15 Search Results for "Manohar, Peter"

Document
Research
DOI: 10.4230/TGDK.3.3.4
Mining Inter-Document Argument Structures in Scientific Papers for an Argument Web

Authors: Florian Ruosch, Cristina Sarasua, and Abraham Bernstein

Published in: TGDK, Volume 3, Issue 3 (2025). Transactions on Graph Data and Knowledge, Volume 3, Issue 3

Abstract
In Argument Mining, predicting argumentative relations between texts (or spans) remains one of the most challenging aspects, even more so in the cross-document setting. This paper makes three key contributions to advance research in this domain. We first extend an existing dataset, the Sci-Arg corpus, by annotating it with explicit inter-document argumentative relations, thereby allowing arguments to be distributed over several documents forming an Argument Web; these new annotations are published using Semantic Web technologies (RDF, OWL). Second, we explore and evaluate three automated approaches for predicting these inter-document argumentative relations, establishing critical baselines on the new dataset. We find that a simple classifier based on discourse indicators with access to context outperforms neural methods. Third, we conduct a comparative analysis of these approaches for both intra- and inter-document settings, identifying statistically significant differences in results that indicate the necessity of distinguishing between these two scenarios. Our findings highlight significant challenges in this complex domain and open crucial avenues for future research on the Argument Web of Science, particularly for those interested in leveraging Semantic Web technologies and knowledge graphs to understand scholarly discourse. With this, we provide the first stepping stones in the form of a benchmark dataset, three baseline methods, and an initial analysis for a systematic exploration of this field relevant to the Web of Data and Science.
Cite as

Florian Ruosch, Cristina Sarasua, and Abraham Bernstein. Mining Inter-Document Argument Structures in Scientific Papers for an Argument Web. In Transactions on Graph Data and Knowledge (TGDK), Volume 3, Issue 3, pp. 4:1-4:33, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@Article{ruosch_et_al:TGDK.3.3.4,
  author =	{Ruosch, Florian and Sarasua, Cristina and Bernstein, Abraham},
  title =	{{Mining Inter-Document Argument Structures in Scientific Papers for an Argument Web}},
  journal =	{Transactions on Graph Data and Knowledge},
  pages =	{4:1--4:33},
  ISSN =	{2942-7517},
  year =	{2025},
  volume =	{3},
  number =	{3},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/TGDK.3.3.4},
  URN =		{urn:nbn:de:0030-drops-252159},
  doi =		{10.4230/TGDK.3.3.4},
  annote =	{Keywords: Argument Mining, Large Language Models, Knowledge Graphs, Link Prediction}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.17
Spectral Refutations of Semirandom k-LIN over Larger Fields

Authors: Nicholas Kocurek and Peter Manohar

Published in: LIPIcs, Volume 353, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)

Abstract
We study the problem of strongly refuting semirandom k-LIN(𝔽) instances: systems of k-sparse inhomogeneous linear equations over a finite field 𝔽. For the case of 𝔽 = 𝔽₂, this is the well-studied problem of refuting semirandom instances of k-XOR, where the works of [Venkatesan Guruswami et al., 2022; Jun-Ting Hsieh et al., 2023] establish a tight trade-off between runtime and clause density for refutation: for any choice of a parameter 𝓁, they give an n^{O(𝓁)}-time algorithm to certify that there is no assignment that can satisfy more than 1/2 + ε-fraction of constraints in a semirandom k-XOR instance, provided that the instance has O(n)⋅(n/𝓁)^{k/2 - 1} log n/ε⁴ constraints, and the work of [Pravesh K. Kothari et al., 2017] provides good evidence that this tight up to a polylog(n) factor via lower bounds for the Sum-of-Squares hierarchy. However, for larger fields, the only known results for this problem are established via black-box reductions to the case of 𝔽₂, resulting in a |𝔽|^{3k} gap between the current best upper and lower bounds. In this paper, we give an algorithm for refuting semirandom k-LIN(𝔽) instances with the "correct" dependence on the field size |𝔽|. For any choice of a parameter 𝓁, our algorithm runs in (|𝔽|)^O(𝓁)-time and strongly refutes semirandom k-LIN(𝔽) instances with at least O(n) ⋅ (|𝔽^*| n/𝓁) ^{k/2 - 1} log(n|𝔽^*|)/ε⁴ constraints. We give good evidence that this dependence on the field size |𝔽| is optimal by proving a lower bound for the Sum-of-Squares hierarchy that matches this threshold up to a polylog(n |𝔽^*|) factor. Our results also extend beyond finite fields to the more general case of ℤ_m and arbitrary finite Abelian groups. Our key technical innovation is a generalization of the "𝔽₂ Kikuchi matrices" of [Alexander S. Wein et al., 2019; Venkatesan Guruswami et al., 2022] to larger fields, and finite Abelian groups more generally.
Cite as

