11 Search Results for "Anderson, Matthew"

Document
DOI: 10.4230/LIPIcs.ECOOP.2024.15
Rose: Composable Autodiff for the Interactive Web

Authors: Sam Estep, Wode Ni, Raven Rothkopf, and Joshua Sunshine

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

Abstract
Reverse-mode automatic differentiation (autodiff) has been popularized by deep learning, but its ability to compute gradients is also valuable for interactive use cases such as bidirectional computer-aided design, embedded physics simulations, visualizing causal inference, and more. Unfortunately, the web is ill-served by existing autodiff frameworks, which use autodiff strategies that perform poorly on dynamic scalar programs, and pull in heavy dependencies that would result in unacceptable webpage sizes. This work introduces Rose, a lightweight autodiff framework for the web using a new hybrid approach to reverse-mode autodiff, blending conventional tracing and transformation techniques in a way that uses the host language for metaprogramming while also allowing the programmer to explicitly define reusable functions that comprise a larger differentiable computation. We demonstrate the value of the Rose design by porting two differentiable physics simulations, and evaluate its performance on an optimization-based diagramming application, showing Rose outperforming the state-of-the-art in web-based autodiff by multiple orders of magnitude.
Cite as

Sam Estep, Wode Ni, Raven Rothkopf, and Joshua Sunshine. Rose: Composable Autodiff for the Interactive Web. In 38th European Conference on Object-Oriented Programming (ECOOP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 313, pp. 15:1-15:27, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{estep_et_al:LIPIcs.ECOOP.2024.15,
  author =	{Estep, Sam and Ni, Wode and Rothkopf, Raven and Sunshine, Joshua},
  title =	{{Rose: Composable Autodiff for the Interactive Web}},
  booktitle =	{38th European Conference on Object-Oriented Programming (ECOOP 2024)},
  pages =	{15:1--15:27},
  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.2024.15},
  URN =		{urn:nbn:de:0030-drops-208642},
  doi =		{10.4230/LIPIcs.ECOOP.2024.15},
  annote =	{Keywords: Automatic differentiation, differentiable programming, compilers, web}
}
Document
DOI: 10.4230/LIPIcs.ECOOP.2024.21
Learning Gradual Typing Performance

Authors: Mohammad Wahiduzzaman Khan, Sheng Chen, and Yi He

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

Abstract
Gradual typing has emerged as a promising typing discipline for reconciling static and dynamic typing, which have respective strengths and shortcomings. Thanks to its promises, gradual typing has gained tremendous momentum in both industry and academia. A main challenge in gradual typing is that, however, the performance of its programs can often be unpredictable, and adding or removing the type of a a single parameter may lead to wild performance swings. Many approaches have been proposed to optimize gradual typing performance, but little work has been done to aid the understanding of the performance landscape of gradual typing and navigating the migration process (which adds type annotations to make programs more static) to avert performance slowdowns. Motivated by this situation, this work develops a machine-learning-based approach to predict the performance of each possible way of adding type annotations to a program. On top of that, many supports for program migrations could be developed, such as finding the most performant neighbor of any given configuration. Our approach gauges runtime overheads of dynamic type checks inserted by gradual typing and uses that information to train a machine learning model, which is used to predict the running time of gradual programs. We have evaluated our approach on 12 Python benchmarks for both guarded and transient semantics. For guarded semantics, our evaluation results indicate that with only 40 training instances generated from each benchmark, the predicted times for all other instances differ on average by 4% from the measured times. For transient semantics, the time difference ratio is higher but the time difference is often within 0.1 seconds.
Cite as

Mohammad Wahiduzzaman Khan, Sheng Chen, and Yi He. Learning Gradual Typing Performance. In 38th European Conference on Object-Oriented Programming (ECOOP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 313, pp. 21:1-21:27, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{khan_et_al:LIPIcs.ECOOP.2024.21,
  author =	{Khan, Mohammad Wahiduzzaman and Chen, Sheng and He, Yi},
  title =	{{Learning Gradual Typing Performance}},
  booktitle =	{38th European Conference on Object-Oriented Programming (ECOOP 2024)},
  pages =	{21:1--21:27},
  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.2024.21},
  URN =		{urn:nbn:de:0030-drops-208706},
  doi =		{10.4230/LIPIcs.ECOOP.2024.21},
  annote =	{Keywords: Gradual typing performance, type migration, performance prediction, machine learning}
}
Document
DOI: 10.4230/LIPIcs.ECOOP.2024.29
Generalizing Shape Analysis with Gradual Types

