18 Search Results for "Chen, Xue"

Document
DOI: 10.4230/LIPIcs.AFT.2024.17
Cornucopia: Distributed Randomness at Scale

Authors: Miranda Christ, Kevin Choi, and Joseph Bonneau

Published in: LIPIcs, Volume 316, 6th Conference on Advances in Financial Technologies (AFT 2024)

Abstract
We propose Cornucopia, a protocol framework for distributed randomness beacons combining accumulators and verifiable delay functions. Cornucopia generalizes the Unicorn protocol, using an accumulator to enable efficient verification by each participant that their contribution has been included. The output is unpredictable as long as at least one participant is honest, yielding a scalable distributed randomness beacon with strong security properties. Proving this approach secure requires developing a novel property of accumulators, insertion security, which we show is both necessary and sufficient for Cornucopia-style protocols. We show that not all accumulators are insertion-secure, then prove that common constructions (Merkle trees, RSA accumulators, and bilinear accumulators) are either naturally insertion-secure or can be made so with trivial modifications.
Cite as

Miranda Christ, Kevin Choi, and Joseph Bonneau. Cornucopia: Distributed Randomness at Scale. In 6th Conference on Advances in Financial Technologies (AFT 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 316, pp. 17:1-17:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{christ_et_al:LIPIcs.AFT.2024.17,
  author =	{Christ, Miranda and Choi, Kevin and Bonneau, Joseph},
  title =	{{Cornucopia: Distributed Randomness at Scale}},
  booktitle =	{6th Conference on Advances in Financial Technologies (AFT 2024)},
  pages =	{17:1--17:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-345-4},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{316},
  editor =	{B\"{o}hme, Rainer and Kiffer, Lucianna},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.AFT.2024.17},
  URN =		{urn:nbn:de:0030-drops-209533},
  doi =		{10.4230/LIPIcs.AFT.2024.17},
  annote =	{Keywords: Randomness beacons, accumulators}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2024.61
When Can an Expander Code Correct Ω(n) Errors in O(n) Time?

Authors: Kuan Cheng, Minghui Ouyang, Chong Shangguan, and Yuanting Shen

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

Abstract
Tanner codes are graph-based linear codes whose parity-check matrices can be characterized by a bipartite graph G together with a linear inner code C₀. Expander codes are Tanner codes whose defining bipartite graph G has good expansion property. This paper is motivated by the following natural and fundamental problem in decoding expander codes: What are the sufficient and necessary conditions that δ and d₀ must satisfy, so that every bipartite expander G with vertex expansion ratio δ and every linear inner code C₀ with minimum distance d₀ together define an expander code that corrects Ω(n) errors in O(n) time? For C₀ being the parity-check code, the landmark work of Sipser and Spielman (IEEE-TIT'96) showed that δ > 3/4 is sufficient; later Viderman (ACM-TOCT'13) improved this to δ > 2/3-Ω(1) and he also showed that δ > 1/2 is necessary. For general linear code C₀, the previously best-known result of Dowling and Gao (IEEE-TIT'18) showed that d₀ = Ω(cδ^{-2}) is sufficient, where c is the left-degree of G. In this paper, we give a near-optimal solution to the above question for general C₀ by showing that δ d₀ > 3 is sufficient and δ d₀ > 1 is necessary, thereby also significantly improving Dowling-Gao’s result. We present two novel algorithms for decoding expander codes, where the first algorithm is deterministic, and the second one is randomized and has a larger decoding radius.
Cite as

Kuan Cheng, Minghui Ouyang, Chong Shangguan, and Yuanting Shen. When Can an Expander Code Correct Ω(n) Errors in O(n) Time?. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 317, pp. 61:1-61:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{cheng_et_al:LIPIcs.APPROX/RANDOM.2024.61,
  author =	{Cheng, Kuan and Ouyang, Minghui and Shangguan, Chong and Shen, Yuanting},
  title =	{{When Can an Expander Code Correct \Omega(n) Errors in O(n) Time?}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)},
  pages =	{61:1--61:23},
  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.2024.61},
  URN =		{urn:nbn:de:0030-drops-210543},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2024.61},
  annote =	{Keywords: expander codes, expander graphs, linear-time decoding}
}
Document
DOI: 10.4230/LIPIcs.AFT.2024.7
DeFiAligner: Leveraging Symbolic Analysis and Large Language Models for Inconsistency Detection in Decentralized Finance

Authors: Rundong Gan, Liyi Zhou, Le Wang, Kaihua Qin, and Xiaodong Lin

Published in: LIPIcs, Volume 316, 6th Conference on Advances in Financial Technologies (AFT 2024)

