9 Search Results for "Lin, Bingkai"

Document
DOI: 10.4230/LIPIcs.ESA.2024.93
Parameterized Complexity of MinCSP over the Point Algebra

Authors: George Osipov, Marcin Pilipczuk, and Magnus Wahlström

Published in: LIPIcs, Volume 308, 32nd Annual European Symposium on Algorithms (ESA 2024)

Abstract
The input in the Minimum-Cost Constraint Satisfaction Problem (MinCSP) over the Point Algebra contains a set of variables, a collection of constraints of the form x < y, x = y, x ≤ y and x ≠ y, and a budget k. The goal is to check whether it is possible to assign rational values to the variables while breaking constraints of total cost at most k. This problem generalizes several prominent graph separation and transversal problems: - MinCSP({<}) is equivalent to Directed Feedback Arc Set, - MinCSP({< , ≤}) is equivalent to Directed Subset Feedback Arc Set, - MinCSP({= ,≠}) is equivalent to Edge Multicut, and - MinCSP({≤ ,≠}) is equivalent to Directed Symmetric Multicut. Apart from trivial cases, MinCSP({Γ}) for Γ ⊆ {< , = , ≤ ,≠} is NP-hard even to approximate within any constant factor under the Unique Games Conjecture. Hence, we study parameterized complexity of this problem under a natural parameterization by the solution cost k. We obtain a complete classification: if Γ ⊆ {< , = , ≤ ,≠} contains both ≤ and ≠, then MinCSP({Γ}) is W[1]-hard, otherwise it is fixed-parameter tractable. For the positive cases, we solve MinCSP({< , = ,≠}), generalizing the FPT results for Directed Feedback Arc Set and Edge Multicut as well as their weighted versions. Our algorithm works by reducing the problem into a Boolean MinCSP, which is in turn solved by flow augmentation. For the lower bounds, we prove that Directed Symmetric Multicut is W[1]-hard, solving an open problem.
Cite as

George Osipov, Marcin Pilipczuk, and Magnus Wahlström. Parameterized Complexity of MinCSP over the Point Algebra. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 93:1-93:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{osipov_et_al:LIPIcs.ESA.2024.93,
  author =	{Osipov, George and Pilipczuk, Marcin and Wahlstr\"{o}m, Magnus},
  title =	{{Parameterized Complexity of MinCSP over the Point Algebra}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{93:1--93:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-338-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{308},
  editor =	{Chan, Timothy and Fischer, Johannes and Iacono, John 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.2024.93},
  URN =		{urn:nbn:de:0030-drops-211640},
  doi =		{10.4230/LIPIcs.ESA.2024.93},
  annote =	{Keywords: parameterized complexity, constraint satisfaction, point algebra, multicut, feedback arc set}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2024.38
Approximating the Number of Relevant Variables in a Parity Implies Proper Learning

Authors: Nader H. Bshouty and George Haddad

Published in: LIPIcs, Volume 317, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)

Abstract
Consider the model where we can access a parity function through random uniform labeled examples in the presence of random classification noise. In this paper, we show that approximating the number of relevant variables in the parity function is as hard as properly learning parities. More specifically, let γ:ℝ^+ → ℝ^+, where γ(x) ≥ x, be any strictly increasing function. In our first result, we show that from any polynomial-time algorithm that returns a γ-approximation, D (i.e., γ^{-1}(d(f)) ≤ D ≤ γ(d(f))), of the number of relevant variables d(f) for any parity f, we can, in polynomial time, construct a solution to the long-standing open problem of polynomial-time learning k(n)-sparse parities (parities with k(n) ≤ n relevant variables), where k(n) = ω_n(1). In our second result, we show that from any T(n)-time algorithm that, for any parity f, returns a γ-approximation of the number of relevant variables d(f) of f, we can, in polynomial time, construct a poly(Γ(n))T(Γ(n)²)-time algorithm that properly learns parities, where Γ(x) = γ(γ(x)). If T(Γ(n)²) = exp({o(n/log n)}), this would resolve another long-standing open problem of properly learning parities in the presence of random classification noise in time exp(o(n/log n)).
Cite as