Authors: Zeina Migeed, James Reed, Jason Ansel, and Jens Palsberg

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

Abstract
Tensors are multi-dimensional data structures that can represent the data processed by machine learning tasks. Tensor programs tend to be short and readable, and they can leverage libraries and frameworks such as TensorFlow and PyTorch, as well as modern hardware such as GPUs and TPUs. However, tensor programs also tend to obscure shape information, which can cause shape errors that are difficult to find. Such shape errors can be avoided by a combination of shape annotations and shape analysis, but such annotations are burdensome to come up with manually. In this paper, we use gradual typing to reduce the barrier of entry. Gradual typing offers a way to incrementally introduce type annotations into programs. From there, we focus on tool support for type migration, which is a concept that closely models code-annotation tasks and allows us to do shape reasoning and utilize it for different purposes. We develop a comprehensive gradual typing theory to reason about tensor shapes. We then ask three fundamental questions about a gradually typed tensor program. (1) Does the program have a static migration? (2) Given a program and some arithmetic constraints on shapes, can we migrate the program according to the constraints? (3) Can we eliminate branches that depend on shapes? We develop novel tools to address the three problems. For the third problem, there are currently two PyTorch tools that aim to eliminate branches. They do so by eliminating them for just a single input. Our tool is the first to eliminate branches for an infinite class of inputs, using static shape information. Our tools help prevent bugs, alleviate the burden on the programmer of annotating the program, and improves the process of program transformation.
Cite as

Zeina Migeed, James Reed, Jason Ansel, and Jens Palsberg. Generalizing Shape Analysis with Gradual Types. In 38th European Conference on Object-Oriented Programming (ECOOP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 313, pp. 29:1-29:28, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{migeed_et_al:LIPIcs.ECOOP.2024.29,
  author =	{Migeed, Zeina and Reed, James and Ansel, Jason and Palsberg, Jens},
  title =	{{Generalizing Shape Analysis with Gradual Types}},
  booktitle =	{38th European Conference on Object-Oriented Programming (ECOOP 2024)},
  pages =	{29:1--29:28},
  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.2024.29},
  URN =		{urn:nbn:de:0030-drops-208786},
  doi =		{10.4230/LIPIcs.ECOOP.2024.29},
  annote =	{Keywords: Tensor Shapes, Gradual Types, Migration}
}
Document
DOI: 10.4230/LIPIcs.ECOOP.2024.42
Failure Transparency in Stateful Dataflow Systems

Authors: Aleksey Veresov, Jonas Spenger, Paris Carbone, and Philipp Haller

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

Abstract
Failure transparency enables users to reason about distributed systems at a higher level of abstraction, where complex failure-handling logic is hidden. This is especially true for stateful dataflow systems, which are the backbone of many cloud applications. In particular, this paper focuses on proving failure transparency in Apache Flink, a popular stateful dataflow system. Even though failure transparency is a critical aspect of Apache Flink, to date it has not been formally proven. Showing that the failure transparency mechanism is correct, however, is challenging due to the complexity of the mechanism itself. Nevertheless, this complexity can be effectively hidden behind a failure transparent programming interface. To show that Apache Flink is failure transparent, we model it in small-step operational semantics. Next, we provide a novel definition of failure transparency based on observational explainability, a concept which relates executions according to their observations. Finally, we provide a formal proof of failure transparency for the implementation model; i.e., we prove that the failure-free model correctly abstracts from the failure-related details of the implementation model. We also show liveness of the implementation model under a fair execution assumption. These results are a first step towards a verified stack for stateful dataflow systems.
Cite as