Abstract
Decentralized Finance (DeFi) has witnessed a monumental surge, reaching 53.039 billion USD in total value locked. As this sector continues to expand, ensuring the reliability of DeFi smart contracts becomes increasingly crucial. While some users are adept at reading code or the compiled bytecode to understand smart contracts, many rely on documentation. Therefore, discrepancies between the documentation and the deployed code can pose significant risks, whether these discrepancies are due to errors or intentional fraud. To tackle these challenges, we developed DeFiAligner, an end-to-end system to identify inconsistencies between documentation and smart contracts. DeFiAligner incorporates a symbolic execution tool, SEVM, which explores execution paths of on-chain binary code, recording memory and stack states. It automatically generates symbolic expressions for token balance changes and branch conditions, which, along with related project documents, are processed by LLMs. Using structured prompts, the LLMs evaluate the alignment between the symbolic expressions and the documentation. Our tests across three distinct scenarios demonstrate DeFiAligner’s capability to automate inconsistency detection in DeFi, achieving recall rates of 92% and 90% on two public datasets respectively.
Cite as

Rundong Gan, Liyi Zhou, Le Wang, Kaihua Qin, and Xiaodong Lin. DeFiAligner: Leveraging Symbolic Analysis and Large Language Models for Inconsistency Detection in Decentralized Finance. In 6th Conference on Advances in Financial Technologies (AFT 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 316, pp. 7:1-7:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{gan_et_al:LIPIcs.AFT.2024.7,
  author =	{Gan, Rundong and Zhou, Liyi and Wang, Le and Qin, Kaihua and Lin, Xiaodong},
  title =	{{DeFiAligner: Leveraging Symbolic Analysis and Large Language Models for Inconsistency Detection in Decentralized Finance}},
  booktitle =	{6th Conference on Advances in Financial Technologies (AFT 2024)},
  pages =	{7:1--7:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-345-4},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{316},
  editor =	{B\"{o}hme, Rainer and Kiffer, Lucianna},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.AFT.2024.7},
  URN =		{urn:nbn:de:0030-drops-209431},
  doi =		{10.4230/LIPIcs.AFT.2024.7},
  annote =	{Keywords: Decentralized Finance Security, Large Language Models, Project Review, Symbolic Analysis, Smart Contracts}
}
Document
DOI: 10.4230/LIPIcs.ECOOP.2024.18
A CFL-Reachability Formulation of Callsite-Sensitive Pointer Analysis with Built-In On-The-Fly Call Graph Construction

Authors: Dongjie He, Jingbo Lu, and Jingling Xue

Published in: LIPIcs, Volume 313, 38th European Conference on Object-Oriented Programming (ECOOP 2024)

Abstract
In object-oriented languages, the traditional CFL-reachability formulation for k-callsite-sensitive pointer analysis (kCFA) focuses on modeling field accesses and calling contexts, but it relies on a separate algorithm for call graph construction. This division can result in a loss of precision in kCFA, a problem that persists even when using the most precise call graphs, whether pre-constructed or generated on the fly. Moreover, pre-analyses based on this framework aiming to improve the efficiency of kCFA may inadvertently reduce its precision, due to the framework’s lack of native call graph construction, essential for precise analysis. Addressing this gap, this paper introduces a novel CFL-reachability formulation of kCFA for Java, uniquely integrating on-the-fly call graph construction. This advancement not only addresses the precision loss inherent in the traditional CFL-reachability-based approach but also enhances its overall applicability. In a significant secondary contribution, we present the first precision-preserving pre-analysis to accelerate kCFA. This pre-analysis leverages selective context sensitivity to improve the efficiency of kCFA without sacrificing its precision. Collectively, these contributions represent a substantial step forward in pointer analysis, offering both theoretical and practical advancements that could benefit future developments in the field.
Cite as

Dongjie He, Jingbo Lu, and Jingling Xue. A CFL-Reachability Formulation of Callsite-Sensitive Pointer Analysis with Built-In On-The-Fly Call Graph Construction. In 38th European Conference on Object-Oriented Programming (ECOOP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 313, pp. 18:1-18:29, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{he_et_al:LIPIcs.ECOOP.2024.18,
  author =	{He, Dongjie and Lu, Jingbo and Xue, Jingling},
  title =	{{A CFL-Reachability Formulation of Callsite-Sensitive Pointer Analysis with Built-In On-The-Fly Call Graph Construction}},
  booktitle =	{38th European Conference on Object-Oriented Programming (ECOOP 2024)},
  pages =	{18:1--18:29},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-341-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{313},
  editor =	{Aldrich, Jonathan and Salvaneschi, Guido},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECOOP.2024.18},
  URN =		{urn:nbn:de:0030-drops-208674},
  doi =		{10.4230/LIPIcs.ECOOP.2024.18},
  annote =	{Keywords: Pointer Analysis, CFL Reachability, Call Graph Construction}
}
Document
DOI: 10.4230/LIPIcs.ECOOP.2024.36
Scaling Interprocedural Static Data-Flow Analysis to Large C/C++ Applications: An Experience Report

