19 Search Results for "Rai, Ashutosh"

Document
DOI: 10.4230/LIPIcs.FSTTCS.2025.39
Improved Approximation for Pathwidth One Vertex Deletion and Parameterized Complexity of Its Variants

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

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

Abstract
The pathwidth of a graph is a measure of how path-like the graph is. The Pathwidth One Vertex Deletion (POVD) problem asks whether, given an undirected graph G and an integer k, one can delete at most k vertices from G so that the remaining graph has pathwidth at most one. This is a natural variation of the classical Feedback vertex Set (FVS) problem, where the deletion of at most k vertices results in a graph of treewidth at most one. In this work, we investigate POVD in the realm of approximation algorithms. We first design a 3-approximation algorithm for POVD running in polynomial time. Then, using this constant factor approximation algorithm, we obtain a randomized parameterized approximation algorithm for POVD running in time 𝒪^*((h_β)^k), that improves the fastest existing running times for approximation ratios in the range (1.76147,3). Here the constant h_β depends on the approximation factor β alone and has value 2^{(3-β)}, which lies in the range (1,2.3596), when β ∈ (1.76147,3). Taking inspiration from two extensively studied problems, namely Connected FVS and Independent FVS, we investigate two variations of the POVD problem from the perspective of parameterized algorithms. These variations are the connected variant, called Connected pathwidth One Vertex Deletion (CPOVD) and the independent variant, called Independent Pathwidth One Vertex Deletion (IPOVD). While in CPOVD the subgraph G[S] induced by the vertices to be deleted needs to be connected, in IPOVD it needs to be independent. Specifically, we show the following results. - CPOVD can be solved in {𝒪}^*(14^k) time and admits no polynomial kernel unless NP ⊆ {co-NP/poly}. - IPOVD can be solved in {𝒪}^*(7^k) time, and admits a kernel of size 𝒪(k³).
Cite as

Satyabrata Jana, Soumen Mandal, Ashutosh Rai, and Saket Saurabh. Improved Approximation for Pathwidth One Vertex Deletion and Parameterized Complexity of Its Variants. In 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 360, pp. 39:1-39:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{jana_et_al:LIPIcs.FSTTCS.2025.39,
  author =	{Jana, Satyabrata and Mandal, Soumen and Rai, Ashutosh and Saurabh, Saket},
  title =	{{Improved Approximation for Pathwidth One Vertex Deletion and Parameterized Complexity of Its Variants}},
  booktitle =	{45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)},
  pages =	{39:1--39:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-406-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{360},
  editor =	{Aiswarya, C. and Mehta, Ruta and Roy, Subhajit},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2025.39},
  URN =		{urn:nbn:de:0030-drops-251192},
  doi =		{10.4230/LIPIcs.FSTTCS.2025.39},
  annote =	{Keywords: Pathwidth, Parameterized complexity, Approximation, Kernelization}
}
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.
Cite as

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.2025.11
Finding Diverse Solutions in Combinatorial Problems with a Distributive Lattice Structure

Authors: Mark de Berg, Andrés López Martínez, and Frits Spieksma

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

Abstract
We generalize the polynomial-time solvability of k-Diverse Minimum s-t Cuts (De Berg et al., ISAAC'23) to a wider class of combinatorial problems whose solution sets have a distributive lattice structure. We identify three structural conditions that, when met by a problem, ensure that a k-sized multiset of maximally-diverse solutions - measured by the sum of pairwise Hamming distances - can be found in polynomial time. We apply this framework to obtain polynomial-time algorithms for finding diverse minimum s-t cuts, diverse stable matchings, and diverse market-clearing price vectors. Moreover, we show that the framework extends to two other natural measures of diversity. Lastly, we present a simpler algorithmic framework for finding a largest set of pairwise disjoint solutions in problems that meet these structural conditions.
Cite as

