daniel Vaz

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

Abstract
In this paper we study the Spanning Tree Congestion problem, where we are given an undirected graph G = (V,E) and are asked to find a spanning tree T of minimum maximum congestion. Here, the congestion of an edge e ∈ T is the number of edges uv ∈ E such that the (unique) path from u to v in T traverses e. We consider this well-studied NP-hard problem from the point of view of (structural) parameterized complexity and obtain the following results: - We resolve a natural open problem by showing that Spanning Tree Congestion is not FPT parameterized by treewidth (under standard assumptions). More strongly, we present a generic reduction which applies to (almost) any parameter of the form "vertex-deletion distance to class 𝒞", thus obtaining W[1]-hardness for more restricted parameters, including tree-depth plus feedback vertex set, or incomparable to treewidth, such as twin cover. Via a slight tweak of the same reduction we also show that the problem is NP-complete on graphs of modular-width 4. - Even though it is known that Spanning Tree Congestion remains NP-hard on instances with only one vertex of unbounded degree, it is currently open whether the problem remains hard on bounded-degree graphs. We resolve this question by showing NP-hardness on graphs of maximum degree 8. - Complementing the problem’s W[1]-hardness for treewidth, we formulate an algorithm that runs in time roughly {(k+w)}^{𝒪(w)}, where k is the desired congestion and w the treewidth, improving a previous argument for parameter k+w that was based on Courcelle’s theorem. This explicit algorithm pays off in two ways: it allows us to obtain an FPT approximation scheme for parameter treewidth, that is, a (1+ε)-approximation running in time roughly {(w/ε)}^{𝒪(w)}; and it leads to an exact FPT algorithm for parameter clique-width+k via a Win/Win argument. - Finally, motivated by the problem’s hardness for most standard structural parameters, we present FPT algorithms for several more restricted cases, namely, for the parameters vertex-deletion distance to clique; vertex integrity; and feedback edge set, in the latter case also achieving a single-exponential running time dependence on the parameter.
Cite as

Michael Lampis, Valia Mitsou, Edouard Nemery, Yota Otachi, Manolis Vasilakis, and Daniel Vaz. Parameterized Spanning Tree Congestion. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 65:1-65:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{lampis_et_al:LIPIcs.MFCS.2025.65,
  author =	{Lampis, Michael and Mitsou, Valia and Nemery, Edouard and Otachi, Yota and Vasilakis, Manolis and Vaz, Daniel},
  title =	{{Parameterized Spanning Tree Congestion}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{65:1--65:20},
  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.2025.65},
  URN =		{urn:nbn:de:0030-drops-241724},
  doi =		{10.4230/LIPIcs.MFCS.2025.65},
  annote =	{Keywords: Parameterized Complexity, Treewidth, Graph Width Parameters}
}
Document
DOI: 10.4230/LIPIcs.FORC.2025.12
Infinitely Divisible Noise for Differential Privacy: Nearly Optimal Error in the High ε Regime

Authors: Charlie Harrison and Pasin Manurangsi

Published in: LIPIcs, Volume 329, 6th Symposium on Foundations of Responsible Computing (FORC 2025)

Abstract
Differential privacy (DP) can be achieved in a distributed manner, where multiple parties add independent noise such that their sum protects the overall dataset with DP. A common technique here is for each party to sample their noise from the decomposition of an infinitely divisible distribution. We analyze two mechanisms in this setting: 1) the generalized discrete Laplace (GDL) mechanism, whose distribution (which is closed under summation) follows from differences of i.i.d. negative binomial shares, and 2) the multi-scale discrete Laplace (MSDLap) mechanism, a novel mechanism following the sum of multiple i.i.d. discrete Laplace shares at different scales. For ε ≥ 1, our mechanisms can be parameterized to have O(Δ³ e^{-ε}) and O(min(Δ³ e^{-ε}, Δ² e^{-2ε/3})) MSE, respectively, where Δ denote the sensitivity; the latter bound matches known optimality results. Furthermore, the MSDLap mechanism has the optimal MSE including constants as ε → ∞. We also show a transformation from the discrete setting to the continuous setting, which allows us to transform both mechanisms to the continuous setting and thereby achieve the optimal O(Δ² e^{-2ε / 3}) MSE. To our knowledge, these are the first infinitely divisible additive noise mechanisms that achieve order-optimal MSE under pure DP for either the discrete or continuous setting, so our work shows formally there is no separation in utility when query-independent noise adding mechanisms are restricted to infinitely divisible noise. For the continuous setting, our result improves upon Pagh and Stausholm’s Arete distribution which gives an MSE of O(Δ² e^{-ε/4}) [Pagh and Stausholm, 2022]. Furthermore, we give an exact sampler tuned to efficiently implement the MSDLap mechanism, and we apply our results to improve a state of the art multi-message shuffle DP protocol from [Balle et al., 2020] in the high ε regime.
Cite as

