9 Search Results for "Black, Timothy J. F."

Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.40
Sublinear Space Graph Algorithms in the Continual Release Model

Authors: Alessandro Epasto, Quanquan C. Liu, Tamalika Mukherjee, and Felix Zhou

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

Abstract
The graph continual release model of differential privacy seeks to produce differentially private solutions to graph problems under a stream of edge updates where new private solutions are released after each update. Thus far, previously known edge-differentially private algorithms for most graph problems including densest subgraph and matchings in the continual release setting only output real-value estimates (not vertex subset solutions) and do not use sublinear space. Instead, they rely on computing exact graph statistics on the input [Hendrik Fichtenberger et al., 2021; Shuang Song et al., 2018]. In this paper, we leverage sparsification to address the above shortcomings for edge-insertion streams. Our edge-differentially private algorithms use sublinear space with respect to the number of edges in the graph while some also achieve sublinear space in the number of vertices in the graph. In addition, for the densest subgraph problem, we also output edge-differentially private vertex subset solutions; no previous graph algorithms in the continual release model output such subsets. We make novel use of assorted sparsification techniques from the non-private streaming and static graph algorithms literature to achieve new results in the sublinear space, continual release setting. This includes algorithms for densest subgraph, maximum matching, as well as the first continual release k-core decomposition algorithm. We also develop a novel sparse level data structure for k-core decomposition that may be of independent interest. To complement our insertion-only algorithms, we conclude with polynomial additive error lower bounds for edge-privacy in the fully dynamic setting, where only logarithmic lower bounds were previously known.
Cite as

Alessandro Epasto, Quanquan C. Liu, Tamalika Mukherjee, and Felix Zhou. Sublinear Space Graph Algorithms in the Continual Release Model. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 40:1-40:27, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{epasto_et_al:LIPIcs.APPROX/RANDOM.2025.40,
  author =	{Epasto, Alessandro and Liu, Quanquan C. and Mukherjee, Tamalika and Zhou, Felix},
  title =	{{Sublinear Space Graph Algorithms in the Continual Release Model}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{40:1--40:27},
  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.2025.40},
  URN =		{urn:nbn:de:0030-drops-244064},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.40},
  annote =	{Keywords: Differential Privacy, Continual Release, Densest Subgraph, k-Core Decomposition, Maximum Matching}
}
Document
DOI: 10.4230/LIPIcs.TQC.2025.9
Efficient Quantum Pseudorandomness from Hamiltonian Phase States

Authors: John Bostanci, Jonas Haferkamp, Dominik Hangleiter, and Alexander Poremba

Published in: LIPIcs, Volume 350, 20th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2025)

Abstract
Quantum pseudorandomness has found applications in many areas of quantum information, ranging from entanglement theory, to models of scrambling phenomena in chaotic quantum systems, and, more recently, in the foundations of quantum cryptography. Kretschmer (TQC '21) showed that both pseudorandom states and pseudorandom unitaries exist even in a world without classical one-way functions. To this day, however, all known constructions require classical cryptographic building blocks which are themselves synonymous with the existence of one-way functions, and which are also challenging to implement on realistic quantum hardware. In this work, we seek to make progress on both of these fronts simultaneously - by decoupling quantum pseudorandomness from classical cryptography altogether. We introduce a quantum hardness assumption called the Hamiltonian Phase State (HPS) problem, which is the task of decoding output states of a random instantaneous quantum polynomial-time (IQP) circuit. Hamiltonian phase states can be generated very efficiently using only Hadamard gates, single-qubit Z rotations and CNOT circuits. We show that the hardness of our problem reduces to a worst-case version of the problem, and we provide evidence that our assumption is plausibly fully quantum; meaning, it cannot be used to construct one-way functions. We also show information-theoretic hardness when only few copies of HPS are available by proving an approximate t-design property of our ensemble. Finally, we show that our HPS assumption and its variants allow us to efficiently construct many pseudorandom quantum primitives, ranging from pseudorandom states, to quantum pseudoentanglement, to pseudorandom unitaries, and even primitives such as public-key encryption with quantum keys.
Cite as