Nader H. Bshouty and George Haddad. Approximating the Number of Relevant Variables in a Parity Implies Proper Learning. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 317, pp. 38:1-38:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{bshouty_et_al:LIPIcs.APPROX/RANDOM.2024.38,
  author =	{Bshouty, Nader H. and Haddad, George},
  title =	{{Approximating the Number of Relevant Variables in a Parity Implies Proper Learning}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)},
  pages =	{38:1--38:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-348-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{317},
  editor =	{Kumar, Amit and Ron-Zewi, Noga},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2024.38},
  URN =		{urn:nbn:de:0030-drops-210316},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2024.38},
  annote =	{Keywords: PAC Learning, Random Classification Noise, Uniform Distribution, Parity, Sparcity Approximation}
}
Document
DOI: 10.4230/LIPIcs.CCC.2024.27
Baby PIH: Parameterized Inapproximability of Min CSP

Authors: Venkatesan Guruswami, Xuandi Ren, and Sai Sandeep

Published in: LIPIcs, Volume 300, 39th Computational Complexity Conference (CCC 2024)

Abstract
The Parameterized Inapproximability Hypothesis (PIH) is the analog of the PCP theorem in the world of parameterized complexity. It asserts that no FPT algorithm can distinguish a satisfiable 2CSP instance from one which is only (1-ε)-satisfiable (where the parameter is the number of variables) for some constant 0 < ε < 1. We consider a minimization version of CSPs (Min-CSP), where one may assign r values to each variable, and the goal is to ensure that every constraint is satisfied by some choice among the r × r pairs of values assigned to its variables (call such a CSP instance r-list-satisfiable). We prove the following strong parameterized inapproximability for Min CSP: For every r ≥ 1, it is W[1]-hard to tell if a 2CSP instance is satisfiable or is not even r-list-satisfiable. We refer to this statement as "Baby PIH", following the recently proved Baby PCP Theorem (Barto and Kozik, 2021). Our proof adapts the combinatorial arguments underlying the Baby PCP theorem, overcoming some basic obstacles that arise in the parameterized setting. Furthermore, our reduction runs in time polynomially bounded in both the number of variables and the alphabet size, and thus implies the Baby PCP theorem as well.
Cite as

Venkatesan Guruswami, Xuandi Ren, and Sai Sandeep. Baby PIH: Parameterized Inapproximability of Min CSP. In 39th Computational Complexity Conference (CCC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 300, pp. 27:1-27:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{guruswami_et_al:LIPIcs.CCC.2024.27,
  author =	{Guruswami, Venkatesan and Ren, Xuandi and Sandeep, Sai},
  title =	{{Baby PIH: Parameterized Inapproximability of Min CSP}},
  booktitle =	{39th Computational Complexity Conference (CCC 2024)},
  pages =	{27:1--27:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-331-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{300},
  editor =	{Santhanam, Rahul},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2024.27},
  URN =		{urn:nbn:de:0030-drops-204237},
  doi =		{10.4230/LIPIcs.CCC.2024.27},
  annote =	{Keywords: Parameterized Inapproximability Hypothesis, Constraint Satisfaction Problems}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.51
Computing Tree Decompositions with Small Independence Number

Authors: Clément Dallard, Fedor V. Fomin, Petr A. Golovach, Tuukka Korhonen, and Martin Milanič

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

Abstract
The independence number of a tree decomposition is the maximum of the independence numbers of the subgraphs induced by its bags. The tree-independence number of a graph is the minimum independence number of a tree decomposition of it. Several NP-hard graph problems, like maximum weight independent set, can be solved in time n^𝒪(k) if the input n-vertex graph is given together with a tree decomposition of independence number k. Yolov in [SODA 2018] gave an algorithm that given an n-vertex graph G and an integer k, in time n^𝒪(k³) either constructs a tree decomposition of G whose independence number is 𝒪(k³) or correctly reports that the tree-independence number of G is larger than k. In this paper, we first give an algorithm for computing the tree-independence number with a better approximation ratio and running time and then prove that our algorithm is, in some sense, the best one can hope for. More precisely, our algorithm runs in time 2^𝒪(k²) n^𝒪(k) and either outputs a tree decomposition of G with independence number at most 8k, or determines that the tree-independence number of G is larger than k. This implies 2^𝒪(k²) n^𝒪(k)-time algorithms for various problems, like maximum weight independent set, parameterized by the tree-independence number k without needing the decomposition as an input. Assuming Gap-ETH, an n^Ω(k) factor in the running time is unavoidable for any approximation algorithm for the tree-independence number. Our second result is that the exact computation of the tree-independence number is para-NP-hard: We show that for every constant k ≥ 4 it is NP-hard to decide if a given graph has the tree-independence number at most k.
Cite as