Charlie Harrison and Pasin Manurangsi. Infinitely Divisible Noise for Differential Privacy: Nearly Optimal Error in the High ε Regime. In 6th Symposium on Foundations of Responsible Computing (FORC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 329, pp. 12:1-12:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{harrison_et_al:LIPIcs.FORC.2025.12,
  author =	{Harrison, Charlie and Manurangsi, Pasin},
  title =	{{Infinitely Divisible Noise for Differential Privacy: Nearly Optimal Error in the High \epsilon Regime}},
  booktitle =	{6th Symposium on Foundations of Responsible Computing (FORC 2025)},
  pages =	{12:1--12:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-367-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{329},
  editor =	{Bun, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FORC.2025.12},
  URN =		{urn:nbn:de:0030-drops-231396},
  doi =		{10.4230/LIPIcs.FORC.2025.12},
  annote =	{Keywords: Differential Privacy, Distributed Noise Addition}
}
Document
DOI: 10.4230/LIPIcs.SAND.2025.16
Temporal Dominating Set and Temporal Vertex Cover Under the Lense of Degree Restrictions

Authors: Anton Herrmann, Christian Komusiewicz, Nils Morawietz, and Frank Sommer

Published in: LIPIcs, Volume 330, 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025)

Abstract
We study the Temporal Dominating Set problem, in which one asks whether a temporal graph 𝒢 = (G₁,… , G_T) given as a sequence of snapshot graphs, over the same vertex set V, has a set S of temporal vertices of size at most k such that each vertex v of V is dominated by some w ∈ S in the snapshot that contains w. Additionally, we consider Temporal Partial Dominating Set, where one asks whether at least t (and not necessarily all) vertices of V can be dominated by S and a further generalization in which the solution may only contain a bounded number of temporal vertices from each snapshot. We analyze how the complexity of Temporal (Partial) Dominating Set is influenced by the maximum snapshot degree and the structure of the underlying graph, the graph with vertex set V and whose edge set is the union of all snapshot edge sets. For example, we obtain a complexity dichotomy for the maximum snapshot degree and we show that Temporal Partial Dominating Set is fixed-parameter tractable for tw+Δ, where tw and Δ denote the treewidth and the maximum degree of the underlying graph of 𝒢, respectively. We also show which of our results transfer to the well-studied Temporal Vertex Cover problem. For example, we show that Temporal Vertex Cover is also fixed-parameter tractable for tw+Δ which substantially extends the previously known polynomial-time algorithms for the case that the underlying graph is a path or cycle.
Cite as

Anton Herrmann, Christian Komusiewicz, Nils Morawietz, and Frank Sommer. Temporal Dominating Set and Temporal Vertex Cover Under the Lense of Degree Restrictions. In 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 330, pp. 16:1-16:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{herrmann_et_al:LIPIcs.SAND.2025.16,
  author =	{Herrmann, Anton and Komusiewicz, Christian and Morawietz, Nils and Sommer, Frank},
  title =	{{Temporal Dominating Set and Temporal Vertex Cover Under the Lense of Degree Restrictions}},
  booktitle =	{4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025)},
  pages =	{16:1--16:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-368-3},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{330},
  editor =	{Meeks, Kitty and Scheideler, Christian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2025.16},
  URN =		{urn:nbn:de:0030-drops-230695},
  doi =		{10.4230/LIPIcs.SAND.2025.16},
  annote =	{Keywords: NP-hard problem, FPT-algorithm, Treewidth, Color coding}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.70
Colorful Vertex Recoloring of Bipartite Graphs