Nicholas Kocurek and Peter Manohar. Spectral Refutations of Semirandom k-LIN over Larger Fields. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 17:1-17:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kocurek_et_al:LIPIcs.APPROX/RANDOM.2025.17,
  author =	{Kocurek, Nicholas and Manohar, Peter},
  title =	{{Spectral Refutations of Semirandom k-LIN over Larger Fields}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{17:1--17:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-397-3},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{353},
  editor =	{Ene, Alina and Chattopadhyay, Eshan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2025.17},
  URN =		{urn:nbn:de:0030-drops-243834},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.17},
  annote =	{Keywords: Spectral Algorithms, CSP Refutation, Kikuchi Matrices}
}
Document
DOI: 10.4230/LIPIcs.CCC.2025.32
A Lower Bound for k-DNF Resolution on Random CNF Formulas via Expansion

Authors: Anastasia Sofronova and Dmitry Sokolov

Published in: LIPIcs, Volume 339, 40th Computational Complexity Conference (CCC 2025)

Abstract
Random Δ-CNF formulas are one of the few candidates that are expected to be hard for proof systems and SAT algotirhms. Assume we sample m clauses over n variables. Here, the main complexity parameter is clause density, χ := m/n. For a fixed Δ, there exists a satisfiability threshold c_Δ such that for χ > c_Δ a formula is unsatisfiable with high probability. and for χ < c_Δ it is satisfiable with high probability. Near satisfiability threshold, there are various lower bounds for algorithms and proof systems [Eli Ben-Sasson, 2001; Eli Ben-Sasson and Russell Impagliazzo, 1999; Michael Alekhnovich and Alexander A. Razborov, 2003; Dima Grigoriev, 2001; Grant Schoenebeck, 2008; Pavel Hrubes and Pavel Pudlák, 2017; Noah Fleming et al., 2017; Dmitry Sokolov, 2024], and for high-density regimes, there exist upper bounds [Uriel Feige et al., 2006; Sebastian Müller and Iddo Tzameret, 2014; Jackson Abascal et al., 2021; Venkatesan Guruswami et al., 2022]. One of the frontiers in the direction of proving lower bounds on these formulas is the k-DNF Resolution proof system (aka Res(k)). There are several known results for k = 𝒪(√{log n}/{log log n}}) [Nathan Segerlind et al., 2004; Michael Alekhnovich, 2011], that are applicable only for density regime near the threshold. In this paper, we show the first Res(k) lower bound that is applicable in higher-density regimes. Our results work for slightly larger k = 𝒪(√{log n}).
Cite as

Anastasia Sofronova and Dmitry Sokolov. A Lower Bound for k-DNF Resolution on Random CNF Formulas via Expansion. In 40th Computational Complexity Conference (CCC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 339, pp. 32:1-32:27, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{sofronova_et_al:LIPIcs.CCC.2025.32,
  author =	{Sofronova, Anastasia and Sokolov, Dmitry},
  title =	{{A Lower Bound for k-DNF Resolution on Random CNF Formulas via Expansion}},
  booktitle =	{40th Computational Complexity Conference (CCC 2025)},
  pages =	{32:1--32:27},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-379-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{339},
  editor =	{Srinivasan, Srikanth},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2025.32},
  URN =		{urn:nbn:de:0030-drops-237269},
  doi =		{10.4230/LIPIcs.CCC.2025.32},
  annote =	{Keywords: proof complexity, random CNFs}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2025.10
Steinhaus Filtration and Stable Paths in the Mapper

Authors: Dustin L. Arendt, Matthew Broussard, Bala Krishnamoorthy, Nathaniel Saul, and Amber Thrall

Published in: LIPIcs, Volume 332, 41st International Symposium on Computational Geometry (SoCG 2025)

Abstract
We define a new filtration called the Steinhaus filtration built from a single cover based on a generalized Steinhaus distance, a generalization of Jaccard distance. The homology persistence module of a Steinhaus filtration with infinitely many cover elements may not be q-tame, even when the covers are in a totally bounded space. While this may pose a challenge to derive stability results, we show that the Steinhaus filtration is stable when the cover is finite. We show that while the Čech and Steinhaus filtrations are not isomorphic in general, they are isomorphic for a finite point set in dimension one. Furthermore, the VR filtration completely determines the 1-skeleton of the Steinhaus filtration in arbitrary dimension. We then develop a language and theory for stable paths within the Steinhaus filtration. We demonstrate how the framework can be applied to several applications where a standard metric may not be defined but a cover is readily available. We introduce a new perspective for modeling recommendation system datasets. As an example, we look at a movies dataset and we find the stable paths identified in our framework represent a sequence of movies constituting a gentle transition and ordering from one genre to another. For explainable machine learning, we apply the Mapper algorithm for model induction by building a filtration from a single Mapper complex, and provide explanations in the form of stable paths between subpopulations. For illustration, we build a Mapper complex from a supervised machine learning model trained on the FashionMNIST dataset. Stable paths in the Steinhaus filtration provide improved explanations of relationships between subpopulations of images.
Cite as

