3 Search Results for "Arroyo, Alan"

Document
DOI: 10.4230/LIPIcs.ESA.2024.80
The Algorithmic Power of the Greene-Kleitman Theorem

Authors: Shimon Kogan and Merav Parter

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

Abstract
For a given n-vertex DAG G = (V,E) with transitive-closure TC(G), a chain is a directed path in TC(G) and an antichain is an independent set in TC(G). The maximum k-antichain problem asks for computing the maximum k-colorable subgraph of the transitive closure. The related maximum h-chains problem asks for computing h disjoint chains (i.e., cliques in TC(G)) of largest total lengths. The celebrated Greene-Kleitman (GK) theorem [J. of Comb. Theory, 1976] demonstrates the (combinatorial) connections between these two problems. In this work we translate the combinatorial properties implied by the GK theorem into time-efficient covering algorithms. In contrast to prior results, our algorithms are applied directly on G, and do not require the precomputation of its transitive closure. Let α_k(G) be the maximum number of vertices that can be covered by k antichains. We show: - For every n-vertex m-edge DAG G = (V,E), one can compute at most (2k-1) disjoint antichains that cover α_k(G) vertices in time m^{1+o(1)} (hence, independent in k). This extends the recent m^{1+o(1)}-time Maximum-Antichain algorithm (where k = 1) by [Cáceres et al., SODA 2022] to any value of k. - For every n-vertex m-edge Partially-Ordered-Set (poset) P = (V,E), one can compute (1+ε)k disjoint antichains that cover α_k(P) vertices in time O(√m⋅ α_k(P)⋅ n^{o(1)}/ε), hence at most n^{2+o(1)}/ε. This improves over the exact solution of O(n³) time of [Gavril, Networks 1987] at the cost of producing (1+ε)k antichains instead of exactly k. The heart of our approach is a linear-time greedy-like algorithm that translates suitable chain collections 𝒞 into an parallel set of antichains 𝒜, in which |C_j ∩ A_i| = 1 for every C_j ∈ 𝒞 and A_i ∈ 𝒜. The correctness of this approach is underlined by the GK theorem.
Cite as

Shimon Kogan and Merav Parter. The Algorithmic Power of the Greene-Kleitman Theorem. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 80:1-80:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{kogan_et_al:LIPIcs.ESA.2024.80,
  author =	{Kogan, Shimon and Parter, Merav},
  title =	{{The Algorithmic Power of the Greene-Kleitman Theorem}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{80:1--80:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-338-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{308},
  editor =	{Chan, Timothy and Fischer, Johannes and Iacono, John and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2024.80},
  URN =		{urn:nbn:de:0030-drops-211512},
  doi =		{10.4230/LIPIcs.ESA.2024.80},
  annote =	{Keywords: Chains, Antichains, DAG}
}
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.SoCG.2020.9
Extending Drawings of Graphs to Arrangements of Pseudolines

Authors: Alan Arroyo, Julien Bensmail, and R. Bruce Richter

Published in: LIPIcs, Volume 164, 36th International Symposium on Computational Geometry (SoCG 2020)

Abstract
In the recent study of crossing numbers, drawings of graphs that can be extended to an arrangement of pseudolines (pseudolinear drawings) have played an important role as they are a natural combinatorial extension of rectilinear (or straight-line) drawings. A characterization of the pseudolinear drawings of K_n was found recently. We extend this characterization to all graphs, by describing the set of minimal forbidden subdrawings for pseudolinear drawings. Our characterization also leads to a polynomial-time algorithm to recognize pseudolinear drawings and construct the pseudolines when it is possible.
Cite as

Alan Arroyo, Julien Bensmail, and R. Bruce Richter. Extending Drawings of Graphs to Arrangements of Pseudolines. In 36th International Symposium on Computational Geometry (SoCG 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 164, pp. 9:1-9:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{arroyo_et_al:LIPIcs.SoCG.2020.9,
  author =	{Arroyo, Alan and Bensmail, Julien and Richter, R. Bruce},
  title =	{{Extending Drawings of Graphs to Arrangements of Pseudolines}},
  booktitle =	{36th International Symposium on Computational Geometry (SoCG 2020)},
  pages =	{9:1--9:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-143-6},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{164},
  editor =	{Cabello, Sergio and Chen, Danny Z.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2020.9},
  URN =		{urn:nbn:de:0030-drops-121672},
  doi =		{10.4230/LIPIcs.SoCG.2020.9},
  annote =	{Keywords: graphs, graph drawings, geometric graph drawings, arrangements of pseudolines, crossing numbers, stretchability}
}
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