John Bostanci, Jonas Haferkamp, Dominik Hangleiter, and Alexander Poremba. Efficient Quantum Pseudorandomness from Hamiltonian Phase States. In 20th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 350, pp. 9:1-9:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bostanci_et_al:LIPIcs.TQC.2025.9,
  author =	{Bostanci, John and Haferkamp, Jonas and Hangleiter, Dominik and Poremba, Alexander},
  title =	{{Efficient Quantum Pseudorandomness from Hamiltonian Phase States}},
  booktitle =	{20th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2025)},
  pages =	{9:1--9:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-392-8},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{350},
  editor =	{Fefferman, Bill},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2025.9},
  URN =		{urn:nbn:de:0030-drops-240586},
  doi =		{10.4230/LIPIcs.TQC.2025.9},
  annote =	{Keywords: Quantum pseudorandomness, quantum phase states, quantum cryptography}
}
Document
DOI: 10.4230/LIPIcs.ECRTS.2025.21
Hardware Compute Partitioning on NVIDIA GPUs for Composable Systems

Authors: Joshua Bakita and James H. Anderson

Published in: LIPIcs, Volume 335, 37th Euromicro Conference on Real-Time Systems (ECRTS 2025)

Abstract
As GPU-using tasks become more common in embedded, safety-critical systems, efficiency demands necessitate sharing a single GPU among multiple tasks. Unfortunately, existing ways to schedule multiple tasks onto a GPU often either result in a loss of ability to meet deadlines, or a loss of efficiency. In this work, we develop a system-level spatial compute partitioning mechanism for NVIDIA GPUs and demonstrate that it can be used to execute tasks efficiently without compromising timing predictability. Our tool, called nvtaskset, supports composable systems by not requiring task, driver, or hardware modifications. In our evaluation, we demonstrate sub-1-μs overheads, stronger partition enforcement, and finer-granularity partitioning when using our mechanism instead of NVIDIA’s Multi-Process Service (MPS) or Multi-instance GPU (MiG) features.
Cite as

Joshua Bakita and James H. Anderson. Hardware Compute Partitioning on NVIDIA GPUs for Composable Systems. In 37th Euromicro Conference on Real-Time Systems (ECRTS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 335, pp. 21:1-21:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bakita_et_al:LIPIcs.ECRTS.2025.21,
  author =	{Bakita, Joshua and Anderson, James H.},
  title =	{{Hardware Compute Partitioning on NVIDIA GPUs for Composable Systems}},
  booktitle =	{37th Euromicro Conference on Real-Time Systems (ECRTS 2025)},
  pages =	{21:1--21:25},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-377-5},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{335},
  editor =	{Mancuso, Renato},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECRTS.2025.21},
  URN =		{urn:nbn:de:0030-drops-235998},
  doi =		{10.4230/LIPIcs.ECRTS.2025.21},
  annote =	{Keywords: Real-time systems, composable systems, graphics processing units, CUDA}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.23
On the Instance Optimality of Detecting Collisions and Subgraphs

Authors: Omri Ben-Eliezer, Tomer Grossman, and Moni Naor

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

Abstract
Suppose you are given a function f: [n] → [n] via (black-box) query access to the function. You are looking to find something local, like a collision (a pair x ≠ y s.t. f(x) = f(y)). The question is whether knowing the "shape" of the function helps you or not (by shape we mean that some permutation of the function is known). Formally, we investigate the unlabeled instance optimality of substructure detection problems in graphs and functions. A problem is g(n)-instance optimal if it admits an algorithm A satisfying that for any possible input, the (randomized) query complexity of A is at most g(n) times larger than the query complexity of any algorithm A' which solves the same problem while holding an unlabeled copy of the input (i.e., any A' that "knows the structure of the input"). Our results point to a trichotomy of unlabeled instance optimality among substructure detection problems in graphs and functions: - A few very simple properties have an O(1)-instance optimal algorithm. - Most properties of graphs and functions, with examples such as containing a fixed point or a 3-collision in functions, or a triangle in graphs, are n^{c}-far from instance optimal for some constant c > 0. - The problems of collision detection in functions and finding a claw in a graph serve as a middle ground between the two regimes. We show that these two properties are not Ω(log n)-instance optimal, and conjecture that this bound is tight. We provide evidence towards this conjecture, by proving that finding a claw in a graph is O(log(n))-instance optimal among all input graphs for which the query complexity of an algorithm holding an unlabeled certificate is O(√{n/(log n)}).
Cite as

Omri Ben-Eliezer, Tomer Grossman, and Moni Naor. On the Instance Optimality of Detecting Collisions and Subgraphs. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 23:1-23:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{beneliezer_et_al:LIPIcs.ICALP.2025.23,
  author =	{Ben-Eliezer, Omri and Grossman, Tomer and Naor, Moni},
  title =	{{On the Instance Optimality of Detecting Collisions and Subgraphs}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{23:1--23:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.23},
  URN =		{urn:nbn:de:0030-drops-234002},
  doi =		{10.4230/LIPIcs.ICALP.2025.23},
  annote =	{Keywords: instance optimality, instance complexity, unlabeled certificate, subgraph detection, collision detection}
}
Document
DOI: 10.4230/LIPIcs.FORC.2025.4
Hardness and Approximation Algorithms for Balanced Districting Problems