Dustin L. Arendt, Matthew Broussard, Bala Krishnamoorthy, Nathaniel Saul, and Amber Thrall. Steinhaus Filtration and Stable Paths in the Mapper. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 10:1-10:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{arendt_et_al:LIPIcs.SoCG.2025.10,
  author =	{Arendt, Dustin L. and Broussard, Matthew and Krishnamoorthy, Bala and Saul, Nathaniel and Thrall, Amber},
  title =	{{Steinhaus Filtration and Stable Paths in the Mapper}},
  booktitle =	{41st International Symposium on Computational Geometry (SoCG 2025)},
  pages =	{10:1--10:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-370-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{332},
  editor =	{Aichholzer, Oswin and Wang, Haitao},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2025.10},
  URN =		{urn:nbn:de:0030-drops-231625},
  doi =		{10.4230/LIPIcs.SoCG.2025.10},
  annote =	{Keywords: Cover and nerve, Jaccard distance, persistence stability, Mapper, recommender systems, explainable machine learning}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2025.2
Improved Lower Bounds for 3-Query Matching Vector Codes

Authors: Divesh Aggarwal, Pranjal Dutta, Zeyong Li, Maciej Obremski, and Sidhant Saraogi

Published in: LIPIcs, Volume 325, 16th Innovations in Theoretical Computer Science Conference (ITCS 2025)

Abstract
A Matching Vector (MV) family modulo a positive integer m ≥ 2 is a pair of ordered lists U = (u_1, ⋯, u_K) and V = (v_1, ⋯, v_K) where u_i, v_j ∈ ℤ_m^n with the following property: for any i ∈ [K], the inner product ⟨u_i, v_i⟩ = 0 mod m, and for any i ≠ j, ⟨u_i, v_j⟩ ≠ 0 mod m. An MV family is called r-restricted if inner products ⟨u_i, v_j⟩, for all i,j, take at most r different values. The r-restricted MV families are extremely important since the only known construction of constant-query subexponential locally decodable codes (LDCs) are based on them. Such LDCs constructed via matching vector families are called matching vector codes. Let MV(m,n) (respectively MV(m, n, r)) denote the largest K such that there exists an MV family (respectively r-restricted MV family) of size K in ℤ_m^n. Such a MV family can be transformed in a black-box manner to a good r-query locally decodable code taking messages of length K to codewords of length N = m^n. For small prime m, an almost tight bound MV(m,n) ≤ O(m^{n/2}) was first shown by Dvir, Gopalan, Yekhanin (FOCS'10, SICOMP'11), while for general m, the same paper established an upper bound of O(m^{n-1+o_m(1)}), with o_m(1) denoting a function that goes to zero when m grows. For any arbitrary constant r ≥ 3 and composite m, the best upper bound till date on MV(m,n,r) is O(m^{n/2}), is due to Bhowmick, Dvir and Lovett (STOC'13, SICOMP'14).In a breakthrough work, Alrabiah, Guruswami, Kothari and Manohar (STOC'23) implicitly improve this bound for 3-restricted families to MV(m, n, 3) ≤ O(m^{n/3}). In this work, we present an upper bound for r = 3 where MV(m,n,3) ≤ m^{n/6 +O(log n)}, and as a result, any 3-query matching vector code must have codeword length of N ≥ K^{6-o(1)}.
Cite as

Divesh Aggarwal, Pranjal Dutta, Zeyong Li, Maciej Obremski, and Sidhant Saraogi. Improved Lower Bounds for 3-Query Matching Vector Codes. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 2:1-2:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{aggarwal_et_al:LIPIcs.ITCS.2025.2,
  author =	{Aggarwal, Divesh and Dutta, Pranjal and Li, Zeyong and Obremski, Maciej and Saraogi, Sidhant},
  title =	{{Improved Lower Bounds for 3-Query Matching Vector Codes}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{2:1--2:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-361-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{325},
  editor =	{Meka, Raghu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2025.2},
  URN =		{urn:nbn:de:0030-drops-226308},
  doi =		{10.4230/LIPIcs.ITCS.2025.2},
  annote =	{Keywords: Locally Decodable Codes, Matching Vector Families}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2025.23
Accumulation Without Homomorphism

Authors: Benedikt Bünz, Pratyush Mishra, Wilson Nguyen, and William Wang

Published in: LIPIcs, Volume 325, 16th Innovations in Theoretical Computer Science Conference (ITCS 2025)