Authors: Fabian Schiebel, Florian Sattler, Philipp Dominik Schubert, Sven Apel, and Eric Bodden

Published in: LIPIcs, Volume 313, 38th European Conference on Object-Oriented Programming (ECOOP 2024)

Abstract
Interprocedural data-flow analysis is important for computing precise information on whole programs. In theory, the popular algorithmic framework interprocedural distributive environments (IDE) provides a tool to solve distributive interprocedural data-flow problems efficiently. Yet, unfortunately, available state-of-the-art implementations of the IDE framework start to run into scalability issues for programs with several thousands of lines of code, depending on the static analysis domain. Since the IDE framework is a basic building block for many static program analyses, this presents a serious limitation. In this paper, we report on our experience with making the IDE algorithm scale to C/C++ applications with up to 500 000 lines of code. We analyze the IDE algorithm and its state-of-the-art implementations to identify their weaknesses related to scalability at both a conceptual and implementation level. Based on this analysis, we propose several optimizations to overcome these weaknesses, aiming at a sweet spot between reducing running time and memory consumption. As a result, we provide an improved IDE solver that implements our optimizations within the PhASAR static analysis framework. Our evaluation on real-world C/C++ applications shows that applying the optimizations speeds up the analysis on average by up to 7×, while also reducing memory consumption by 7× on average as well. For the first time, these optimizations allow us to analyze programs with several hundreds of thousands of lines of LLVM-IR code in reasonable time and space.
Cite as

Fabian Schiebel, Florian Sattler, Philipp Dominik Schubert, Sven Apel, and Eric Bodden. Scaling Interprocedural Static Data-Flow Analysis to Large C/C++ Applications: An Experience Report. In 38th European Conference on Object-Oriented Programming (ECOOP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 313, pp. 36:1-36:28, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{schiebel_et_al:LIPIcs.ECOOP.2024.36,
  author =	{Schiebel, Fabian and Sattler, Florian and Schubert, Philipp Dominik and Apel, Sven and Bodden, Eric},
  title =	{{Scaling Interprocedural Static Data-Flow Analysis to Large C/C++ Applications: An Experience Report}},
  booktitle =	{38th European Conference on Object-Oriented Programming (ECOOP 2024)},
  pages =	{36:1--36:28},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-341-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{313},
  editor =	{Aldrich, Jonathan and Salvaneschi, Guido},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECOOP.2024.36},
  URN =		{urn:nbn:de:0030-drops-208859},
  doi =		{10.4230/LIPIcs.ECOOP.2024.36},
  annote =	{Keywords: Interprocedural data-flow analysis, IDE, LLVM, C/C++}
}
Document
DOI: 10.4230/LIPIcs.CP.2024.20
Constraint Modelling with LLMs Using In-Context Learning

Authors: Kostis Michailidis, Dimos Tsouros, and Tias Guns

Published in: LIPIcs, Volume 307, 30th International Conference on Principles and Practice of Constraint Programming (CP 2024)

Abstract
Constraint Programming (CP) allows for the modelling and solving of a wide range of combinatorial problems. However, modelling such problems using constraints over decision variables still requires significant expertise, both in conceptual thinking and syntactic use of modelling languages. In this work, we explore the potential of using pre-trained Large Language Models (LLMs) as coding assistants, to transform textual problem descriptions into concrete and executable CP specifications. We present different transformation pipelines with explicit intermediate representations, and we investigate the potential benefit of various retrieval-augmented example selection strategies for in-context learning. We evaluate our approach on 2 datasets from the literature, namely NL4Opt (optimisation) and Logic Grid Puzzles (satisfaction), and a heterogeneous set of exercises from a CP course. The results show that pre-trained LLMs have promising potential for initialising the modelling process, with retrieval-augmented in-context learning significantly enhancing their modelling capabilities.
Cite as

Kostis Michailidis, Dimos Tsouros, and Tias Guns. Constraint Modelling with LLMs Using In-Context Learning. In 30th International Conference on Principles and Practice of Constraint Programming (CP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 307, pp. 20:1-20:27, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{michailidis_et_al:LIPIcs.CP.2024.20,
  author =	{Michailidis, Kostis and Tsouros, Dimos and Guns, Tias},
  title =	{{Constraint Modelling with LLMs Using In-Context Learning}},
  booktitle =	{30th International Conference on Principles and Practice of Constraint Programming (CP 2024)},
  pages =	{20:1--20:27},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-336-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{307},
  editor =	{Shaw, Paul},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CP.2024.20},
  URN =		{urn:nbn:de:0030-drops-207053},
  doi =		{10.4230/LIPIcs.CP.2024.20},
  annote =	{Keywords: Constraint Modelling, Constraint Acquisition, Constraint Programming, Large Language Models, In-Context Learning, Natural Language Processing, Named Entity Recognition, Retrieval-Augmented Generation, Optimisation}
}
Document
DOI: 10.4230/LIPIcs.CP.2024.25
Combining Constraint Programming Reasoning with Large Language Model Predictions