Aleksey Veresov, Jonas Spenger, Paris Carbone, and Philipp Haller. Failure Transparency in Stateful Dataflow Systems. In 38th European Conference on Object-Oriented Programming (ECOOP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 313, pp. 42:1-42:31, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{veresov_et_al:LIPIcs.ECOOP.2024.42,
  author =	{Veresov, Aleksey and Spenger, Jonas and Carbone, Paris and Haller, Philipp},
  title =	{{Failure Transparency in Stateful Dataflow Systems}},
  booktitle =	{38th European Conference on Object-Oriented Programming (ECOOP 2024)},
  pages =	{42:1--42:31},
  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.2024.42},
  URN =		{urn:nbn:de:0030-drops-208911},
  doi =		{10.4230/LIPIcs.ECOOP.2024.42},
  annote =	{Keywords: Failure transparency, stateful dataflow, operational semantics, checkpoint recovery}
}
Document
DOI: 10.4230/LIPIcs.DNA.30.5
Learning and Inference in a Lattice Model of Multicomponent Condensates

Authors: Cameron Chalk, Salvador Buse, Krishna Shrinivas, Arvind Murugan, and Erik Winfree

Published in: LIPIcs, Volume 314, 30th International Conference on DNA Computing and Molecular Programming (DNA 30) (2024)

Abstract
Life is chemical intelligence. What is the source of intelligent behavior in molecular systems? Here we illustrate how, in contrast to the common belief that energy use in non-equilibrium reactions is essential, the detailed balance equilibrium properties of multicomponent liquid interactions are sufficient for sophisticated information processing. Our approach derives from the classical Boltzmann machine model for probabilistic neural networks, inheriting key principles such as representing probability distributions via quadratic energy functions, clamping input variables to infer conditional probability distributions, accommodating omnidirectional computation, and learning energy parameters via a wake phase / sleep phase algorithm that performs gradient descent on the relative entropy with respect to the target distribution. While the cubic lattice model of multicomponent liquids is standard, the behaviors exhibited by the trained molecules capture both previously-observed phenomena such as core-shell condensate architectures as well as novel phenomena such as an analog of Hopfield associative memories that perform recall by contact with a patterned surface. Our final example demonstrates equilibrium classification of MNIST digits. Experimental implementation using DNA nanostar liquids is conceptually straightforward.
Cite as

Cameron Chalk, Salvador Buse, Krishna Shrinivas, Arvind Murugan, and Erik Winfree. Learning and Inference in a Lattice Model of Multicomponent Condensates. In 30th International Conference on DNA Computing and Molecular Programming (DNA 30). Leibniz International Proceedings in Informatics (LIPIcs), Volume 314, pp. 5:1-5:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{chalk_et_al:LIPIcs.DNA.30.5,
  author =	{Chalk, Cameron and Buse, Salvador and Shrinivas, Krishna and Murugan, Arvind and Winfree, Erik},
  title =	{{Learning and Inference in a Lattice Model of Multicomponent Condensates}},
  booktitle =	{30th International Conference on DNA Computing and Molecular Programming (DNA 30)},
  pages =	{5:1--5:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-344-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{314},
  editor =	{Seki, Shinnosuke and Stewart, Jaimie Marie},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DNA.30.5},
  URN =		{urn:nbn:de:0030-drops-209330},
  doi =		{10.4230/LIPIcs.DNA.30.5},
  annote =	{Keywords: multicomponent liquid, Boltzmann machine, phase separation}
}
Document
DOI: 10.4230/LIPIcs.WABI.2024.20
The Path-Label Reconciliation (PLR) Dissimilarity Measure for Gene Trees

Authors: Alitzel López Sánchez, José Antonio Ramírez-Rafael, Alejandro Flores-Lamas, Maribel Hernández-Rosales, and Manuel Lafond

Published in: LIPIcs, Volume 312, 24th International Workshop on Algorithms in Bioinformatics (WABI 2024)

Abstract
In this study, we investigate the problem of comparing gene trees reconciled with the same species tree using a novel semi-metric, called the Path-Label Reconciliation (PLR) dissimilarity measure. This approach not only quantifies differences in the topology of reconciled gene trees, but also considers discrepancies in predicted ancestral gene-species maps and speciation/duplication events, offering a refinement of existing metrics such as Robinson-Foulds (RF) and their labeled extensions LRF and ELRF. A tunable parameter α also allows users to adjust the balance between its species map and event labeling components. We show that PLR can be computed in linear time and that it is a semi-metric. We also discuss the diameters of reconciled gene tree measures, which are important in practice for normalization, and provide initial bounds on PLR, LRF, and ELRF. To validate PLR, we simulate reconciliations and perform comparisons with LRF and ELRF. The results show that PLR provides a more evenly distributed range of distances, making it less susceptible to overestimating differences in the presence of small topological changes, while at the same time being computationally efficient. Our findings suggest that the theoretical diameter is rarely reached in practice. The PLR measure advances phylogenetic reconciliation by combining theoretical rigor with practical applicability. Future research will refine its mathematical properties, explore its performance on different tree types, and integrate it with existing bioinformatics tools for large-scale evolutionary analyses. The open source code is available at: https://pypi.org/project/parle/.
Cite as