Abstract
Accumulation schemes are a simple yet powerful primitive that enable highly efficient constructions of incrementally verifiable computation (IVC). Unfortunately, all prior accumulation schemes rely on homomorphic vector commitments whose security is based on public-key assumptions. It is an interesting open question to construct efficient accumulation schemes that avoid the need for such assumptions. In this paper, we answer this question affirmatively by constructing an accumulation scheme from non-homomorphic vector commitments which can be realized from solely symmetric-key assumptions (e.g., Merkle trees). We overcome the need for homomorphisms by instead performing spot-checks over error-correcting encodings of the committed vectors. Unlike prior accumulation schemes, our scheme only supports a bounded number of accumulation steps. We show that such bounded-depth accumulation still suffices to construct proof-carrying data (a generalization of IVC). We also demonstrate several optimizations to our PCD construction which greatly improve concrete efficiency.
Cite as

Benedikt Bünz, Pratyush Mishra, Wilson Nguyen, and William Wang. Accumulation Without Homomorphism. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 23:1-23:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bunz_et_al:LIPIcs.ITCS.2025.23,
  author =	{B\"{u}nz, Benedikt and Mishra, Pratyush and Nguyen, Wilson and Wang, William},
  title =	{{Accumulation Without Homomorphism}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{23:1--23:25},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-361-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{325},
  editor =	{Meka, Raghu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2025.23},
  URN =		{urn:nbn:de:0030-drops-226510},
  doi =		{10.4230/LIPIcs.ITCS.2025.23},
  annote =	{Keywords: Proof-carrying data, incrementally verifiable computation, accumulation schemes}
}
Document
Survey
DOI: 10.4230/TGDK.1.1.4
Knowledge Graph Embeddings: Open Challenges and Opportunities

Authors: Russa Biswas, Lucie-Aimée Kaffee, Michael Cochez, Stefania Dumbrava, Theis E. Jendal, Matteo Lissandrini, Vanessa Lopez, Eneldo Loza Mencía, Heiko Paulheim, Harald Sack, Edlira Kalemi Vakaj, and Gerard de Melo

Published in: TGDK, Volume 1, Issue 1 (2023): Special Issue on Trends in Graph Data and Knowledge. Transactions on Graph Data and Knowledge, Volume 1, Issue 1

Abstract
While Knowledge Graphs (KGs) have long been used as valuable sources of structured knowledge, in recent years, KG embeddings have become a popular way of deriving numeric vector representations from them, for instance, to support knowledge graph completion and similarity search. This study surveys advances as well as open challenges and opportunities in this area. For instance, the most prominent embedding models focus primarily on structural information. However, there has been notable progress in incorporating further aspects, such as semantics, multi-modal, temporal, and multilingual features. Most embedding techniques are assessed using human-curated benchmark datasets for the task of link prediction, neglecting other important real-world KG applications. Many approaches assume a static knowledge graph and are unable to account for dynamic changes. Additionally, KG embeddings may encode data biases and lack interpretability. Overall, this study provides an overview of promising research avenues to learn improved KG embeddings that can address a more diverse range of use cases.
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Russa Biswas, Lucie-Aimée Kaffee, Michael Cochez, Stefania Dumbrava, Theis E. Jendal, Matteo Lissandrini, Vanessa Lopez, Eneldo Loza Mencía, Heiko Paulheim, Harald Sack, Edlira Kalemi Vakaj, and Gerard de Melo. Knowledge Graph Embeddings: Open Challenges and Opportunities. In Special Issue on Trends in Graph Data and Knowledge. Transactions on Graph Data and Knowledge (TGDK), Volume 1, Issue 1, pp. 4:1-4:32, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@Article{biswas_et_al:TGDK.1.1.4,
  author =	{Biswas, Russa and Kaffee, Lucie-Aim\'{e}e and Cochez, Michael and Dumbrava, Stefania and Jendal, Theis E. and Lissandrini, Matteo and Lopez, Vanessa and Menc{\'\i}a, Eneldo Loza and Paulheim, Heiko and Sack, Harald and Vakaj, Edlira Kalemi and de Melo, Gerard},
  title =	{{Knowledge Graph Embeddings: Open Challenges and Opportunities}},
  journal =	{Transactions on Graph Data and Knowledge},
  pages =	{4:1--4:32},
  year =	{2023},
  volume =	{1},
  number =	{1},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/TGDK.1.1.4},
  URN =		{urn:nbn:de:0030-drops-194783},
  doi =		{10.4230/TGDK.1.1.4},
  annote =	{Keywords: Knowledge Graphs, KG embeddings, Link prediction, KG applications}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2023.15
Oblivious Algorithms for the Max-kAND Problem

Authors: Noah G. Singer

Published in: LIPIcs, Volume 275, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023)