Authors: Prathamesh Dharangutte, Jie Gao, Shang-En Huang, and Fang-Yi Yu

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

Abstract
We introduce and study the problem of balanced districting, where given an undirected graph with vertices carrying two types of weights (different population, resource types, etc) the goal is to maximize the total weights covered in vertex disjoint districts such that each district is a star or (in general) a connected induced subgraph with the two weights to be balanced. This problem is strongly motivated by political redistricting, where contiguity, population balance, and compactness are essential. We provide hardness and approximation algorithms for this problem. In particular, we show NP-hardness for an approximation better than n^{1/2-δ} for any constant δ > 0 in general graphs even when the districts are star graphs, as well as NP-hardness on complete graphs, tree graphs, planar graphs and other restricted settings. On the other hand, we develop an algorithm for balanced star districting that gives an O(√n)-approximation on any graph (which is basically tight considering matching hardness of approximation results), an O(log n) approximation on planar graphs with extensions to minor-free graphs. Our algorithm uses a modified Whack-a-Mole algorithm [Bhattacharya, Kiss, and Saranurak, SODA 2023] to find a sparse solution of a fractional packing linear program (despite exponentially many variables) which requires a new design of a separation oracle specific for our balanced districting problem. To turn the fractional solution to a feasible integer solution, we adopt the randomized rounding algorithm by [Chan and Har-Peled, SoCG 2009]. To get a good approximation ratio of the rounding procedure, a crucial element in the analysis is the balanced scattering separators for planar graphs and minor-free graphs - separators that can be partitioned into a small number of k-hop independent sets for some constant k - which may find independent interest in solving other packing style problems. Further, our algorithm is versatile - the very same algorithm can be analyzed in different ways on various graph classes, which leads to class-dependent approximation ratios. We also provide a FPTAS algorithm for complete graphs and tree graphs, as well as greedy algorithms and approximation ratios when the district cardinality is bounded, the graph has bounded degree or the weights are binary. We refer the readers to the full version of the paper for complete set of results and proofs.
Cite as

Prathamesh Dharangutte, Jie Gao, Shang-En Huang, and Fang-Yi Yu. Hardness and Approximation Algorithms for Balanced Districting Problems. In 6th Symposium on Foundations of Responsible Computing (FORC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 329, pp. 4:1-4:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{dharangutte_et_al:LIPIcs.FORC.2025.4,
  author =	{Dharangutte, Prathamesh and Gao, Jie and Huang, Shang-En and Yu, Fang-Yi},
  title =	{{Hardness and Approximation Algorithms for Balanced Districting Problems}},
  booktitle =	{6th Symposium on Foundations of Responsible Computing (FORC 2025)},
  pages =	{4:1--4:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-367-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{329},
  editor =	{Bun, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FORC.2025.4},
  URN =		{urn:nbn:de:0030-drops-231310},
  doi =		{10.4230/LIPIcs.FORC.2025.4},
  annote =	{Keywords: Approximation algorithms, algorithmic fairness}
}
Document
DOI: 10.4230/LIPIcs.SAND.2025.4
On b-Matching and Fully-Dynamic Maximum k-Edge Coloring

Authors: Antoine El-Hayek, Kathrin Hanauer, and Monika Henzinger

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

Abstract
Given a graph G that undergoes a sequence of edge insertions and deletions, we study the Maximum k-Edge Coloring problem (MkEC): Having access to k different colors, color as many edges of G as possible such that no two adjacent edges share the same color. While this problem is different from simply maintaining a b-matching with b = k, the two problems are related. However, maximum b-matching can be solved efficiently in the static setting, whereas MkEC is NP-hard and even APX-hard for k ≥ 2. We present new results on both problems: For b-matching, we show a new integrality gap result and we adapt Wajc’s matching sparsification scheme [David Wajc, 2020] for the case where b is a constant. Using these as basis, we give three new algorithms for the dynamic MkEC problem: Our MatchO algorithm builds on the dynamic (2+ε)-approximation algorithm of Bhattacharya, Gupta, and Mohan [Sayan Bhattacharya et al., 2017] for b-matching and achieves a (2+ε)(k+1)/k-approximation in O(poly(log n, ε^-1)) update time against an oblivious adversary. Our MatchA algorithm builds on the dynamic (7+ε)-approximation algorithm by Bhattacharya, Henzinger, and Italiano [Sayan Bhattacharya et al., 2015] for fractional b-matching and achieves a (7+ε)(3k+3)/(3k-1)-approximation in O(poly(log n, ε^-1)) update time against an adaptive adversary. Moreover, our reductions use the dynamic b-matching algorithm as a black box, so any future improvement in the approximation ratio for dynamic b-matching will automatically translate into a better approximation ratio for our algorithms. Finally, we present a greedy algorithm with O(Δ+k) update time, which guarantees a 2.16 approximation factor.
Cite as