Clément Dallard, Fedor V. Fomin, Petr A. Golovach, Tuukka Korhonen, and Martin Milanič. Computing Tree Decompositions with Small Independence Number. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 51:1-51:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{dallard_et_al:LIPIcs.ICALP.2024.51,
  author =	{Dallard, Cl\'{e}ment and Fomin, Fedor V. and Golovach, Petr A. and Korhonen, Tuukka and Milani\v{c}, Martin},
  title =	{{Computing Tree Decompositions with Small Independence Number}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{51:1--51:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.51},
  URN =		{urn:nbn:de:0030-drops-201945},
  doi =		{10.4230/LIPIcs.ICALP.2024.51},
  annote =	{Keywords: tree-independence number, approximation, parameterized algorithms}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.107
Improved Lower Bounds for Approximating Parameterized Nearest Codeword and Related Problems Under ETH

Authors: Shuangle Li, Bingkai Lin, and Yuwei Liu

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

Abstract
In this paper we present a new gap-creating randomized self-reduction for the parameterized Maximum Likelihood Decoding problem over 𝔽_p (k-MLD_p). The reduction takes a k-MLD_p instance with k⋅ n d-dimensional vectors as input, runs in O(d2^{O(k)}n^{1.01}) time for some computable function f, outputs a (3/2-ε)-Gap-k'-MLD_p instance for any ε > 0, where k' = O(k²log k). Using this reduction, we show that assuming the randomized Exponential Time Hypothesis (ETH), no algorithms can approximate k-MLD_p (and therefore its dual problem k-NCP_p) within factor (3/2-ε) in f(k)⋅ n^{o(√{k/log k})} time for any ε > 0. We then use reduction by Bhattacharyya, Ghoshal, Karthik and Manurangsi (ICALP 2018) to amplify the (3/2-ε)-gap to any constant. As a result, we show that assuming ETH, no algorithms can approximate k-NCP_p and k-MDP_p within γ-factor in f(k)⋅ n^{o(k^{ε_γ})} time for some constant ε_γ > 0. Combining with the gap-preserving reduction by Bennett, Cheraghchi, Guruswami and Ribeiro (STOC 2023), we also obtain similar lower bounds for k-MDP_p, k-CVP_p and k-SVP_p. These results improve upon the previous f(k)⋅ n^{Ω(poly log k)} lower bounds for these problems under ETH using reductions by Bhattacharyya et al. (J.ACM 2021) and Bennett et al. (STOC 2023).
Cite as

Shuangle Li, Bingkai Lin, and Yuwei Liu. Improved Lower Bounds for Approximating Parameterized Nearest Codeword and Related Problems Under ETH. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 107:1-107:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{li_et_al:LIPIcs.ICALP.2024.107,
  author =	{Li, Shuangle and Lin, Bingkai and Liu, Yuwei},
  title =	{{Improved Lower Bounds for Approximating Parameterized Nearest Codeword and Related Problems Under ETH}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{107:1--107:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.107},
  URN =		{urn:nbn:de:0030-drops-202500},
  doi =		{10.4230/LIPIcs.ICALP.2024.107},
  annote =	{Keywords: Nearest Codeword Problem, Hardness of Approximations, Fine-grained Complexity, Parameterized Complexity, Minimum Distance Problem, Shortest Vector Problem}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2023.19
FPT Approximation Using Treewidth: Capacitated Vertex Cover, Target Set Selection and Vector Dominating Set

Authors: Huairui Chu and Bingkai Lin

Published in: LIPIcs, Volume 283, 34th International Symposium on Algorithms and Computation (ISAAC 2023)

Abstract
Treewidth is a useful tool in designing graph algorithms. Although many NP-hard graph problems can be solved in linear time when the input graphs have small treewidth, there are problems which remain hard on graphs of bounded treewidth. In this paper, we consider three vertex selection problems that are W[1]-hard when parameterized by the treewidth of the input graph, namely the capacitated vertex cover problem, the target set selection problem and the vector dominating set problem. We provide two new methods to obtain FPT approximation algorithms for these problems. For the capacitated vertex cover problem and the vector dominating set problem, we obtain (1+o(1))-approximation FPT algorithms. For the target set selection problem, we give an FPT algorithm providing a tradeoff between its running time and the approximation ratio.
Cite as