Abstract
Motivated by recent works on streaming algorithms for constraint satisfaction problems (CSPs), we define and analyze oblivious algorithms for the Max-kAND problem. This is a class of simple, combinatorial algorithms which round each variable with probability depending only on a quantity called the variable’s bias. Our definition generalizes a class of algorithms defined by Feige and Jozeph (Algorithmica '15) for Max-DICUT, a special case of Max-2AND. For each oblivious algorithm, we design a so-called factor-revealing linear program (LP) which captures its worst-case instance, generalizing one of Feige and Jozeph for Max-DICUT. Then, departing from their work, we perform a fully explicit analysis of these (infinitely many!) LPs. In particular, we show that for all k, oblivious algorithms for Max-kAND provably outperform a special subclass of algorithms we call "superoblivious" algorithms. Our result has implications for streaming algorithms: Generalizing the result for Max-DICUT of Saxena, Singer, Sudan, and Velusamy (SODA'23), we prove that certain separation results hold between streaming models for infinitely many CSPs: for every k, O(log n)-space sketching algorithms for Max-kAND known to be optimal in o(√n)-space can be beaten in (a) O(log n)-space under a random-ordering assumption, and (b) O(n^{1-1/k} D^{1/k}) space under a maximum-degree-D assumption. Even in the previously-known case of Max-DICUT, our analytic proof gives a fuller, computer-free picture of these separation results.
Cite as

Noah G. Singer. Oblivious Algorithms for the Max-kAND Problem. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 275, pp. 15:1-15:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{singer:LIPIcs.APPROX/RANDOM.2023.15,
  author =	{Singer, Noah G.},
  title =	{{Oblivious Algorithms for the Max-kAND Problem}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023)},
  pages =	{15:1--15:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-296-9},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{275},
  editor =	{Megow, Nicole and Smith, Adam},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2023.15},
  URN =		{urn:nbn:de:0030-drops-188409},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2023.15},
  annote =	{Keywords: streaming algorithm, approximation algorithm, constraint satisfaction problem (CSP), factor-revealing linear program}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2022.42
Bypassing the XOR Trick: Stronger Certificates for Hypergraph Clique Number

Authors: Venkatesan Guruswami, Pravesh K. Kothari, and Peter Manohar

Published in: LIPIcs, Volume 245, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)

Abstract
Let H(k,n,p) be the distribution on k-uniform hypergraphs where every subset of [n] of size k is included as an hyperedge with probability p independently. In this work, we design and analyze a simple spectral algorithm that certifies a bound on the size of the largest clique, ω(H), in hypergraphs H ∼ H(k,n,p). For example, for any constant p, with high probability over the choice of the hypergraph, our spectral algorithm certifies a bound of Õ(√n) on the clique number in polynomial time. This matches, up to polylog(n) factors, the best known certificate for the clique number in random graphs, which is the special case of k = 2. Prior to our work, the best known refutation algorithms [Amin Coja-Oghlan et al., 2004; Sarah R. Allen et al., 2015] rely on a reduction to the problem of refuting random k-XOR via Feige’s XOR trick [Uriel Feige, 2002], and yield a polynomially worse bound of Õ(n^{3/4}) on the clique number when p = O(1). Our algorithm bypasses the XOR trick and relies instead on a natural generalization of the Lovász theta semidefinite programming relaxation for cliques in hypergraphs.
Cite as

Venkatesan Guruswami, Pravesh K. Kothari, and Peter Manohar. Bypassing the XOR Trick: Stronger Certificates for Hypergraph Clique Number. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 245, pp. 42:1-42:7, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{guruswami_et_al:LIPIcs.APPROX/RANDOM.2022.42,
  author =	{Guruswami, Venkatesan and Kothari, Pravesh K. and Manohar, Peter},
  title =	{{Bypassing the XOR Trick: Stronger Certificates for Hypergraph Clique Number}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)},
  pages =	{42:1--42:7},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-249-5},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{245},
  editor =	{Chakrabarti, Amit and Swamy, Chaitanya},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2022.42},
  URN =		{urn:nbn:de:0030-drops-171642},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2022.42},
  annote =	{Keywords: Planted clique, Average-case complexity, Spectral refutation, Random matrix theory}
}
Document
DOI: 10.4230/LIPIcs.CCC.2022.7
𝓁_p-Spread and Restricted Isometry Properties of Sparse Random Matrices