Mark de Berg, Andrés López Martínez, and Frits Spieksma. Finding Diverse Solutions in Combinatorial Problems with a Distributive Lattice Structure. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 11:1-11:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{deberg_et_al:LIPIcs.ISAAC.2025.11,
  author =	{de Berg, Mark and L\'{o}pez Mart{\'\i}nez, Andr\'{e}s and Spieksma, Frits},
  title =	{{Finding Diverse Solutions in Combinatorial Problems with a Distributive Lattice Structure}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{11:1--11:19},
  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.2025.11},
  URN =		{urn:nbn:de:0030-drops-249197},
  doi =		{10.4230/LIPIcs.ISAAC.2025.11},
  annote =	{Keywords: Diversity, Lattice Theory, Submodular Function Minimization}
}
Document
DOI: 10.4230/LIPIcs.AFT.2025.35
On-Chain Decentralized Learning and Cost-Effective Inference for DeFi Attack Mitigation

Authors: Abdulrahman Alhaidari, Balaji Palanisamy, and Prashant Krishnamurthy

Published in: LIPIcs, Volume 354, 7th Conference on Advances in Financial Technologies (AFT 2025)

Abstract
Billions of dollars are lost every year in DeFi platforms by transactions exploiting business logic or accounting vulnerabilities. Existing defenses focus on static code analysis, public mempool screening, attacker contract detection, or trusted off-chain monitors, none of which prevents exploits submitted through private relays or malicious contracts that execute within the same block. We present the first decentralized, fully on-chain learning framework that: (i) performs gas-prohibitive computation on Layer-2 to reduce cost, (ii) propagates verified model updates to Layer-1, and (iii) enables gas-bounded, low-latency inference inside smart contracts. A novel Proof-of-Improvement (PoIm) protocol governs the training process and verifies each decentralized micro update as a self-verifying training transaction. Updates are accepted by PoIm only if they demonstrably improve at least one core metric (e.g., accuracy, F1-score, precision, or recall) on a public benchmark without degrading any of the other core metrics, while adversarial proposals get financially penalized through an adaptable test set for evolving threats. We develop quantization and loop-unrolling techniques that enable inference for logistic regression, SVM, MLPs, CNNs, and gated RNNs (with support for formally verified decision tree inference) within the Ethereum block gas limit, while remaining bit-exact to their off-chain counterparts, formally proven in Z3. We curate 298 unique real-world exploits (2020 - 2025) with 402 exploit transactions across eight EVM chains, collectively responsible for $3.74 B in losses. We demonstrate that on-chain ML governed by PoIm detects previously unseen attacks with over 97% attack detection accuracy and 82.0% F1. A single inference, such as one made via an external call, typically incurs zero cost. Fully on-chain inference consumes 57,603 gas (≈ $0.18) for linear models, 143,647 gas (≈ $0.49) for CNN(F2, K1), and 506,397 gas (≈ $1.77) for CNN(F8, K4) on L1 (e.g., Ethereum). Our results show that practical and continually evolving DeFi defenses can be embedded directly in protocol logic without trusted guardians, and our solution achieves highly cost-effective protection while filling a critical gap between vulnerability scanners and real-time transaction screening.
Cite as

Abdulrahman Alhaidari, Balaji Palanisamy, and Prashant Krishnamurthy. On-Chain Decentralized Learning and Cost-Effective Inference for DeFi Attack Mitigation. In 7th Conference on Advances in Financial Technologies (AFT 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 354, pp. 35:1-35:27, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{alhaidari_et_al:LIPIcs.AFT.2025.35,
  author =	{Alhaidari, Abdulrahman and Palanisamy, Balaji and Krishnamurthy, Prashant},
  title =	{{On-Chain Decentralized Learning and Cost-Effective Inference for DeFi Attack Mitigation}},
  booktitle =	{7th Conference on Advances in Financial Technologies (AFT 2025)},
  pages =	{35:1--35:27},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-400-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{354},
  editor =	{Avarikioti, Zeta and Christin, Nicolas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.AFT.2025.35},
  URN =		{urn:nbn:de:0030-drops-247548},
  doi =		{10.4230/LIPIcs.AFT.2025.35},
  annote =	{Keywords: DeFi attacks, on-chain machine learning, decentralized learning, real-time defense}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.46
Max-Distance Sparsification for Diversification and Clustering