Alitzel López Sánchez, José Antonio Ramírez-Rafael, Alejandro Flores-Lamas, Maribel Hernández-Rosales, and Manuel Lafond. The Path-Label Reconciliation (PLR) Dissimilarity Measure for Gene Trees. In 24th International Workshop on Algorithms in Bioinformatics (WABI 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 312, pp. 20:1-20:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{lopezsanchez_et_al:LIPIcs.WABI.2024.20,
  author =	{L\'{o}pez S\'{a}nchez, Alitzel and Ram{\'\i}rez-Rafael, Jos\'{e} Antonio and Flores-Lamas, Alejandro and Hern\'{a}ndez-Rosales, Maribel and Lafond, Manuel},
  title =	{{The Path-Label Reconciliation (PLR) Dissimilarity Measure for Gene Trees}},
  booktitle =	{24th International Workshop on Algorithms in Bioinformatics (WABI 2024)},
  pages =	{20:1--20:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-340-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{312},
  editor =	{Pissis, Solon P. and Sung, Wing-Kin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WABI.2024.20},
  URN =		{urn:nbn:de:0030-drops-206645},
  doi =		{10.4230/LIPIcs.WABI.2024.20},
  annote =	{Keywords: Reconciliation, gene trees, species trees, evolutionary scenarios}
}
Document
DOI: 10.4230/LIPIcs.TQC.2024.2
Stochastic Error Cancellation in Analog Quantum Simulation

Authors: Yiyi Cai, Yu Tong, and John Preskill

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

Abstract
Analog quantum simulation is a promising path towards solving classically intractable problems in many-body physics on near-term quantum devices. However, the presence of noise limits the size of the system and the length of time that can be simulated. In our work, we consider an error model in which the actual Hamiltonian of the simulator differs from the target Hamiltonian we want to simulate by small local perturbations, which are assumed to be random and unbiased. We analyze the error accumulated in observables in this setting and show that, due to stochastic error cancellation, with high probability the error scales as the square root of the number of qubits instead of linearly. We explore the concentration phenomenon of this error as well as its implications for local observables in the thermodynamic limit. Moreover, we show that stochastic error cancellation also manifests in the fidelity between the target state at the end of time-evolution and the actual state we obtain in the presence of noise. This indicates that, to reach a certain fidelity, more noise can be tolerated than implied by the worst-case bound if the noise comes from many statistically independent sources.
Cite as

Yiyi Cai, Yu Tong, and John Preskill. Stochastic Error Cancellation in Analog Quantum Simulation. In 19th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 310, pp. 2:1-2:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{cai_et_al:LIPIcs.TQC.2024.2,
  author =	{Cai, Yiyi and Tong, Yu and Preskill, John},
  title =	{{Stochastic Error Cancellation in Analog Quantum Simulation}},
  booktitle =	{19th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2024)},
  pages =	{2:1--2:15},
  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.2024.2},
  URN =		{urn:nbn:de:0030-drops-206720},
  doi =		{10.4230/LIPIcs.TQC.2024.2},
  annote =	{Keywords: Analog quantum simulation, error cancellation, concentration of measure}
}
Document
DOI: 10.4230/LIPIcs.CCC.2024.20
Lower Bounds for Set-Multilinear Branching Programs