Huairui Chu and Bingkai Lin. FPT Approximation Using Treewidth: Capacitated Vertex Cover, Target Set Selection and Vector Dominating Set. In 34th International Symposium on Algorithms and Computation (ISAAC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 283, pp. 19:1-19:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@InProceedings{chu_et_al:LIPIcs.ISAAC.2023.19,
  author =	{Chu, Huairui and Lin, Bingkai},
  title =	{{FPT Approximation Using Treewidth: Capacitated Vertex Cover, Target Set Selection and Vector Dominating Set}},
  booktitle =	{34th International Symposium on Algorithms and Computation (ISAAC 2023)},
  pages =	{19:1--19:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-289-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{283},
  editor =	{Iwata, Satoru and Kakimura, Naonori},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2023.19},
  URN =		{urn:nbn:de:0030-drops-193216},
  doi =		{10.4230/LIPIcs.ISAAC.2023.19},
  annote =	{Keywords: FPT approximation algorithm, Treewidth, Capacitated vertex cover, Target set selection, Vector dominating set}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2022.90
On Lower Bounds of Approximating Parameterized k-Clique

Authors: Bingkai Lin, Xuandi Ren, Yican Sun, and Xiuhan Wang

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

Abstract
Given a simple graph G and an integer k, the goal of the k-Clique problem is to decide if G contains a complete subgraph of size k. We say an algorithm approximates k-Clique within a factor g(k) if it can find a clique of size at least k/g(k) when G is guaranteed to have a k-clique. Recently, it was shown that approximating k-Clique within a constant factor is W[1]-hard [Bingkai Lin, 2021]. We study the approximation of k-Clique under the Exponential Time Hypothesis (ETH). The reduction of [Bingkai Lin, 2021] already implies an n^Ω(√[6]{log k})-time lower bound under ETH. We improve this lower bound to n^Ω(log k). Using the gap-amplification technique by expander graphs, we also prove that there is no k^o(1) factor FPT-approximation algorithm for k-Clique under ETH. We also suggest a new way to prove the Parameterized Inapproximability Hypothesis (PIH) under ETH. We show that if there is no n^O(k/(log k))-time algorithm to approximate k-Clique within a constant factor, then PIH is true.
Cite as

Bingkai Lin, Xuandi Ren, Yican Sun, and Xiuhan Wang. On Lower Bounds of Approximating Parameterized k-Clique. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 90:1-90:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

Copy BibTex To Clipboard

@InProceedings{lin_et_al:LIPIcs.ICALP.2022.90,
  author =	{Lin, Bingkai and Ren, Xuandi and Sun, Yican and Wang, Xiuhan},
  title =	{{On Lower Bounds of Approximating Parameterized k-Clique}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{90:1--90:18},
  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.2022.90},
  URN =		{urn:nbn:de:0030-drops-164317},
  doi =		{10.4230/LIPIcs.ICALP.2022.90},
  annote =	{Keywords: parameterized complexity, k-clique, hardness of approximation}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2019.81
A Simple Gap-Producing Reduction for the Parameterized Set Cover Problem

Authors: Bingkai Lin

Published in: LIPIcs, Volume 132, 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)

Abstract
Given an n-vertex bipartite graph I=(S,U,E), the goal of set cover problem is to find a minimum sized subset of S such that every vertex in U is adjacent to some vertex of this subset. It is NP-hard to approximate set cover to within a (1-o(1))ln n factor [I. Dinur and D. Steurer, 2014]. If we use the size of the optimum solution k as the parameter, then it can be solved in n^{k+o(1)} time [Eisenbrand and Grandoni, 2004]. A natural question is: can we approximate set cover to within an o(ln n) factor in n^{k-epsilon} time? In a recent breakthrough result[Karthik et al., 2018], Karthik, Laekhanukit and Manurangsi showed that assuming the Strong Exponential Time Hypothesis (SETH), for any computable function f, no f(k)* n^{k-epsilon}-time algorithm can approximate set cover to a factor below (log n)^{1/poly(k,e(epsilon))} for some function e. This paper presents a simple gap-producing reduction which, given a set cover instance I=(S,U,E) and two integers k<h <=(1-o(1))sqrt[k]{log |S|/log log |S|}, outputs a new set cover instance I'=(S,U',E') with |U'|=|U|^{h^k}|S|^{O(1)} in |U|^{h^k}* |S|^{O(1)} time such that - if I has a k-sized solution, then so does I'; - if I has no k-sized solution, then every solution of I' must contain at least h vertices. Setting h=(1-o(1))sqrt[k]{log |S|/log log |S|}, we show that assuming SETH, for any computable function f, no f(k)* n^{k-epsilon}-time algorithm can distinguish between a set cover instance with k-sized solution and one whose minimum solution size is at least (1-o(1))* sqrt[k]((log n)/(log log n)). This improves the result in [Karthik et al., 2018].
Cite as