Authors: Soh Kumabe

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

Abstract
Let 𝒟 be a set family that is the solution domain of some combinatorial problem. The max-min diversification problem on 𝒟 is the problem to select k sets from 𝒟 such that the Hamming distance between any two selected sets is at least d. FPT algorithms parameterized by k+𝓁, where 𝓁 = max_{D ∈ 𝒟}|D|, and k+d have been actively studied recently for several specific domains. This paper provides unified algorithmic frameworks to solve this problem. Specifically, for each parameterization k+𝓁 and k+d, we provide an FPT oracle algorithm for the max-min diversification problem using oracles related to 𝒟. We then demonstrate that our frameworks provide the first FPT algorithms on several new domains 𝒟, including the domain of t-linear matroid intersection, almost 2-SAT, minimum edge s,t-flows, vertex sets of s,t-mincut, vertex sets of edge bipartization, and Steiner trees. We also demonstrate that our frameworks generalize most of the existing domain-specific tractability results. Our main technical breakthrough is introducing the notion of max-distance sparsifier of 𝒟, a domain on which the max-min diversification problem is equivalent to the same problem on the original domain 𝒟. The core of our framework is to design FPT oracle algorithms that construct a constant-size max-distance sparsifier of 𝒟. Using max-distance sparsifiers, we provide FPT algorithms for the max-min and max-sum diversification problems on 𝒟, as well as k-center and k-sum-of-radii clustering problems on 𝒟, which are also natural problems in the context of diversification and have their own interests.
Cite as

Soh Kumabe. Max-Distance Sparsification for Diversification and Clustering. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 46:1-46:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kumabe:LIPIcs.ESA.2025.46,
  author =	{Kumabe, Soh},
  title =	{{Max-Distance Sparsification for Diversification and Clustering}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{46:1--46:14},
  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.2025.46},
  URN =		{urn:nbn:de:0030-drops-245146},
  doi =		{10.4230/LIPIcs.ESA.2025.46},
  annote =	{Keywords: Fixed-Parameter Tractability, Diversification, Clustering}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.43
Edge Clique Partition and Cover Beyond Independence

Authors: Fedor V. Fomin, Petr A. Golovach, Danil Sagunov, and Kirill Simonov

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

Abstract
Covering and partitioning the edges of a graph into cliques are classical problems at the intersection of combinatorial optimization and graph theory, having been studied through a range of algorithmic and complexity-theoretic lenses. Despite the well-known fixed-parameter tractability of these problems when parameterized by the total number of cliques, such a parameterization often fails to be meaningful for sparse graphs. In many real-world instances, on the other hand, the minimum number of cliques in an edge cover or partition can be very close to the size of a maximum independent set α(G). Motivated by this observation, we investigate above-α parameterizations of the edge clique cover and partition problems. Concretely, we introduce and study Edge Clique Cover Above Independent Set (ECC/α) and Edge Clique Partition Above Independent Set (ECP/α), where the goal is to cover or partition all edges of a graph using at most α(G) + k cliques, and k is the parameter. Our main results reveal a distinct complexity landscape for the two variants. We show that ECP/α is fixed-parameter tractable, whereas ECC/α is NP-complete for all k ≥ 2, yet can be solved in polynomial time for k ∈ {0,1}. These findings highlight intriguing differences between the two problems when viewed through the lens of parameterization above a natural lower bound. Finally, we demonstrate that ECC/α becomes fixed-parameter tractable when parameterized by k + ω(G), where ω(G) is the size of a maximum clique of the graph G. This result is particularly relevant for sparse graphs, in which ω is typically small. For H-minor free graphs, we design a subexponential algorithm of running time f(H)^√k ⋅ n^𝒪(1).
Cite as