Authors: Florian Régin, Elisabetta De Maria, and Alexandre Bonlarron

Published in: LIPIcs, Volume 307, 30th International Conference on Principles and Practice of Constraint Programming (CP 2024)

Abstract
Constraint Programming (CP) and Machine Learning (ML) face challenges in text generation due to CP’s struggle with implementing "meaning" and ML’s difficulty with structural constraints. This paper proposes a solution by combining both approaches and embedding a Large Language Model (LLM) in CP. The LLM handles word generation and meaning, while CP manages structural constraints. This approach builds on GenCP, an improved version of On-the-fly Constraint Programming Search (OTFS) using LLM-generated domains. Compared to Beam Search (BS), a standard NLP method, this combined approach (GenCP with LLM) is faster and produces better results, ensuring all constraints are satisfied. This fusion of CP and ML presents new possibilities for enhancing text generation under constraints.
Cite as

Florian Régin, Elisabetta De Maria, and Alexandre Bonlarron. Combining Constraint Programming Reasoning with Large Language Model Predictions. In 30th International Conference on Principles and Practice of Constraint Programming (CP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 307, pp. 25:1-25:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{regin_et_al:LIPIcs.CP.2024.25,
  author =	{R\'{e}gin, Florian and De Maria, Elisabetta and Bonlarron, Alexandre},
  title =	{{Combining Constraint Programming Reasoning with Large Language Model Predictions}},
  booktitle =	{30th International Conference on Principles and Practice of Constraint Programming (CP 2024)},
  pages =	{25:1--25:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-336-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{307},
  editor =	{Shaw, Paul},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CP.2024.25},
  URN =		{urn:nbn:de:0030-drops-207109},
  doi =		{10.4230/LIPIcs.CP.2024.25},
  annote =	{Keywords: Solver and Tools, ML-augmented CP, Constrained Text Generation, ML alongside CO}
}
Document
DOI: 10.4230/LIPIcs.TQC.2024.1
Multi-qubit Lattice Surgery Scheduling

Authors: Allyson Silva, Xiangyi Zhang, Zak Webb, Mia Kramer, Chan-Woo Yang, Xiao Liu, Jessica Lemieux, Ka-Wai Chen, Artur Scherer, and Pooya Ronagh

Published in: LIPIcs, Volume 310, 19th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2024)

Abstract
Fault-tolerant quantum computation using two-dimensional topological quantum error correcting codes can benefit from multi-qubit long-range operations. By using simple commutation rules, a quantum circuit can be transpiled into a sequence of solely non-Clifford multi-qubit gates. Prior work on fault-tolerant compilation avoids optimal scheduling of such gates since they reduce the parallelizability of the circuit. We observe that the reduced parallelization potential is outweighed by the significant reduction in the number of gates. We therefore devise a method for scheduling multi-qubit lattice surgery using an earliest-available-first policy, solving the associated forest packing problem using a representation of the multi-qubit gates as Steiner trees. Our extensive testing on random and various Hamiltonian simulation circuits demonstrates the method’s scalability and performance. We show that the transpilation significantly reduces the circuit length on the set of circuits tested, and that the resulting circuit of multi-qubit gates has a further reduction in the expected circuit execution time compared to serial execution.
Cite as

Allyson Silva, Xiangyi Zhang, Zak Webb, Mia Kramer, Chan-Woo Yang, Xiao Liu, Jessica Lemieux, Ka-Wai Chen, Artur Scherer, and Pooya Ronagh. Multi-qubit Lattice Surgery Scheduling. In 19th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 310, pp. 1:1-1:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{silva_et_al:LIPIcs.TQC.2024.1,
  author =	{Silva, Allyson and Zhang, Xiangyi and Webb, Zak and Kramer, Mia and Yang, Chan-Woo and Liu, Xiao and Lemieux, Jessica and Chen, Ka-Wai and Scherer, Artur and Ronagh, Pooya},
  title =	{{Multi-qubit Lattice Surgery Scheduling}},
  booktitle =	{19th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2024)},
  pages =	{1:1--1:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-328-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{310},
  editor =	{Magniez, Fr\'{e}d\'{e}ric and Grilo, Alex Bredariol},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2024.1},
  URN =		{urn:nbn:de:0030-drops-206712},
  doi =		{10.4230/LIPIcs.TQC.2024.1},
  annote =	{Keywords: Scheduling, Large-Scale Optimization, Surface Code, Quantum Compilation, Circuit Optimization}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2024.40
On Fourier Analysis of Sparse Boolean Functions over Certain Abelian Groups