Authors: Venkatesan Guruswami, Peter Manohar, and Jonathan Mosheiff

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

Abstract
Random subspaces X of ℝⁿ of dimension proportional to n are, with high probability, well-spread with respect to the 𝓁₂-norm. Namely, every nonzero x ∈ X is "robustly non-sparse" in the following sense: x is ε ‖x‖₂-far in 𝓁₂-distance from all δ n-sparse vectors, for positive constants ε, δ bounded away from 0. This "𝓁₂-spread" property is the natural counterpart, for subspaces over the reals, of the minimum distance of linear codes over finite fields, and corresponds to X being a Euclidean section of the 𝓁₁ unit ball. Explicit 𝓁₂-spread subspaces of dimension Ω(n), however, are unknown, and the best known explicit constructions (which achieve weaker spread properties), are analogs of low density parity check (LDPC) codes over the reals, i.e., they are kernels of certain sparse matrices. Motivated by this, we study the spread properties of the kernels of sparse random matrices. We prove that with high probability such subspaces contain vectors x that are o(1)⋅‖x‖₂-close to o(n)-sparse with respect to the 𝓁₂-norm, and in particular are not 𝓁₂-spread. This is strikingly different from the case of random LDPC codes, whose distance is asymptotically almost as good as that of (dense) random linear codes. On the other hand, for p < 2 we prove that such subspaces are 𝓁_p-spread with high probability. The spread property of sparse random matrices thus exhibits a threshold behavior at p = 2. Our proof for p < 2 moreover shows that a random sparse matrix has the stronger restricted isometry property (RIP) with respect to the 𝓁_p norm, and in fact this follows solely from the unique expansion of a random biregular graph, yielding a somewhat unexpected generalization of a similar result for the 𝓁₁ norm [Berinde et al., 2008]. Instantiating this with suitable explicit expanders, we obtain the first explicit constructions of 𝓁_p-RIP matrices for 1 ≤ p < p₀, where 1 < p₀ < 2 is an absolute constant.
Cite as

Venkatesan Guruswami, Peter Manohar, and Jonathan Mosheiff. 𝓁_p-Spread and Restricted Isometry Properties of Sparse Random Matrices. In 37th Computational Complexity Conference (CCC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 234, pp. 7:1-7:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{guruswami_et_al:LIPIcs.CCC.2022.7,
  author =	{Guruswami, Venkatesan and Manohar, Peter and Mosheiff, Jonathan},
  title =	{{𝓁\underlinep-Spread and Restricted Isometry Properties of Sparse Random Matrices}},
  booktitle =	{37th Computational Complexity Conference (CCC 2022)},
  pages =	{7:1--7:17},
  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.2022.7},
  URN =		{urn:nbn:de:0030-drops-165695},
  doi =		{10.4230/LIPIcs.CCC.2022.7},
  annote =	{Keywords: Spread Subspaces, Euclidean Sections, Restricted Isometry Property, Sparse Matrices}
}
Document
DOI: 10.4230/LIPIcs.CCC.2021.23
A Stress-Free Sum-Of-Squares Lower Bound for Coloring

Authors: Pravesh K. Kothari and Peter Manohar

Published in: LIPIcs, Volume 200, 36th Computational Complexity Conference (CCC 2021)

Abstract
We prove that with high probability over the choice of a random graph G from the Erdős-Rényi distribution G(n, 1/2), a natural n^{O(ε² log n)}-time, degree O(ε² log n) sum-of-squares semidefinite program cannot refute the existence of a valid k-coloring of G for k = n^{1/2 + ε}. Our result implies that the refutation guarantee of the basic semidefinite program (a close variant of the Lovász theta function) cannot be appreciably improved by a natural o(log n)-degree sum-of-squares strengthening, and this is tight up to a n^{o(1)} slack in k. To the best of our knowledge, this is the first lower bound for coloring G(n, 1/2) for even a single round strengthening of the basic SDP in any SDP hierarchy. Our proof relies on a new variant of instance-preserving non-pointwise complete reduction within SoS from coloring a graph to finding large independent sets in it. Our proof is (perhaps surprisingly) short, simple and does not require complicated spectral norm bounds on random matrices with dependent entries that have been otherwise necessary in the proofs of many similar results [Boaz Barak et al., 2016; S. B. {Hopkins} et al., 2017; Dmitriy Kunisky and Afonso S. Bandeira, 2019; Mrinalkanti Ghosh et al., 2020; Mohanty et al., 2020]. Our result formally holds for a constraint system where vertices are allowed to belong to multiple color classes; we leave the extension to the formally stronger formulation of coloring, where vertices must belong to unique colors classes, as an outstanding open problem.
Cite as

Pravesh K. Kothari and Peter Manohar. A Stress-Free Sum-Of-Squares Lower Bound for Coloring. In 36th Computational Complexity Conference (CCC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 200, pp. 23:1-23:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{kothari_et_al:LIPIcs.CCC.2021.23,
  author =	{Kothari, Pravesh K. and Manohar, Peter},
  title =	{{A Stress-Free Sum-Of-Squares Lower Bound for Coloring}},
  booktitle =	{36th Computational Complexity Conference (CCC 2021)},
  pages =	{23:1--23:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-193-1},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{200},
  editor =	{Kabanets, Valentine},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2021.23},
  URN =		{urn:nbn:de:0030-drops-142978},
  doi =		{10.4230/LIPIcs.CCC.2021.23},
  annote =	{Keywords: Sum-of-Squares, Graph Coloring, Independent Set, Lower Bounds}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2020.26
On Local Testability in the Non-Signaling Setting