Authors: Boaz Patt-Shamir, Adi Rosén, and Seeun William Umboh

Published in: LIPIcs, Volume 327, 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)

Abstract
We consider the problem of vertex recoloring: we are given n vertices with their initial coloring, and edges arrive in an online fashion. The algorithm is required to maintain a valid coloring by means of vertex recoloring, where recoloring a vertex incurs a cost. The problem abstracts a scenario of job placement in machines (possibly in the cloud), where vertices represent jobs, colors represent machines, and edges represent "anti affinity" (disengagement) constraints. Online coloring in this setting is a hard problem, and only a few cases were analyzed. One family of instances which is fairly well-understood is bipartite graphs, i.e., instances in which two colors are sufficient to satisfy all constraints. In this case it is known that the competitive ratio of vertex recoloring is Θ(log n). In this paper we propose a generalization of the problem, which allows using additional colors (possibly at a higher cost), to improve overall performance. Concretely, we analyze the simple case of bipartite graphs of bounded largest bond (a bond of a connected graph is an edge-cut that partitions the graph into two connected components). From the upper bound perspective, we propose two algorithms. One algorithm exhibits a trade-off for the uniform-cost case: given Ω(logβ) ≤ c ≤ O(log n) colors, the algorithm guarantees that its cost is at most O((log n)/c) times the optimal offline cost for two colors, where n is the number of vertices and β is the size of the largest bond of the graph. The other algorithm is designed for the case where the additional colors come at a higher cost, D > 1: given Δ additional colors, where Δ is the maximum degree in the graph, the algorithm guarantees a competitive ratio of O(log D). From the lower bounds viewpoint, we show that if the cost of the extra colors is D > 1, no algorithm (even randomized) can achieve a competitive ratio of o(log D). We also show that in the case of general bipartite graphs (i.e., of unbounded bond size), any deterministic online algorithm has competitive ratio Ω(min(D,log n)).
Cite as

Boaz Patt-Shamir, Adi Rosén, and Seeun William Umboh. Colorful Vertex Recoloring of Bipartite Graphs. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 70:1-70:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{pattshamir_et_al:LIPIcs.STACS.2025.70,
  author =	{Patt-Shamir, Boaz and Ros\'{e}n, Adi and Umboh, Seeun William},
  title =	{{Colorful Vertex Recoloring of Bipartite Graphs}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{70:1--70:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-365-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{327},
  editor =	{Beyersdorff, Olaf and Pilipczuk, Micha{\l} and Pimentel, Elaine and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2025.70},
  URN =		{urn:nbn:de:0030-drops-228955},
  doi =		{10.4230/LIPIcs.STACS.2025.70},
  annote =	{Keywords: online algorithms, competitive analysis, resource augmentation, graph coloring}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.33
Metric Dimension and Geodetic Set Parameterized by Vertex Cover

Authors: Florent Foucaud, Esther Galby, Liana Khazaliya, Shaohua Li, Fionn Mc Inerney, Roohani Sharma, and Prafullkumar Tale

Published in: LIPIcs, Volume 327, 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)