Authors: Sourav Chakraborty, Swarnalipa Datta, Pranjal Dutta, Arijit Ghosh, and Swagato Sanyal

Published in: LIPIcs, Volume 306, 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)

Abstract
Given an Abelian group 𝒢, a Boolean-valued function f: 𝒢 → {-1,+1}, is said to be s-sparse, if it has at most s-many non-zero Fourier coefficients over the domain 𝒢. In a seminal paper, Gopalan et al. [Gopalan et al., 2011] proved "Granularity" for Fourier coefficients of Boolean valued functions over ℤ₂ⁿ, that have found many diverse applications in theoretical computer science and combinatorics. They also studied structural results for Boolean functions over ℤ₂ⁿ which are approximately Fourier-sparse. In this work, we obtain structural results for approximately Fourier-sparse Boolean valued functions over Abelian groups 𝒢 of the form, 𝒢: = ℤ_{p_1}^{n_1} × ⋯ × ℤ_{p_t}^{n_t}, for distinct primes p_i. We also obtain a lower bound of the form 1/(m²s)^⌈φ(m)/2⌉, on the absolute value of the smallest non-zero Fourier coefficient of an s-sparse function, where m = p_1 ⋯ p_t, and φ(m) = (p_1-1) ⋯ (p_t-1). We carefully apply probabilistic techniques from [Gopalan et al., 2011], to obtain our structural results, and use some non-trivial results from algebraic number theory to get the lower bound. We construct a family of at most s-sparse Boolean functions over ℤ_pⁿ, where p > 2, for arbitrarily large enough s, where the minimum non-zero Fourier coefficient is o(1/s). The "Granularity" result of Gopalan et al. implies that the absolute values of non-zero Fourier coefficients of any s-sparse Boolean valued function over ℤ₂ⁿ are Ω(1/s). So, our result shows that one cannot expect such a lower bound for general Abelian groups. Using our new structural results on the Fourier coefficients of sparse functions, we design an efficient sparsity testing algorithm for Boolean function, which tests whether the given function is s-sparse, or ε-far from any sparse Boolean function, and it requires poly((ms)^φ(m),1/ε)-many queries. Further, we generalize the notion of degree of a Boolean function over an Abelian group 𝒢. We use it to prove an Ω(√s) lower bound on the query complexity of any adaptive sparsity testing algorithm.
Cite as

Sourav Chakraborty, Swarnalipa Datta, Pranjal Dutta, Arijit Ghosh, and Swagato Sanyal. On Fourier Analysis of Sparse Boolean Functions over Certain Abelian Groups. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 40:1-40:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{chakraborty_et_al:LIPIcs.MFCS.2024.40,
  author =	{Chakraborty, Sourav and Datta, Swarnalipa and Dutta, Pranjal and Ghosh, Arijit and Sanyal, Swagato},
  title =	{{On Fourier Analysis of Sparse Boolean Functions over Certain Abelian Groups}},
  booktitle =	{49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
  pages =	{40:1--40:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-335-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{306},
  editor =	{Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.40},
  URN =		{urn:nbn:de:0030-drops-205963},
  doi =		{10.4230/LIPIcs.MFCS.2024.40},
  annote =	{Keywords: Fourier coefficients, sparse, Abelian, granularity}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2024.84
Faster Approximation Schemes for (Constrained) k-Means with Outliers

Authors: Zhen Zhang, Junyu Huang, and Qilong Feng

Published in: LIPIcs, Volume 306, 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)

Abstract
Given a set of n points in ℝ^d and two positive integers k and m, the Euclidean k-means with outliers problem aims to remove at most m points, referred to as outliers, and minimize the k-means cost function for the remaining points. Developing algorithms for this problem remains an active area of research due to its prevalence in applications involving noisy data. In this paper, we give a (1+ε)-approximation algorithm that runs in n²d((k+m)ε^{-1})^O(kε^{-1}) time for the problem. When combined with a coreset construction method, the running time of the algorithm can be improved to be linear in n. For the case where k is a constant, this represents the first polynomial-time approximation scheme for the problem: Existing algorithms with the same approximation guarantee run in polynomial time only when both k and m are constants. Furthermore, our approach generalizes to variants of k-means with outliers incorporating additional constraints on instances, such as those related to capacities and fairness.
Cite as

Zhen Zhang, Junyu Huang, and Qilong Feng. Faster Approximation Schemes for (Constrained) k-Means with Outliers. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 84:1-84:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{zhang_et_al:LIPIcs.MFCS.2024.84,
  author =	{Zhang, Zhen and Huang, Junyu and Feng, Qilong},
  title =	{{Faster Approximation Schemes for (Constrained) k-Means with Outliers}},
  booktitle =	{49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
  pages =	{84:1--84:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-335-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{306},
  editor =	{Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.84},
  URN =		{urn:nbn:de:0030-drops-206408},
  doi =		{10.4230/LIPIcs.MFCS.2024.84},
  annote =	{Keywords: Approximation algorithms, clustering}
}
Document
DOI: 10.4230/LIPIcs.SAT.2024.8
Enhancing MaxSAT Local Search via a Unified Soft Clause Weighting Scheme