Authors: Alessandro Chiesa, Peter Manohar, and Igor Shinkar

Published in: LIPIcs, Volume 151, 11th Innovations in Theoretical Computer Science Conference (ITCS 2020)

Abstract
Non-signaling strategies are a generalization of quantum strategies that have been studied in physics for decades, and have recently found applications in theoretical computer science. These applications motivate the study of local-to-global phenomena for non-signaling functions. We prove that low-degree testing in the non-signaling setting is possible, assuming that the locality of the non-signaling function exceeds a threshold. We additionally show that if the locality is below the threshold then the test fails spectacularly, in that there exists a non-signaling function which passes the test with probability 1 and yet is maximally far from being low-degree. Along the way, we present general results about the local testability of linear codes in the non-signaling setting. These include formulating natural definitions that capture the condition that a non-signaling function "belongs" to a given code, and characterizing the sets of local constraints that imply membership in the code. We prove these results by formulating a logical inference system for linear constraints on non-signaling functions that is complete and sound.
Cite as

Alessandro Chiesa, Peter Manohar, and Igor Shinkar. On Local Testability in the Non-Signaling Setting. In 11th Innovations in Theoretical Computer Science Conference (ITCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 151, pp. 26:1-26:37, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{chiesa_et_al:LIPIcs.ITCS.2020.26,
  author =	{Chiesa, Alessandro and Manohar, Peter and Shinkar, Igor},
  title =	{{On Local Testability in the Non-Signaling Setting}},
  booktitle =	{11th Innovations in Theoretical Computer Science Conference (ITCS 2020)},
  pages =	{26:1--26:37},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-134-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{151},
  editor =	{Vidick, Thomas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2020.26},
  URN =		{urn:nbn:de:0030-drops-117112},
  doi =		{10.4230/LIPIcs.ITCS.2020.26},
  annote =	{Keywords: non-signaling strategies, locally testable codes, low-degree testing, Fourier analysis}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2019.25
Probabilistic Checking Against Non-Signaling Strategies from Linearity Testing

Authors: Alessandro Chiesa, Peter Manohar, and Igor Shinkar

Published in: LIPIcs, Volume 124, 10th Innovations in Theoretical Computer Science Conference (ITCS 2019)

Abstract
Non-signaling strategies are a generalization of quantum strategies that have been studied in physics over the past three decades. Recently, they have found applications in theoretical computer science, including to proving inapproximability results for linear programming and to constructing protocols for delegating computation. A central tool for these applications is probabilistically checkable proofs (PCPs) that are sound against non-signaling strategies. In this paper we prove that the exponential-length constant-query PCP construction due to Arora et al. (JACM 1998) is sound against non-signaling strategies. Our result offers a new length-vs-query tradeoff when compared to the non-signaling PCP of Kalai, Raz, and Rothblum (STOC 2013 and 2014) and, moreover, may serve as an intermediate step to a proof of a non-signaling analogue of the PCP Theorem.
Cite as

Alessandro Chiesa, Peter Manohar, and Igor Shinkar. Probabilistic Checking Against Non-Signaling Strategies from Linearity Testing. In 10th Innovations in Theoretical Computer Science Conference (ITCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 124, pp. 25:1-25:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{chiesa_et_al:LIPIcs.ITCS.2019.25,
  author =	{Chiesa, Alessandro and Manohar, Peter and Shinkar, Igor},
  title =	{{Probabilistic Checking Against Non-Signaling Strategies from Linearity Testing}},
  booktitle =	{10th Innovations in Theoretical Computer Science Conference (ITCS 2019)},
  pages =	{25:1--25:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-095-8},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{124},
  editor =	{Blum, Avrim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2019.25},
  URN =		{urn:nbn:de:0030-drops-101188},
  doi =		{10.4230/LIPIcs.ITCS.2019.25},
  annote =	{Keywords: probabilistically checkable proofs, linearity testing, non-signaling strategies}
}
Document
DOI: 10.4230/LIPIcs.CCC.2018.17
Testing Linearity against Non-Signaling Strategies

Authors: Alessandro Chiesa, Peter Manohar, and Igor Shinkar

Published in: LIPIcs, Volume 102, 33rd Computational Complexity Conference (CCC 2018)