Bingkai Lin. A Simple Gap-Producing Reduction for the Parameterized Set Cover Problem. In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, pp. 81:1-81:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

Copy BibTex To Clipboard

@InProceedings{lin:LIPIcs.ICALP.2019.81,
  author =	{Lin, Bingkai},
  title =	{{A Simple Gap-Producing Reduction for the Parameterized Set Cover Problem}},
  booktitle =	{46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)},
  pages =	{81:1--81:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-109-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{132},
  editor =	{Baier, Christel and Chatzigiannakis, Ioannis and Flocchini, Paola and Leonardi, Stefano},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2019.81},
  URN =		{urn:nbn:de:0030-drops-106573},
  doi =		{10.4230/LIPIcs.ICALP.2019.81},
  annote =	{Keywords: set cover, FPT inapproximability, gap-producing reduction, (n, k)-universal set}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2019.84
Short Proofs Are Hard to Find

Authors: Ian Mertz, Toniann Pitassi, and Yuanhao Wei

Published in: LIPIcs, Volume 132, 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)

Abstract
We obtain a streamlined proof of an important result by Alekhnovich and Razborov [Michael Alekhnovich and Alexander A. Razborov, 2008], showing that it is hard to automatize both tree-like and general Resolution. Under a different assumption than [Michael Alekhnovich and Alexander A. Razborov, 2008], our simplified proof gives improved bounds: we show under ETH that these proof systems are not automatizable in time n^f(n), whenever f(n) = o(log^{1/7 - epsilon} log n) for any epsilon > 0. Previously non-automatizability was only known for f(n) = O(1). Our proof also extends fairly straightforwardly to prove similar hardness results for PCR and Res(r).
Cite as

Ian Mertz, Toniann Pitassi, and Yuanhao Wei. Short Proofs Are Hard to Find. In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, pp. 84:1-84:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

Copy BibTex To Clipboard

@InProceedings{mertz_et_al:LIPIcs.ICALP.2019.84,
  author =	{Mertz, Ian and Pitassi, Toniann and Wei, Yuanhao},
  title =	{{Short Proofs Are Hard to Find}},
  booktitle =	{46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)},
  pages =	{84:1--84:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-109-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{132},
  editor =	{Baier, Christel and Chatzigiannakis, Ioannis and Flocchini, Paola and Leonardi, Stefano},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2019.84},
  URN =		{urn:nbn:de:0030-drops-106605},
  doi =		{10.4230/LIPIcs.ICALP.2019.84},
  annote =	{Keywords: automatizability, Resolution, SAT solvers, proof complexity}
}
  • Refine by Author
  • 4 Lin, Bingkai
  • 2 Ren, Xuandi
  • 1 Bshouty, Nader H.
  • 1 Chu, Huairui
  • 1 Dallard, Clément
  • Show More...

  • Refine by Classification
  • 4 Theory of computation → Problems, reductions and completeness
  • 2 Theory of computation → Fixed parameter tractability
  • 2 Theory of computation → Parameterized complexity and exact algorithms
  • 1 Hardware → Theorem proving and SAT solving
  • 1 Mathematics of computing → Graph algorithms
  • Show More...

  • Refine by Keyword
  • 2 parameterized complexity
  • 1 (n
  • 1 Capacitated vertex cover
  • 1 Constraint Satisfaction Problems
  • 1 FPT approximation algorithm
  • Show More...

  • Refine by Type
  • 9 document

  • Refine by Publication Year
  • 5 2024
  • 2 2019
  • 1 2022
  • 1 2023

Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2024 Schloss Dagstuhl – LZI GmbH Imprint Privacy Contact