Authors: Yi Chu, Chu-Min Li, Furong Ye, and Shaowei Cai

Published in: LIPIcs, Volume 305, 27th International Conference on Theory and Applications of Satisfiability Testing (SAT 2024)

Abstract
Local search has been widely applied to solve the well-known (weighted) partial MaxSAT problem, significantly influencing many real-world applications. The main difficulty to overcome when designing a local search algorithm is that it can easily fall into local optima. Clause weighting is a beneficial technique that dynamically adjusts the landscape of search space to help the algorithm escape from local optima. Existing works tend to increase the weights of falsified clauses, and such strategies may result in an unpredictable landscape of search space during the optimization process. Therefore, in this paper, we propose a Unified Soft Clause Weighting Scheme called Unified-SW, which increases the weights of all soft clauses in feasible local optima, whether they are satisfied or not, while preserving the hierarchy among them. We implemented Unified-SW in a new local search solver called USW-LS. Experimental results demonstrate that USW-LS, outperforms the state-of-the-art local search solvers across benchmarks from anytime tracks of recent MaxSAT Evaluations. More promisingly, a hybrid solver combining USW-LS and TT-Open-WBO-Inc won all four categories in the anytime track of MaxSAT Evaluation 2023.
Cite as

Yi Chu, Chu-Min Li, Furong Ye, and Shaowei Cai. Enhancing MaxSAT Local Search via a Unified Soft Clause Weighting Scheme. In 27th International Conference on Theory and Applications of Satisfiability Testing (SAT 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 305, pp. 8:1-8:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{chu_et_al:LIPIcs.SAT.2024.8,
  author =	{Chu, Yi and Li, Chu-Min and Ye, Furong and Cai, Shaowei},
  title =	{{Enhancing MaxSAT Local Search via a Unified Soft Clause Weighting Scheme}},
  booktitle =	{27th International Conference on Theory and Applications of Satisfiability Testing (SAT 2024)},
  pages =	{8:1--8:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-334-8},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{305},
  editor =	{Chakraborty, Supratik and Jiang, Jie-Hong Roland},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAT.2024.8},
  URN =		{urn:nbn:de:0030-drops-205301},
  doi =		{10.4230/LIPIcs.SAT.2024.8},
  annote =	{Keywords: Weighted Partial MaxSAT, Local Search Method, Weighting Scheme}
}
Document
DOI: 10.4230/LIPIcs.SEA.2024.6
Faster Treewidth-Based Approximations for Wiener Index

Authors: Giovanna Kobus Conrado, Amir Kafshdar Goharshady, Pavel Hudec, Pingjiang Li, and Harshit Jitendra Motwani

Published in: LIPIcs, Volume 301, 22nd International Symposium on Experimental Algorithms (SEA 2024)

Abstract
The Wiener index of a graph G is the sum of distances between all pairs of its vertices. It is a widely-used graph property in chemistry, initially introduced to examine the link between boiling points and structural properties of alkanes, which later found notable applications in drug design. Thus, computing or approximating the Wiener index of molecular graphs, i.e. graphs in which every vertex models an atom of a molecule and every edge models a bond, is of significant interest to the computational chemistry community. In this work, we build upon the observation that molecular graphs are sparse and tree-like and focus on developing efficient algorithms parameterized by treewidth to approximate the Wiener index. We present a new randomized approximation algorithm using a combination of tree decompositions and centroid decompositions. Our algorithm approximates the Wiener index within any desired multiplicative factor (1 ± ε) in time O(n ⋅ log n ⋅ k³ + √n ⋅ k/ε²), where n is the number of vertices of the graph and k is the treewidth. This time bound is almost-linear in n. Finally, we provide experimental results over standard benchmark molecules from PubChem and the Protein Data Bank, showcasing the applicability and scalability of our approach on real-world chemical graphs and comparing it with previous methods.
Cite as

Giovanna Kobus Conrado, Amir Kafshdar Goharshady, Pavel Hudec, Pingjiang Li, and Harshit Jitendra Motwani. Faster Treewidth-Based Approximations for Wiener Index. In 22nd International Symposium on Experimental Algorithms (SEA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 301, pp. 6:1-6:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{conrado_et_al:LIPIcs.SEA.2024.6,
  author =	{Conrado, Giovanna Kobus and Goharshady, Amir Kafshdar and Hudec, Pavel and Li, Pingjiang and Motwani, Harshit Jitendra},
  title =	{{Faster Treewidth-Based Approximations for Wiener Index}},
  booktitle =	{22nd International Symposium on Experimental Algorithms (SEA 2024)},
  pages =	{6:1--6:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-325-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{301},
  editor =	{Liberti, Leo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2024.6},
  URN =		{urn:nbn:de:0030-drops-203718},
  doi =		{10.4230/LIPIcs.SEA.2024.6},
  annote =	{Keywords: Computational Chemistry, Treewidth, Wiener Index}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.66
Problems in NP Can Admit Double-Exponential Lower Bounds When Parameterized by Treewidth or Vertex Cover