Abstract
For a graph G, a subset S ⊆ V(G) is called a resolving set of G if, for any two vertices u,v ∈ V(G), there exists a vertex w ∈ S such that d(w,u) ≠ d(w,v). The Metric Dimension problem takes as input a graph G on n vertices and a positive integer k, and asks whether there exists a resolving set of size at most k. In another metric-based graph problem, Geodetic Set, the input is a graph G and an integer k, and the objective is to determine whether there exists a subset S ⊆ V(G) of size at most k such that, for any vertex u ∈ V(G), there are two vertices s₁, s₂ ∈ S such that u lies on a shortest path from s₁ to s₂. These two classical problems are known to be intractable with respect to the natural parameter, i.e., the solution size, as well as most structural parameters, including the feedback vertex set number and pathwidth. We observe that both problems admit an FPT algorithm running in 2^𝒪(vc²) ⋅ n^𝒪(1) time, and a kernelization algorithm that outputs a kernel with 2^𝒪(vc) vertices, where vc is the vertex cover number. We prove that unless the Exponential Time Hypothesis (ETH) fails, Metric Dimension and Geodetic Set, even on graphs of bounded diameter, do not admit - an FPT algorithm running in 2^o(vc²) ⋅ n^𝒪(1) time, nor - a kernelization algorithm that does not increase the solution size and outputs a kernel with 2^o(vc) vertices. We only know of one other problem in the literature that admits such a tight algorithmic lower bound with respect to vc. Similarly, the list of known problems with exponential lower bounds on the number of vertices in kernelized instances is very short.
Cite as

Florent Foucaud, Esther Galby, Liana Khazaliya, Shaohua Li, Fionn Mc Inerney, Roohani Sharma, and Prafullkumar Tale. Metric Dimension and Geodetic Set Parameterized by Vertex Cover. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 33:1-33:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{foucaud_et_al:LIPIcs.STACS.2025.33,
  author =	{Foucaud, Florent and Galby, Esther and Khazaliya, Liana and Li, Shaohua and Mc Inerney, Fionn and Sharma, Roohani and Tale, Prafullkumar},
  title =	{{Metric Dimension and Geodetic Set Parameterized by Vertex Cover}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{33:1--33:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-365-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{327},
  editor =	{Beyersdorff, Olaf and Pilipczuk, Micha{\l} and Pimentel, Elaine and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2025.33},
  URN =		{urn:nbn:de:0030-drops-228593},
  doi =		{10.4230/LIPIcs.STACS.2025.33},
  annote =	{Keywords: Parameterized Complexity, ETH-based Lower Bounds, Kernelization, Vertex Cover, Metric Dimension, Geodetic Set}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.28
Can You Link Up With Treewidth?

Authors: Radu Curticapean, Simon Döring, Daniel Neuen, and Jiaheng Wang

Published in: LIPIcs, Volume 327, 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)

Abstract
A central result by Marx [ToC '10] constructs k-vertex graphs H of maximum degree 3 such that n^o(k/log k) time algorithms for detecting colorful H-subgraphs would refute the Exponential-Time Hypothesis (ETH). This result is widely used to obtain almost-tight conditional lower bounds for parameterized problems under ETH. Our first contribution is a new and fully self-contained proof of this result that further simplifies a recent work by Karthik et al. [SOSA 2024]. In our proof, we introduce a novel graph parameter of independent interest, the linkage capacity γ(H), and show that detecting colorful H-subgraphs in time n^o(γ(H)) refutes ETH. Then, we use a simple construction of communication networks credited to Beneš to obtain k-vertex graphs of maximum degree 3 and linkage capacity Ω(k/log k), avoiding arguments involving expander graphs, which were required in previous papers. We also show that every graph H of treewidth t has linkage capacity Ω(t/log t), thus recovering a stronger result shown by Marx [ToC '10] with a simplified proof. Additionally, we obtain new tight lower bounds on the complexity of subgraph detection for certain types of patterns by analyzing their linkage capacity: We prove that almost all k-vertex graphs of polynomial average degree Ω(k^β) for β > 0 have linkage capacity Θ(k), which implies tight lower bounds for finding such patterns H. As an application of these results, we also obtain tight lower bounds for counting small induced subgraphs having a fixed property Φ, improving bounds from, e.g., [Roth et al., FOCS 2020].
Cite as

Radu Curticapean, Simon Döring, Daniel Neuen, and Jiaheng Wang. Can You Link Up With Treewidth?. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 28:1-28:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{curticapean_et_al:LIPIcs.STACS.2025.28,
  author =	{Curticapean, Radu and D\"{o}ring, Simon and Neuen, Daniel and Wang, Jiaheng},
  title =	{{Can You Link Up With Treewidth?}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{28:1--28:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-365-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{327},
  editor =	{Beyersdorff, Olaf and Pilipczuk, Micha{\l} and Pimentel, Elaine and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2025.28},
  URN =		{urn:nbn:de:0030-drops-228534},
  doi =		{10.4230/LIPIcs.STACS.2025.28},
  annote =	{Keywords: subgraph isomorphism, constraint satisfaction problems, linkage capacity, exponential-time hypothesis, parameterized complexity, counting complexity}
}
Document
DOI: 10.4230/LIPIcs.SWAT.2024.4
Succinct Data Structure for Chordal Graphs with Bounded Vertex Leafage