Fedor V. Fomin, Petr A. Golovach, Danil Sagunov, and Kirill Simonov. Edge Clique Partition and Cover Beyond Independence. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 43:1-43:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{fomin_et_al:LIPIcs.ESA.2025.43,
  author =	{Fomin, Fedor V. and Golovach, Petr A. and Sagunov, Danil and Simonov, Kirill},
  title =	{{Edge Clique Partition and Cover Beyond Independence}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{43:1--43:16},
  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.2025.43},
  URN =		{urn:nbn:de:0030-drops-245113},
  doi =		{10.4230/LIPIcs.ESA.2025.43},
  annote =	{Keywords: edge clique partition, edge clique cover, independence number, parameterized complexity, above guarantee}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.39
Sampling with a Black Box: Faster Parameterized Approximation Algorithms for Vertex Deletion Problems

Authors: Barış Can Esmer and Ariel Kulik

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

Abstract
In this paper, we present Sampling with a Black Box, a unified framework for the design of parameterized approximation algorithms for vertex deletion problems (e.g., Vertex Cover, Feedback Vertex Set, etc.). The framework relies on two components: - A Sampling Step. A polynomial-time randomized algorithm that, given a graph G, returns a random vertex v such that the optimum of G⧵ {v} is smaller by 1 than the optimum of G, with some prescribed probability q. We show that such algorithms exist for multiple vertex deletion problems. - A Black Box algorithm which is either an exact parameterized algorithm, a polynomial-time approximation algorithm, or a parameterized-approximation algorithm. The framework combines these two components together. The sampling step is applied iteratively to remove vertices from the input graph, and then the solution is extended using the black box algorithm. The process is repeated sufficiently many times so that the target approximation ratio is attained with a constant probability. We use the technique to derive parameterized approximation algorithms for several vertex deletion problems, including Feedback Vertex Set, d-Hitting Set and 𝓁-Path Vertex Cover. In particular, for every approximation ratio 1 < β < 2, we attain a parameterized β-approximation for Feedback Vertex Set, which is faster than the parameterized β-approximation of [Jana, Lokshtanov, Mandal, Rai and Saurabh, MFCS 23']. Furthermore, our algorithms are always faster than the algorithms attained using Fidelity Preserving Transformations [Fellows, Kulik, Rosamond, and Shachnai, JCSS 18'].
Cite as

Barış Can Esmer and Ariel Kulik. Sampling with a Black Box: Faster Parameterized Approximation Algorithms for Vertex Deletion Problems. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 39:1-39:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{canesmer_et_al:LIPIcs.ICALP.2025.39,
  author =	{Can Esmer, Bar{\i}\c{s} and Kulik, Ariel},
  title =	{{Sampling with a Black Box: Faster Parameterized Approximation Algorithms for Vertex Deletion Problems}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{39:1--39:20},
  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.2025.39},
  URN =		{urn:nbn:de:0030-drops-234165},
  doi =		{10.4230/LIPIcs.ICALP.2025.39},
  annote =	{Keywords: Parameterized Approximation Algorithms, Random Sampling}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.52
Polynomial Kernel and Incompressibility for Prison-Free Edge Deletion and Completion

Authors: Séhane Bel Houari-Durand, Eduard Eiben, and Magnus Wahlström

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

Abstract
Given a graph G and an integer k, the H-free Edge Deletion problem asks whether there exists a set of at most k edges of G whose deletion makes G free of induced copies of H. Significant attention has been given to the kernelizability aspects of this problem - i.e., for which graphs H does the problem admit an "efficient preprocessing" procedure, known as a polynomial kernelization, where an instance I of the problem with parameter k is reduced to an equivalent instance I' whose size and parameter value are bounded polynomially in k? Although such routines are known for many graphs H where the class of H-free graphs has significant restricted structure, it is also clear that for most graphs H the problem is incompressible, i.e., admits no polynomial kernelization parameterized by k unless the polynomial hierarchy collapses. These results led Marx and Sandeep to the conjecture that H-free Edge Deletion is incompressible for any graph H with at least five vertices, unless H is complete or has at most one edge (JCSS 2022). This conjecture was reduced to the incompressibility of H-free Edge Deletion for a finite list of graphs H. We consider one of these graphs, which we dub the prison, and show that Prison-Free Edge Deletion has a polynomial kernel, refuting the conjecture. On the other hand, the same problem for the complement of the prison is incompressible.
Cite as