Antoine El-Hayek, Kathrin Hanauer, and Monika Henzinger. On b-Matching and Fully-Dynamic Maximum k-Edge Coloring. In 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 330, pp. 4:1-4:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{elhayek_et_al:LIPIcs.SAND.2025.4,
  author =	{El-Hayek, Antoine and Hanauer, Kathrin and Henzinger, Monika},
  title =	{{On b-Matching and Fully-Dynamic Maximum k-Edge Coloring}},
  booktitle =	{4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025)},
  pages =	{4:1--4:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-368-3},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{330},
  editor =	{Meeks, Kitty and Scheideler, Christian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2025.4},
  URN =		{urn:nbn:de:0030-drops-230571},
  doi =		{10.4230/LIPIcs.SAND.2025.4},
  annote =	{Keywords: dynamic algorithm, graph algorithm, matching, b-matching, edge coloring}
}
Document
DOI: 10.4230/LIPIcs.OPODIS.2024.20
How Robust Are Synchronous Consensus Protocols?

Authors: Nenad Milošević, Daniel Cason, Zarko Milošević, and Fernando Pedone

Published in: LIPIcs, Volume 324, 28th International Conference on Principles of Distributed Systems (OPODIS 2024)

Abstract
Synchronous Byzantine fault-tolerant (BFT) protocols have long been a reality in an academic setting, yet their practicality remains debated. The main concern of skeptics of synchronous systems is that the correctness of these protocols depends on the timely delivery of all messages within a predefined synchronous bound, Δ. This dependency creates a challenging tradeoff between protocol correctness and performance, as Δ directly impacts both. In this paper, we examine this tradeoff in detail. Specifically, we introduce BoundBFT, a new synchronous BFT consensus protocol. We analyze how BoundBFT’s correctness can be compromised and use this analysis to design and implement the most effective attack strategies that malicious processes could employ. Furthermore, we experimentally determine the synchronous bound Δ that provides sufficient confidence in maintaining protocol correctness even in the presence of malicious replicas. Finally, we apply this discovered bound to BoundBFT, evaluate its performance, and compare it to state-of-the-art synchronous and partially synchronous protocols.
Cite as

Nenad Milošević, Daniel Cason, Zarko Milošević, and Fernando Pedone. How Robust Are Synchronous Consensus Protocols?. In 28th International Conference on Principles of Distributed Systems (OPODIS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 324, pp. 20:1-20:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{milosevic_et_al:LIPIcs.OPODIS.2024.20,
  author =	{Milo\v{s}evi\'{c}, Nenad and Cason, Daniel and Milo\v{s}evi\'{c}, Zarko and Pedone, Fernando},
  title =	{{How Robust Are Synchronous Consensus Protocols?}},
  booktitle =	{28th International Conference on Principles of Distributed Systems (OPODIS 2024)},
  pages =	{20:1--20:25},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-360-7},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{324},
  editor =	{Bonomi, Silvia and Galletta, Letterio and Rivi\`{e}re, Etienne and Schiavoni, Valerio},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2024.20},
  URN =		{urn:nbn:de:0030-drops-225560},
  doi =		{10.4230/LIPIcs.OPODIS.2024.20},
  annote =	{Keywords: Synchronous Consensus, Byzantine Failures, Blockchain}
}
Document
Vision
DOI: 10.4230/TGDK.1.1.8
Machine Learning and Knowledge Graphs: Existing Gaps and Future Research Challenges