Abstract
Non-signaling strategies are collections of distributions with certain non-local correlations. They have been studied in Physics as a strict generalization of quantum strategies to understand the power and limitations of Nature's apparent non-locality. Recently, they have received attention in Theoretical Computer Science due to connections to Complexity and Cryptography. We initiate the study of Property Testing against non-signaling strategies, focusing first on the classical problem of linearity testing (Blum, Luby, and Rubinfeld; JCSS 1993). We prove that any non-signaling strategy that passes the linearity test with high probability must be close to a quasi-distribution over linear functions. Quasi-distributions generalize the notion of probability distributions over global objects (such as functions) by allowing negative probabilities, while at the same time requiring that "local views" follow standard distributions (with non-negative probabilities). Quasi-distributions arise naturally in the study of Quantum Mechanics as a tool to describe various non-local phenomena. Our analysis of the linearity test relies on Fourier analytic techniques applied to quasi-distributions. Along the way, we also establish general equivalences between non-signaling strategies and quasi-distributions, which we believe will provide a useful perspective on the study of Property Testing against non-signaling strategies beyond linearity testing.
Cite as

Alessandro Chiesa, Peter Manohar, and Igor Shinkar. Testing Linearity against Non-Signaling Strategies. In 33rd Computational Complexity Conference (CCC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 102, pp. 17:1-17:37, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{chiesa_et_al:LIPIcs.CCC.2018.17,
  author =	{Chiesa, Alessandro and Manohar, Peter and Shinkar, Igor},
  title =	{{Testing Linearity against Non-Signaling Strategies}},
  booktitle =	{33rd Computational Complexity Conference (CCC 2018)},
  pages =	{17:1--17:37},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-069-9},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{102},
  editor =	{Servedio, Rocco A.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2018.17},
  URN =		{urn:nbn:de:0030-drops-88731},
  doi =		{10.4230/LIPIcs.CCC.2018.17},
  annote =	{Keywords: property testing, linearity testing, non-signaling strategies, quasi-distributions}
}
Document
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2017.39
On Axis-Parallel Tests for Tensor Product Codes

Authors: Alessandro Chiesa, Peter Manohar, and Igor Shinkar

Published in: LIPIcs, Volume 81, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017)

Abstract
Many low-degree tests examine the input function via its restrictions to random hyperplanes of a certain dimension. Examples include the line-vs-line (Arora, Sudan 2003), plane-vs-plane (Raz, Safra 1997), and cube-vs-cube (Bhangale, Dinur, Livni 2017) tests. In this paper we study tests that only consider restrictions along axis-parallel hyperplanes, which have been studied by Polishchuk and Spielman (1994) and Ben-Sasson and Sudan (2006). While such tests are necessarily "weaker", they work for a more general class of codes, namely tensor product codes. Moreover, axis-parallel tests play a key role in constructing LTCs with inverse polylogarithmic rate and short PCPs (Polishchuk, Spielman 1994; Ben-Sasson, Sudan 2008; Meir 2010). We present two results on axis-parallel tests. (1) Bivariate low-degree testing with low-agreement. We prove an analogue of the Bivariate Low-Degree Testing Theorem of Polishchuk and Spielman in the low-agreement regime, albeit with much larger field size. Namely, for the 2-wise tensor product of the Reed-Solomon code, we prove that for sufficiently large fields, the 2-query variant of the axis-parallel line test (row-vs-column test) works for arbitrarily small agreement. Prior analyses of axis-parallel tests assumed high agreement, and no results for such tests in the low-agreement regime were known. Our proof technique deviates significantly from that of Polishchuk and Spielman, which relies on algebraic methods such as Bezout's Theorem, and instead leverages a fundamental result in extremal graph theory by Kovari, Sos, and Turan. To our knowledge, this is the first time this result is used in the context of low-degree testing. (2) Improved robustness for tensor product codes. Robustness is a strengthening of local testability that underlies many applications. We prove that the axis-parallel hyperplane test for the m-wise tensor product of a linear code with block length n and distance d is Omega(d^m/n^m)-robust. This improves on a theorem of Viderman (2012) by a factor of 1/poly(m). While the improvement is not large, we believe that our proof is a notable simplification compared to prior work.
Cite as

Alessandro Chiesa, Peter Manohar, and Igor Shinkar. On Axis-Parallel Tests for Tensor Product Codes. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 81, pp. 39:1-39:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{chiesa_et_al:LIPIcs.APPROX-RANDOM.2017.39,
  author =	{Chiesa, Alessandro and Manohar, Peter and Shinkar, Igor},
  title =	{{On Axis-Parallel Tests for Tensor Product Codes}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017)},
  pages =	{39:1--39:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-044-6},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{81},
  editor =	{Jansen, Klaus and Rolim, Jos\'{e} D. P. and Williamson, David P. and Vempala, Santosh S.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2017.39},
  URN =		{urn:nbn:de:0030-drops-75882},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2017.39},
  annote =	{Keywords: tensor product codes, locally testable codes, low-degree testing, extremal graph theory}
}
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