Séhane Bel Houari-Durand, Eduard Eiben, and Magnus Wahlström. Polynomial Kernel and Incompressibility for Prison-Free Edge Deletion and Completion. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 52:1-52:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{houaridurand_et_al:LIPIcs.STACS.2025.52,
  author =	{Houari-Durand, S\'{e}hane Bel and Eiben, Eduard and Wahlstr\"{o}m, Magnus},
  title =	{{Polynomial Kernel and Incompressibility for Prison-Free Edge Deletion and Completion}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{52:1--52:17},
  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.2025.52},
  URN =		{urn:nbn:de:0030-drops-228770},
  doi =		{10.4230/LIPIcs.STACS.2025.52},
  annote =	{Keywords: Graph modification problems, parameterized complexity, polynomial kernelization}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2024.50
On the Parameterized Complexity of Diverse SAT

Authors: Neeldhara Misra, Harshil Mittal, and Ashutosh Rai

Published in: LIPIcs, Volume 322, 35th International Symposium on Algorithms and Computation (ISAAC 2024)

Abstract
We study the Boolean Satisfiability problem (SAT) in the framework of diversity, where one asks for multiple solutions that are mutually far apart (i.e., sufficiently dissimilar from each other) for a suitable notion of distance/dissimilarity between solutions. Interpreting assignments as bit vectors, we take their Hamming distance to quantify dissimilarity, and we focus on the problem of finding two solutions. Specifically, we define the problem Max Differ SAT (resp. Exact Differ SAT) as follows: Given a Boolean formula ϕ on n variables, decide whether ϕ has two satisfying assignments that differ on at least (resp. exactly) d variables. We study the classical and parameterized (in parameters d and n-d) complexities of Max Differ SAT and Exact Differ SAT, when restricted to some classes of formulas on which SAT is known to be polynomial-time solvable. In particular, we consider affine formulas, Krom formulas (i.e., 2-CNF formulas) and hitting formulas. For affine formulas, we show the following: Both problems are polynomial-time solvable when each equation has at most two variables. Exact Differ SAT is NP-hard, even when each equation has at most three variables and each variable appears in at most four equations. Also, Max Differ SAT is NP-hard, even when each equation has at most four variables. Both problems are 𝖶[1]-hard in the parameter n-d. In contrast, when parameterized by d, Exact Differ SAT is 𝖶[1]-hard, but Max Differ SAT admits a single-exponential FPT algorithm and a polynomial-kernel. For Krom formulas, we show the following: Both problems are polynomial-time solvable when each variable appears in at most two clauses. Also, both problems are 𝖶[1]-hard in the parameter d (and therefore, it turns out, also NP-hard), even on monotone inputs (i.e., formulas with no negative literals). Finally, for hitting formulas, we show that both problems can be solved in polynomial-time.
Cite as

Neeldhara Misra, Harshil Mittal, and Ashutosh Rai. On the Parameterized Complexity of Diverse SAT. In 35th International Symposium on Algorithms and Computation (ISAAC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 322, pp. 50:1-50:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{misra_et_al:LIPIcs.ISAAC.2024.50,
  author =	{Misra, Neeldhara and Mittal, Harshil and Rai, Ashutosh},
  title =	{{On the Parameterized Complexity of Diverse SAT}},
  booktitle =	{35th International Symposium on Algorithms and Computation (ISAAC 2024)},
  pages =	{50:1--50:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-354-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{322},
  editor =	{Mestre, Juli\'{a}n and Wirth, Anthony},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2024.50},
  URN =		{urn:nbn:de:0030-drops-221773},
  doi =		{10.4230/LIPIcs.ISAAC.2024.50},
  annote =	{Keywords: Diverse solutions, Affine formulas, 2-CNF formulas, Hitting formulas}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2023.56
Parameterized Approximation Scheme for Feedback Vertex Set