Authors: Claudia d'Amato, Louis Mahon, Pierre Monnin, and Giorgos Stamou

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
The graph model is nowadays largely adopted to model a wide range of knowledge and data, spanning from social networks to knowledge graphs (KGs), representing a successful paradigm of how symbolic and transparent AI can scale on the World Wide Web. However, due to their unprecedented volume, they are generally tackled by Machine Learning (ML) and mostly numeric based methods such as graph embedding models (KGE) and deep neural networks (DNNs). The latter methods have been proved lately very efficient, leading the current AI spring. In this vision paper, we introduce some of the main existing methods for combining KGs and ML, divided into two categories: those using ML to improve KGs, and those using KGs to improve results on ML tasks. From this introduction, we highlight research gaps and perspectives that we deem promising and currently under-explored for the involved research communities, spanning from KG support for LLM prompting, integration of KG semantics in ML models to symbol-based methods, interpretability of ML models, and the need for improved benchmark datasets. In our opinion, such perspectives are stepping stones in an ultimate view of KGs as central assets for neuro-symbolic and explainable AI.
Cite as

Claudia d'Amato, Louis Mahon, Pierre Monnin, and Giorgos Stamou. Machine Learning and Knowledge Graphs: Existing Gaps and Future Research Challenges. In Special Issue on Trends in Graph Data and Knowledge. Transactions on Graph Data and Knowledge (TGDK), Volume 1, Issue 1, pp. 8:1-8:35, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@Article{damato_et_al:TGDK.1.1.8,
  author =	{d'Amato, Claudia and Mahon, Louis and Monnin, Pierre and Stamou, Giorgos},
  title =	{{Machine Learning and Knowledge Graphs: Existing Gaps and Future Research Challenges}},
  journal =	{Transactions on Graph Data and Knowledge},
  pages =	{8:1--8:35},
  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.1.1.8},
  URN =		{urn:nbn:de:0030-drops-194824},
  doi =		{10.4230/TGDK.1.1.8},
  annote =	{Keywords: Graph-based Learning, Knowledge Graph Embeddings, Large Language Models, Explainable AI, Knowledge Graph Completion \& Curation}
}
Document
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2018.29
List-Decoding Homomorphism Codes with Arbitrary Codomains

Authors: László Babai, Timothy J. F. Black, and Angela Wuu

Published in: LIPIcs, Volume 116, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018)

Abstract
The codewords of the homomorphism code aHom(G,H) are the affine homomorphisms between two finite groups, G and H, generalizing Hadamard codes. Following the work of Goldreich-Levin (1989), Grigorescu et al. (2006), Dinur et al. (2008), and Guo and Sudan (2014), we further expand the range of groups for which local list-decoding is possible up to mindist, the minimum distance of the code. In particular, for the first time, we do not require either G or H to be solvable. Specifically, we demonstrate a poly(1/epsilon) bound on the list size, i. e., on the number of codewords within distance (mindist-epsilon) from any received word, when G is either abelian or an alternating group, and H is an arbitrary (finite or infinite) group. We conjecture that a similar bound holds for all finite simple groups as domains; the alternating groups serve as the first test case. The abelian vs. arbitrary result permits us to adapt previous techniques to obtain efficient local list-decoding for this case. We also obtain efficient local list-decoding for the permutation representations of alternating groups (the codomain is a symmetric group) under the restriction that the domain G=A_n is paired with codomain H=S_m satisfying m < 2^{n-1}/sqrt{n}. The limitations on the codomain in the latter case arise from severe technical difficulties stemming from the need to solve the homomorphism extension (HomExt) problem in certain cases; these are addressed in a separate paper (Wuu 2018). We introduce an intermediate "semi-algorithmic" model we call Certificate List-Decoding that bypasses the HomExt bottleneck and works in the alternating vs. arbitrary setting. A certificate list-decoder produces partial homomorphisms that uniquely extend to the homomorphisms in the list. A homomorphism extender applied to a list of certificates yields the desired list.
Cite as

László Babai, Timothy J. F. Black, and Angela Wuu. List-Decoding Homomorphism Codes with Arbitrary Codomains. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 116, pp. 29:1-29:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{babai_et_al:LIPIcs.APPROX-RANDOM.2018.29,
  author =	{Babai, L\'{a}szl\'{o} and Black, Timothy J. F. and Wuu, Angela},
  title =	{{List-Decoding Homomorphism Codes with Arbitrary Codomains}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018)},
  pages =	{29:1--29:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-085-9},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{116},
  editor =	{Blais, Eric and Jansen, Klaus and D. P. Rolim, Jos\'{e} and Steurer, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2018.29},
  URN =		{urn:nbn:de:0030-drops-94338},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2018.29},
  annote =	{Keywords: Error-correcting codes, Local algorithms, Local list-decoding, Finite groups, Homomorphism codes}
}
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