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

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

Abstract
Treewidth serves as an important parameter that, when bounded, yields tractability for a wide class of problems. For example, graph problems expressible in Monadic Second Order (MSO) logic and Quantified SAT or, more generally, Quantified CSP, are fixed-parameter tractable parameterized by the treewidth {of the input’s (primal) graph} plus the length of the MSO-formula [Courcelle, Information & Computation 1990] and the quantifier rank [Chen, ECAI 2004], respectively. The algorithms generated by these (meta-)results have running times whose dependence on treewidth is a tower of exponents. A conditional lower bound by Fichte, Hecher, and Pfandler [LICS 2020] shows that, for Quantified SAT, the height of this tower is equal to the number of quantifier alternations. These types of lower bounds, which show that at least double-exponential factors in the running time are necessary, exhibit the extraordinary level of computational hardness for such problems, and are rare in the current literature: there are only a handful of such lower bounds (for treewidth and vertex cover parameterizations) and all of them are for problems that are #NP-complete, Σ₂^p-complete, Π₂^p-complete, or complete for even higher levels of the polynomial hierarchy. Our results demonstrate, for the first time, that it is not necessary to go higher up in the polynomial hierarchy to achieve double-exponential lower bounds: we derive double-exponential lower bounds in the treewidth (tw) and the vertex cover number (vc), for natural, important, and well-studied NP-complete graph problems. Specifically, we design a technique to obtain such lower bounds and show its versatility by applying it to three different problems: Metric Dimension, Strong Metric Dimension, and Geodetic Set. We prove that these problems do not admit 2^{2^o(tw)}⋅n^𝒪(1)-time algorithms, even on bounded diameter graphs, unless the ETH fails (here, n is the number of vertices in the graph). In fact, for Strong Metric Dimension, the double-exponential lower bound holds even for the vertex cover number. We further complement all our lower bounds with matching (and sometimes non-trivial) upper bounds. For the conditional lower bounds, we design and use a novel, yet simple technique based on Sperner families of sets. We believe that the amenability of our technique will lead to obtaining such lower bounds for many other problems in NP.
Cite as

Florent Foucaud, Esther Galby, Liana Khazaliya, Shaohua Li, Fionn Mc Inerney, Roohani Sharma, and Prafullkumar Tale. Problems in NP Can Admit Double-Exponential Lower Bounds When Parameterized by Treewidth or Vertex Cover. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 66:1-66:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{foucaud_et_al:LIPIcs.ICALP.2024.66,
  author =	{Foucaud, Florent and Galby, Esther and Khazaliya, Liana and Li, Shaohua and Mc Inerney, Fionn and Sharma, Roohani and Tale, Prafullkumar},
  title =	{{Problems in NP Can Admit Double-Exponential Lower Bounds When Parameterized by Treewidth or Vertex Cover}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{66:1--66:19},
  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.2024.66},
  URN =		{urn:nbn:de:0030-drops-202091},
  doi =		{10.4230/LIPIcs.ICALP.2024.66},
  annote =	{Keywords: Parameterized Complexity, ETH-based Lower Bounds, Double-Exponential Lower Bounds, Kernelization, Vertex Cover, Treewidth, Diameter, Metric Dimension, Strong Metric Dimension, Geodetic Sets}
}
Document
DOI: 10.4230/LIPIcs.ESA.2023.29
Effective Resistances in Non-Expander Graphs

Authors: Dongrun Cai, Xue Chen, and Pan Peng

Published in: LIPIcs, Volume 274, 31st Annual European Symposium on Algorithms (ESA 2023)