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

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

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

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

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@InProceedings{jana_et_al:LIPIcs.MFCS.2023.56,
  author =	{Jana, Satyabrata and Lokshtanov, Daniel and Mandal, Soumen and Rai, Ashutosh and Saurabh, Saket},
  title =	{{Parameterized Approximation Scheme for Feedback Vertex Set}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{56:1--56:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.56},
  URN =		{urn:nbn:de:0030-drops-185902},
  doi =		{10.4230/LIPIcs.MFCS.2023.56},
  annote =	{Keywords: Feedback Vertex Set, Parameterized Approximation}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2022.88
Parameterized Complexity of Untangling Knots

Authors: Clément Legrand-Duchesne, Ashutosh Rai, and Martin Tancer

Published in: LIPIcs, Volume 229, 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)

Abstract
Deciding whether a diagram of a knot can be untangled with a given number of moves (as a part of the input) is known to be NP-complete. In this paper we determine the parameterized complexity of this problem with respect to a natural parameter called defect. Roughly speaking, it measures the efficiency of the moves used in the shortest untangling sequence of Reidemeister moves. We show that the II^- moves in a shortest untangling sequence can be essentially performed greedily. Using that, we show that this problem belongs to W[P] when parameterized by the defect. We also show that this problem is W[P]-hard by a reduction from Minimum axiom set.
Cite as

Clément Legrand-Duchesne, Ashutosh Rai, and Martin Tancer. Parameterized Complexity of Untangling Knots. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 88:1-88:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{legrandduchesne_et_al:LIPIcs.ICALP.2022.88,
  author =	{Legrand-Duchesne, Cl\'{e}ment and Rai, Ashutosh and Tancer, Martin},
  title =	{{Parameterized Complexity of Untangling Knots}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{88:1--88:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-235-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{229},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.88},
  URN =		{urn:nbn:de:0030-drops-164296},
  doi =		{10.4230/LIPIcs.ICALP.2022.88},
  annote =	{Keywords: unknot recognition, parameterized complexity, Reidemeister moves, W\lbrackP\rbrack-complete}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2021.18
On Extended Formulations For Parameterized Steiner Trees

Authors: Andreas Emil Feldmann and Ashutosh Rai

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

Abstract
We present a novel linear program (LP) for the Steiner Tree problem, where a set of terminal vertices needs to be connected by a minimum weight tree in a graph G = (V,E) with non-negative edge weights. This well-studied problem is NP-hard and therefore does not have a compact extended formulation (describing the convex hull of all Steiner trees) of polynomial size, unless P=NP. On the other hand, Steiner Tree is fixed-parameter tractable (FPT) when parameterized by the number k of terminals, and can be solved in O(3^k|V|+2^k|V|²) time via the Dreyfus-Wagner algorithm. A natural question thus is whether the Steiner Tree problem admits an extended formulation of comparable size. We first answer this in the negative by proving a lower bound on the extension complexity of the Steiner Tree polytope, which, for some constant c > 0, implies that no extended formulation of size f(k)2^{cn} exists for any function f. However, we are able to circumvent this lower bound due to the fact that the edge weights are non-negative: we prove that Steiner Tree admits an integral LP with O(3^k|E|) variables and constraints. The size of our LP matches the runtime of the Dreyfus-Wagner algorithm, and our poof gives a polyhedral perspective on this classic algorithm. Our proof is simple, and additionally improves on a previous result by Siebert et al. [2018], who gave an integral LP of size O((2k/e)^k)|V|^{O(1)}.
Cite as

Andreas Emil Feldmann and Ashutosh Rai. On Extended Formulations For Parameterized Steiner Trees. In 16th International Symposium on Parameterized and Exact Computation (IPEC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 214, pp. 18:1-18:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{feldmann_et_al:LIPIcs.IPEC.2021.18,
  author =	{Feldmann, Andreas Emil and Rai, Ashutosh},
  title =	{{On Extended Formulations For Parameterized Steiner Trees}},
  booktitle =	{16th International Symposium on Parameterized and Exact Computation (IPEC 2021)},
  pages =	{18:1--18:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-216-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{214},
  editor =	{Golovach, Petr A. and Zehavi, Meirav},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2021.18},
  URN =		{urn:nbn:de:0030-drops-154010},
  doi =		{10.4230/LIPIcs.IPEC.2021.18},
  annote =	{Keywords: Steiner trees, integral linear program, extension complexity, fixed-parameter tractability}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2020.17
Fixed-Parameter Tractability of the Weighted Edge Clique Partition Problem