Authors: Girish Balakrishnan, Sankardeep Chakraborty, N. S. Narayanaswamy, and Kunihiko Sadakane

Published in: LIPIcs, Volume 294, 19th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2024)

Abstract
Chordal graphs is a well-studied large graph class that is also a strict super-class of path graphs. Munro and Wu (ISAAC 2018) have given an (n²/4+o(n²))-bit succinct representation for n-vertex unlabeled chordal graphs. A chordal graph G = (V,E) is the intersection graph of sub-trees of a tree T. Based on this characterization, the two parameters of chordal graphs which we consider in this work are leafage, introduced by Lin, McKee and West (Discussiones Mathematicae Graph Theory 1998) and vertex leafage, introduced by Chaplick and Stacho (Discret. Appl. Math. 2014). Leafage is the minimum number of leaves in any possible tree T characterizing G. Let L(u) denote the number of leaves of the sub-tree in T corresponding to u ∈ V and k = max_{u ∈ V} L(u). The smallest k for which there exists a tree T for G is called its vertex leafage. In this work, we improve the worst-case information theoretic lower bound of Munro and Wu (ISAAC 2018) for n-vertex unlabeled chordal graphs when vertex leafage is bounded and leafage is unbounded. The class of unlabeled k-vertex leafage chordal graphs that consists of all chordal graphs with vertex leafage at most k and unbounded leafage, denoted 𝒢_k, is introduced for the first time. For k > 0 in o(n^c), c > 0, we obtain a lower bound of ((k-1)n log n -kn log k - O(log n))-bits on the size of any data structure that encodes a graph in 𝒢_k. Further, for every k-vertex leafage chordal graph G and k > 1 in o(n^c), c > 0, we present a ((k-1)n log n + o(kn log n))-bit succinct data structure, constructed using the succinct data structure for path graphs with (k-1)n vertices. Our data structure supports adjacency query in O(k log n) time and using additional 2n log n bits, an O(k² d_v log n + log² n) time neighbourhood query where d_v is degree of v ∈ V.
Cite as

Girish Balakrishnan, Sankardeep Chakraborty, N. S. Narayanaswamy, and Kunihiko Sadakane. Succinct Data Structure for Chordal Graphs with Bounded Vertex Leafage. In 19th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 294, pp. 4:1-4:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{balakrishnan_et_al:LIPIcs.SWAT.2024.4,
  author =	{Balakrishnan, Girish and Chakraborty, Sankardeep and Narayanaswamy, N. S. and Sadakane, Kunihiko},
  title =	{{Succinct Data Structure for Chordal Graphs with Bounded Vertex Leafage}},
  booktitle =	{19th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2024)},
  pages =	{4:1--4:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-318-8},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{294},
  editor =	{Bodlaender, Hans L.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2024.4},
  URN =		{urn:nbn:de:0030-drops-200446},
  doi =		{10.4230/LIPIcs.SWAT.2024.4},
  annote =	{Keywords: succinct data structure, chordal graphs, leafage, vertex leafage, path graphs}
}
Document
DOI: 10.4230/LIPIcs.STACS.2024.40
A Faster Algorithm for Vertex Cover Parameterized by Solution Size

Authors: David G. Harris and N. S. Narayanaswamy

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

Abstract
We describe a new algorithm for vertex cover with runtime O^*(1.25284^k), where k is the size of the desired solution and O^* hides polynomial factors in the input size. This improves over the previous runtime of O^*(1.2738^k) due to Chen, Kanj, & Xia (2010) standing for more than a decade. The key to our algorithm is to use a measure which simultaneously tracks k as well as the optimal value λ of the vertex cover LP relaxation. This allows us to make use of prior algorithms for Maximum Independent Set in bounded-degree graphs and Above-Guarantee Vertex Cover. The main step in the algorithm is to branch on high-degree vertices, while ensuring that both k and μ = k - λ are decreased at each step. There can be local obstructions in the graph that prevent μ from decreasing in this process; we develop a number of novel branching steps to handle these situations.
Cite as