Authors: Prerona Chatterjee, Deepanshu Kush, Shubhangi Saraf, and Amir Shpilka

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

Abstract
In this paper, we prove super-polynomial lower bounds for the model of sum of ordered set-multilinear algebraic branching programs, each with a possibly different ordering (∑smABP). Specifically, we give an explicit nd-variate polynomial of degree d such that any ∑smABP computing it must have size n^ω(1) for d as low as ω(log n). Notably, this constitutes the first such lower bound in the low degree regime. Moreover, for d = poly(n), we demonstrate an exponential lower bound. This result generalizes the seminal work of Nisan (STOC, 1991), which proved an exponential lower bound for a single ordered set-multilinear ABP. The significance of our lower bounds is underscored by the recent work of Bhargav, Dwivedi, and Saxena (TAMC, 2024), which showed that super-polynomial lower bounds against a sum of ordered set-multilinear branching programs - for a polynomial of sufficiently low degree - would imply super-polynomial lower bounds against general ABPs, thereby resolving Valiant’s longstanding conjecture that the permanent polynomial can not be computed efficiently by ABPs. More precisely, their work shows that if one could obtain such lower bounds when the degree is bounded by O(log n/ log log n), then it would imply super-polynomial lower bounds against general ABPs. Our results strengthen the works of Arvind & Raja (Chic. J. Theor. Comput. Sci., 2016) and Bhargav, Dwivedi & Saxena (TAMC, 2024), as well as the works of Ramya & Rao (Theor. Comput. Sci., 2020) and Ghoshal & Rao (International Computer Science Symposium in Russia, 2021), each of which established lower bounds for related or restricted versions of this model. They also strongly answer a question from the former two, which asked to prove super-polynomial lower bounds for general ∑smABP.
Cite as

Prerona Chatterjee, Deepanshu Kush, Shubhangi Saraf, and Amir Shpilka. Lower Bounds for Set-Multilinear Branching Programs. In 39th Computational Complexity Conference (CCC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 300, pp. 20:1-20:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{chatterjee_et_al:LIPIcs.CCC.2024.20,
  author =	{Chatterjee, Prerona and Kush, Deepanshu and Saraf, Shubhangi and Shpilka, Amir},
  title =	{{Lower Bounds for Set-Multilinear Branching Programs}},
  booktitle =	{39th Computational Complexity Conference (CCC 2024)},
  pages =	{20:1--20:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-331-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{300},
  editor =	{Santhanam, Rahul},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2024.20},
  URN =		{urn:nbn:de:0030-drops-204167},
  doi =		{10.4230/LIPIcs.CCC.2024.20},
  annote =	{Keywords: Lower Bounds, Algebraic Branching Programs, Set-multilinear polynomials}
}
Document
Media Exposition
DOI: 10.4230/LIPIcs.SoCG.2021.61
An Interactive Tool for Experimenting with Bounded-Degree Plane Geometric Spanners (Media Exposition)

Authors: Fred Anderson, Anirban Ghosh, Matthew Graham, Lucas Mougeot, and David Wisnosky

Published in: LIPIcs, Volume 189, 37th International Symposium on Computational Geometry (SoCG 2021)

Abstract
The construction of bounded-degree plane geometric spanners has been a focus of interest in the field of geometric spanners for a long time. To date, several algorithms have been designed with various trade-offs in degree and stretch factor. Using JSXGraph, a state-of-the-art JavaScript library for geometry, we have implemented seven of these sophisticated algorithms so that they can be used for further research and teaching computational geometry. We believe that our interactive tool can be used by researchers from related fields to understand and apply the algorithms in their research. Our tool can be run in any modern browser. The tool will be permanently maintained by the second author at https://ghoshanirban.github.io/bounded-degree-plane-spanners/index.html
Cite as

Fred Anderson, Anirban Ghosh, Matthew Graham, Lucas Mougeot, and David Wisnosky. An Interactive Tool for Experimenting with Bounded-Degree Plane Geometric Spanners (Media Exposition). In 37th International Symposium on Computational Geometry (SoCG 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 189, pp. 61:1-61:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{anderson_et_al:LIPIcs.SoCG.2021.61,
  author =	{Anderson, Fred and Ghosh, Anirban and Graham, Matthew and Mougeot, Lucas and Wisnosky, David},
  title =	{{An Interactive Tool for Experimenting with Bounded-Degree Plane Geometric Spanners}},
  booktitle =	{37th International Symposium on Computational Geometry (SoCG 2021)},
  pages =	{61:1--61:4},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-184-9},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{189},
  editor =	{Buchin, Kevin and Colin de Verdi\`{e}re, \'{E}ric},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2021.61},
  URN =		{urn:nbn:de:0030-drops-138607},
  doi =		{10.4230/LIPIcs.SoCG.2021.61},
  annote =	{Keywords: graph approximation, Delaunay triangulations, geometric spanners, plane spanners, bounded-degree spanners}
}
Document
DOI: 10.4230/LIPIcs.CCC.2016.30
Identity Testing and Lower Bounds for Read-k Oblivious Algebraic Branching Programs