Authors: Andreas Emil Feldmann, Davis Issac, and Ashutosh Rai

Published in: LIPIcs, Volume 180, 15th International Symposium on Parameterized and Exact Computation (IPEC 2020)

Abstract
We develop an FPT algorithm and a compression for the Weighted Edge Clique Partition (WECP) problem, where a graph with n vertices and integer edge weights is given together with an integer k, and the aim is to find k cliques, such that every edge appears in exactly as many cliques as its weight. The problem has been previously only studied in the unweighted version called Edge Clique Partition (ECP), where the edges need to be partitioned into k cliques. It was shown that ECP admits a kernel with k² vertices [Mujuni and Rosamond, 2008], but this kernel does not extend to WECP. The previously fastest algorithm known for ECP has a runtime of 2^𝒪(k²)n^O(1) [Issac, 2019]. For WECP we develop a compression (to a slightly more general problem) with 4^k vertices, and an algorithm with runtime 2^𝒪(k^(3/2)w^(1/2)log(k/w))n^O(1), where w is the maximum edge weight. The latter in particular improves the runtime for ECP to 2^𝒪(k^(3/2)log k)n^O(1).
Cite as

Andreas Emil Feldmann, Davis Issac, and Ashutosh Rai. Fixed-Parameter Tractability of the Weighted Edge Clique Partition Problem. In 15th International Symposium on Parameterized and Exact Computation (IPEC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 180, pp. 17:1-17:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{feldmann_et_al:LIPIcs.IPEC.2020.17,
  author =	{Feldmann, Andreas Emil and Issac, Davis and Rai, Ashutosh},
  title =	{{Fixed-Parameter Tractability of the Weighted Edge Clique Partition Problem}},
  booktitle =	{15th International Symposium on Parameterized and Exact Computation (IPEC 2020)},
  pages =	{17:1--17:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-172-6},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{180},
  editor =	{Cao, Yixin and Pilipczuk, Marcin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2020.17},
  URN =		{urn:nbn:de:0030-drops-133206},
  doi =		{10.4230/LIPIcs.IPEC.2020.17},
  annote =	{Keywords: Edge Clique Partition, fixed-parameter tractability, kernelization}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2020.70
Quick Separation in Chordal and Split Graphs

Authors: Pranabendu Misra, Fahad Panolan, Ashutosh Rai, Saket Saurabh, and Roohani Sharma

Published in: LIPIcs, Volume 170, 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)