Abstract
Effective resistances are ubiquitous in graph algorithms and network analysis. For an undirected graph G, its effective resistance R_G(s,t) between two vertices s and t is defined as the equivalent resistance between s and t if G is thought of as an electrical network with unit resistance on each edge. If we use L_G to denote the Laplacian matrix of G and L_G^† to denote its pseudo-inverse, we have R_G(s,t) = (𝟏_s-𝟏_t)^⊤ L^† (𝟏_s-𝟏_t) such that classical Laplacian solvers [Daniel A. Spielman and Shang{-}Hua Teng, 2014] provide almost-linear time algorithms to approximate R_G(s,t). In this work, we study sublinear time algorithms to approximate the effective resistance of an adjacent pair s and t. We consider the classical adjacency list model [Ron, 2019] for local algorithms. While recent works [Andoni et al., 2018; Peng et al., 2021; Li and Sachdeva, 2023] have provided sublinear time algorithms for expander graphs, we prove several lower bounds for general graphs of n vertices and m edges: 1) It needs Ω(n) queries to obtain 1.01-approximations of the effective resistance of an adjacent pair s and t, even for graphs of degree at most 3 except s and t. 2) For graphs of degree at most d and any parameter 𝓁, it needs Ω(m/𝓁) queries to obtain c ⋅ min{d,𝓁}-approximations where c > 0 is a universal constant. Moreover, we supplement the first lower bound by providing a sublinear time (1+ε)-approximation algorithm for graphs of degree 2 except the pair s and t. One of our technical ingredients is to bound the expansion of a graph in terms of the smallest non-trivial eigenvalue of its Laplacian matrix after removing edges. We discover a new lower bound on the eigenvalues of perturbed graphs (resp. perturbed matrices) by incorporating the effective resistance of the removed edge (resp. the leverage scores of the removed rows), which may be of independent interest.
Cite as

Dongrun Cai, Xue Chen, and Pan Peng. Effective Resistances in Non-Expander Graphs. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 29:1-29:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{cai_et_al:LIPIcs.ESA.2023.29,
  author =	{Cai, Dongrun and Chen, Xue and Peng, Pan},
  title =	{{Effective Resistances in Non-Expander Graphs}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{29:1--29:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-295-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{274},
  editor =	{G{\o}rtz, Inge Li and Farach-Colton, Martin and Puglisi, Simon J. 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.2023.29},
  URN =		{urn:nbn:de:0030-drops-186823},
  doi =		{10.4230/LIPIcs.ESA.2023.29},
  annote =	{Keywords: Sublinear Time Algorithm, Effective Resistance, Leverage Scores, Matrix Perturbation}
}
Document
DOI: 10.4230/LIPIcs.CCC.2022.34
Improved Pseudorandom Generators for AC⁰ Circuits

Authors: Xin Lyu

Published in: LIPIcs, Volume 234, 37th Computational Complexity Conference (CCC 2022)

Abstract
We give PRG for depth-d, size-m AC⁰ circuits with seed length O(log^{d-1}(m)log(m/ε)log log(m)). Our PRG improves on previous work [Luca Trevisan and Tongke Xue, 2013; Rocco A. Servedio and Li-Yang Tan, 2019; Zander Kelley, 2021] from various aspects. It has optimal dependence on 1/ε and is only one "log log(m)" away from the lower bound barrier. For the case of d = 2, the seed length tightly matches the best-known PRG for CNFs [Anindya De et al., 2010; Avishay Tal, 2017]. There are two technical ingredients behind our new result; both of them might be of independent interest. First, we use a partitioning-based approach to construct PRGs based on restriction lemmas for AC⁰. Previous works [Luca Trevisan and Tongke Xue, 2013; Rocco A. Servedio and Li-Yang Tan, 2019; Zander Kelley, 2021] usually built PRGs on the Ajtai-Wigderson framework [Miklós Ajtai and Avi Wigderson, 1989]. Compared with them, the partitioning approach avoids the extra "log(n)" factor that usually arises from the Ajtai-Wigderson framework, allowing us to get the almost-tight seed length. The partitioning approach is quite general, and we believe it can help design PRGs for classes beyond constant-depth circuits. Second, improving and extending [Luca Trevisan and Tongke Xue, 2013; Rocco A. Servedio and Li-Yang Tan, 2019; Zander Kelley, 2021], we prove a full derandomization of the powerful multi-switching lemma [Johan Håstad, 2014]. We show that one can use a short random seed to sample a restriction, such that a family of DNFs simultaneously simplifies under the restriction with high probability. This answers an open question in [Zander Kelley, 2021]. Previous derandomizations were either partial (that is, they pseudorandomly choose variables to restrict, and then fix those variables to truly-random bits) or had sub-optimal seed length. In our application, having a fully-derandomized switching lemma is crucial, and the randomness-efficiency of our derandomization allows us to get an almost-tight seed length.
Cite as

Xin Lyu. Improved Pseudorandom Generators for AC⁰ Circuits. In 37th Computational Complexity Conference (CCC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 234, pp. 34:1-34:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{lyu:LIPIcs.CCC.2022.34,
  author =	{Lyu, Xin},
  title =	{{Improved Pseudorandom Generators for AC⁰ Circuits}},
  booktitle =	{37th Computational Complexity Conference (CCC 2022)},
  pages =	{34:1--34:25},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-241-9},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{234},
  editor =	{Lovett, Shachar},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2022.34},
  URN =		{urn:nbn:de:0030-drops-165963},
  doi =		{10.4230/LIPIcs.CCC.2022.34},
  annote =	{Keywords: pseudorandom generators, derandomization, switching Lemmas, AC⁰}
}
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