Authors: Matthew Anderson, Michael A. Forbes, Ramprasad Saptharishi, Amir Shpilka, and Ben Lee Volk

Published in: LIPIcs, Volume 50, 31st Conference on Computational Complexity (CCC 2016)

Abstract
Read-k oblivious algebraic branching programs are a natural generalization of the well-studied model of read-once oblivious algebraic branching program (ROABPs). In this work, we give an exponential lower bound of exp(n/k^{O(k)}) on the width of any read-k oblivious ABP computing some explicit multilinear polynomial f that is computed by a polynomial size depth-3 circuit. We also study the polynomial identity testing (PIT) problem for this model and obtain a white-box subexponential-time PIT algorithm. The algorithm runs in time 2^{~O(n^{1-1/2^{k-1}})} and needs white box access only to know the order in which the variables appear in the ABP.
Cite as

Matthew Anderson, Michael A. Forbes, Ramprasad Saptharishi, Amir Shpilka, and Ben Lee Volk. Identity Testing and Lower Bounds for Read-k Oblivious Algebraic Branching Programs. In 31st Conference on Computational Complexity (CCC 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 50, pp. 30:1-30:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{anderson_et_al:LIPIcs.CCC.2016.30,
  author =	{Anderson, Matthew and Forbes, Michael A. and Saptharishi, Ramprasad and Shpilka, Amir and Volk, Ben Lee},
  title =	{{Identity Testing and Lower Bounds for Read-k Oblivious Algebraic Branching Programs}},
  booktitle =	{31st Conference on Computational Complexity (CCC 2016)},
  pages =	{30:1--30:25},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-008-8},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{50},
  editor =	{Raz, Ran},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2016.30},
  URN =		{urn:nbn:de:0030-drops-58255},
  doi =		{10.4230/LIPIcs.CCC.2016.30},
  annote =	{Keywords: Algebraic Complexity, Lower Bounds, Derandomization, Polynomial Identity Testing}
}
Document
DOI: 10.4230/LIPIcs.STACS.2014.41
On Symmetric Circuits and Fixed-Point Logics

Authors: Matthew Anderson and Anuj Dawar

Published in: LIPIcs, Volume 25, 31st International Symposium on Theoretical Aspects of Computer Science (STACS 2014)

Abstract
We study properties of relational structures such as graphs that are decided by families of Boolean circuits. Circuits that decide such properties are necessarily invariant to permutations of the elements of the input structures. We focus on families of circuits that are symmetric, i.e., circuits whose invariance is witnessed by automorphisms of the circuit induced by the permutation of the input structure. We show that the expressive power of such families is closely tied to definability in logic. In particular, we show that the queries defined on structures by uniform families of symmetric Boolean circuits with majority gates are exactly those definable in fixed-point logic with counting. This shows that inexpressibility results in the latter logic lead to lower bounds against polynomial-size families of symmetric circuits.
Cite as

Matthew Anderson and Anuj Dawar. On Symmetric Circuits and Fixed-Point Logics. In 31st International Symposium on Theoretical Aspects of Computer Science (STACS 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 25, pp. 41-52, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@InProceedings{anderson_et_al:LIPIcs.STACS.2014.41,
  author =	{Anderson, Matthew and Dawar, Anuj},
  title =	{{On Symmetric Circuits and Fixed-Point Logics}},
  booktitle =	{31st International Symposium on Theoretical Aspects of Computer Science (STACS 2014)},
  pages =	{41--52},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-65-1},
  ISSN =	{1868-8969},
  year =	{2014},
  volume =	{25},
  editor =	{Mayr, Ernst W. and Portier, Natacha},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2014.41},
  URN =		{urn:nbn:de:0030-drops-44455},
  doi =		{10.4230/LIPIcs.STACS.2014.41},
  annote =	{Keywords: symmetric circuit, fixed-point logic, majority, counting, uniformity}
}
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