Abstract
In this paper we study two classical cut problems, namely Multicut and Multiway Cut on chordal graphs and split graphs. In the Multicut problem, the input is a graph G, a collection of 𝓁 vertex pairs (s_i, t_i), i ∈ [𝓁], and a positive integer k and the goal is to decide if there exists a vertex subset S ⊆ V(G)⧵ {s_i,t_i : i ∈ [𝓁]} of size at most k such that for every vertex pair (s_i,t_i), s_i and t_i are in two different connected components of G-S. In Unrestricted Multicut, the solution S can possibly pick the vertices in the vertex pairs {(s_i,t_i): i ∈ [𝓁]}. An important special case of the Multicut problem is the Multiway Cut problem, where instead of vertex pairs, we are given a set T of terminal vertices, and the goal is to separate every pair of distinct vertices in T× T. The fixed parameter tractability (FPT) of these problems was a long-standing open problem and has been resolved fairly recently. Multicut and Multiway Cut now admit algorithms with running times 2^{{𝒪}(k³)}n^{{𝒪}(1)} and 2^k n^{{𝒪}(1)}, respectively. However, the kernelization complexity of both these problems is not fully resolved: while Multicut cannot admit a polynomial kernel under reasonable complexity assumptions, it is a well known open problem to construct a polynomial kernel for Multiway Cut. Towards designing faster FPT algorithms and polynomial kernels for the above mentioned problems, we study them on chordal and split graphs. In particular we obtain the following results. 1) Multicut on chordal graphs admits a polynomial kernel with {𝒪}(k³ 𝓁⁷) vertices. Multiway Cut on chordal graphs admits a polynomial kernel with {𝒪}(k^{13}) vertices. 2) Multicut on chordal graphs can be solved in time min {𝒪(2^{k} ⋅ (k³+𝓁) ⋅ (n+m)), 2^{𝒪(𝓁 log k)} ⋅ (n+m) + 𝓁 (n+m)}. Hence Multicut on chordal graphs parameterized by the number of terminals is in XP. 3) Multicut on split graphs can be solved in time min {𝒪(1.2738^k + kn+𝓁(n+m), 𝒪(2^{𝓁} ⋅ 𝓁 ⋅ (n+m))}. Unrestricted Multicut on split graphs can be solved in time 𝒪(4^{𝓁}⋅ 𝓁 ⋅ (n+m)).
Cite as

Pranabendu Misra, Fahad Panolan, Ashutosh Rai, Saket Saurabh, and Roohani Sharma. Quick Separation in Chordal and Split Graphs. In 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 170, pp. 70:1-70:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{misra_et_al:LIPIcs.MFCS.2020.70,
  author =	{Misra, Pranabendu and Panolan, Fahad and Rai, Ashutosh and Saurabh, Saket and Sharma, Roohani},
  title =	{{Quick Separation in Chordal and Split Graphs}},
  booktitle =	{45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)},
  pages =	{70:1--70:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-159-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{170},
  editor =	{Esparza, Javier and Kr\'{a}l', Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2020.70},
  URN =		{urn:nbn:de:0030-drops-127391},
  doi =		{10.4230/LIPIcs.MFCS.2020.70},
  annote =	{Keywords: chordal graphs, multicut, multiway cut, FPT, kernel}
}
Document
DOI: 10.4230/LIPIcs.ESA.2018.10
A Polynomial Kernel for Diamond-Free Editing

Authors: Yixin Cao, Ashutosh Rai, R. B. Sandeep, and Junjie Ye

Published in: LIPIcs, Volume 112, 26th Annual European Symposium on Algorithms (ESA 2018)

Abstract
Given a fixed graph H, the H-free editing problem asks whether we can edit at most k edges to make a graph contain no induced copy of H. We obtain a polynomial kernel for this problem when H is a diamond. The incompressibility dichotomy for H being a 3-connected graph and the classical complexity dichotomy suggest that except for H being a complete/empty graph, H-free editing problems admit polynomial kernels only for a few small graphs H. Therefore, we believe that our result is an essential step toward a complete dichotomy on the compressibility of H-free editing. Additionally, we give a cubic-vertex kernel for the diamond-free edge deletion problem, which is far simpler than the previous kernel of the same size for the problem.
Cite as

Yixin Cao, Ashutosh Rai, R. B. Sandeep, and Junjie Ye. A Polynomial Kernel for Diamond-Free Editing. In 26th Annual European Symposium on Algorithms (ESA 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 112, pp. 10:1-10:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{cao_et_al:LIPIcs.ESA.2018.10,
  author =	{Cao, Yixin and Rai, Ashutosh and Sandeep, R. B. and Ye, Junjie},
  title =	{{A Polynomial Kernel for Diamond-Free Editing}},
  booktitle =	{26th Annual European Symposium on Algorithms (ESA 2018)},
  pages =	{10:1--10:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-081-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{112},
  editor =	{Azar, Yossi and Bast, Hannah 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.2018.10},
  URN =		{urn:nbn:de:0030-drops-94732},
  doi =		{10.4230/LIPIcs.ESA.2018.10},
  annote =	{Keywords: Kernelization, Diamond-free, H-free editing, Graph modification problem}
}
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