David G. Harris and N. S. Narayanaswamy. A Faster Algorithm for Vertex Cover Parameterized by Solution Size. In 41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 289, pp. 40:1-40:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{harris_et_al:LIPIcs.STACS.2024.40,
  author =	{Harris, David G. and Narayanaswamy, N. S.},
  title =	{{A Faster Algorithm for Vertex Cover Parameterized by Solution Size}},
  booktitle =	{41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024)},
  pages =	{40:1--40:18},
  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.2024.40},
  URN =		{urn:nbn:de:0030-drops-197508},
  doi =		{10.4230/LIPIcs.STACS.2024.40},
  annote =	{Keywords: Vertex cover, FPT, Graph algorithm}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2021.32
Budgeted Dominating Sets in Uncertain Graphs

Authors: Keerti Choudhary, Avi Cohen, N. S. Narayanaswamy, David Peleg, and R. Vijayaragunathan

Published in: LIPIcs, Volume 202, 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)

Abstract
We study the Budgeted Dominating Set (BDS) problem on uncertain graphs, namely, graphs with a probability distribution p associated with the edges, such that an edge e exists in the graph with probability p(e). The input to the problem consists of a vertex-weighted uncertain graph 𝒢 = (V, E, p, ω) and an integer budget (or solution size) k, and the objective is to compute a vertex set S of size k that maximizes the expected total domination (or total weight) of vertices in the closed neighborhood of S. We refer to the problem as the Probabilistic Budgeted Dominating Set (PBDS) problem. In this article, we present the following results on the complexity of the PBDS problem. 1) We show that the PBDS problem is NP-complete even when restricted to uncertain trees of diameter at most four. This is in sharp contrast with the well-known fact that the BDS problem is solvable in polynomial time in trees. We further show that PBDS is 𝖶[1]-hard for the budget parameter k, and under the Exponential time hypothesis it cannot be solved in n^o(k) time. 2) We show that if one is willing to settle for (1-ε) approximation, then there exists a PTAS for PBDS on trees. Moreover, for the scenario of uniform edge-probabilities, the problem can be solved optimally in polynomial time. 3) We consider the parameterized complexity of the PBDS problem, and show that Uni-PBDS (where all edge probabilities are identical) is 𝖶[1]-hard for the parameter pathwidth. On the other hand, we show that it is FPT in the combined parameters of the budget k and the treewidth. 4) Finally, we extend some of our parameterized results to planar and apex-minor-free graphs. Our first hardness proof (Thm. 1) makes use of the new problem of k-Subset Σ-Π Maximization (k-SPM), which we believe is of independent interest. We prove its NP-hardness by a reduction from the well-known k-SUM problem, presenting a close relationship between the two problems.
Cite as

Keerti Choudhary, Avi Cohen, N. S. Narayanaswamy, David Peleg, and R. Vijayaragunathan. Budgeted Dominating Sets in Uncertain Graphs. In 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 202, pp. 32:1-32:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{choudhary_et_al:LIPIcs.MFCS.2021.32,
  author =	{Choudhary, Keerti and Cohen, Avi and Narayanaswamy, N. S. and Peleg, David and Vijayaragunathan, R.},
  title =	{{Budgeted Dominating Sets in Uncertain Graphs}},
  booktitle =	{46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)},
  pages =	{32:1--32:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-201-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{202},
  editor =	{Bonchi, Filippo and Puglisi, Simon J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2021.32},
  URN =		{urn:nbn:de:0030-drops-144723},
  doi =		{10.4230/LIPIcs.MFCS.2021.32},
  annote =	{Keywords: Uncertain graphs, Dominating set, NP-hard, PTAS, treewidth, planar graph}
}
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