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Documents authored by Ramírez-Romero, Diego

Document
DOI: 10.4230/LIPIcs.SoCG.2021.39
Improved Approximation Algorithms for 2-Dimensional Knapsack: Packing into Multiple L-Shapes, Spirals, and More

Authors: Waldo Gálvez, Fabrizio Grandoni, Arindam Khan, Diego Ramírez-Romero, and Andreas Wiese

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

Abstract
In the 2-Dimensional Knapsack problem (2DK) we are given a square knapsack and a collection of n rectangular items with integer sizes and profits. Our goal is to find the most profitable subset of items that can be packed non-overlappingly into the knapsack. The currently best known polynomial-time approximation factor for 2DK is 17/9+ε < 1.89 and there is a (3/2+ε)-approximation algorithm if we are allowed to rotate items by 90 degrees [Gálvez et al., FOCS 2017]. In this paper, we give (4/3+ε)-approximation algorithms in polynomial time for both cases, assuming that all input data are integers polynomially bounded in n. Gálvez et al.’s algorithm for 2DK partitions the knapsack into a constant number of rectangular regions plus one L-shaped region and packs items into those in a structured way. We generalize this approach by allowing up to a constant number of more general regions that can have the shape of an L, a U, a Z, a spiral, and more, and therefore obtain an improved approximation ratio. In particular, we present an algorithm that computes the essentially optimal structured packing into these regions.
Cite as

Waldo Gálvez, Fabrizio Grandoni, Arindam Khan, Diego Ramírez-Romero, and Andreas Wiese. Improved Approximation Algorithms for 2-Dimensional Knapsack: Packing into Multiple L-Shapes, Spirals, and More. In 37th International Symposium on Computational Geometry (SoCG 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 189, pp. 39:1-39:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{galvez_et_al:LIPIcs.SoCG.2021.39,
  author =	{G\'{a}lvez, Waldo and Grandoni, Fabrizio and Khan, Arindam and Ram{\'\i}rez-Romero, Diego and Wiese, Andreas},
  title =	{{Improved Approximation Algorithms for 2-Dimensional Knapsack: Packing into Multiple L-Shapes, Spirals, and More}},
  booktitle =	{37th International Symposium on Computational Geometry (SoCG 2021)},
  pages =	{39:1--39:17},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2021.39},
  URN =		{urn:nbn:de:0030-drops-138386},
  doi =		{10.4230/LIPIcs.SoCG.2021.39},
  annote =	{Keywords: Approximation algorithms, two-dimensional knapsack, geometric packing}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2020.51
Shared vs Private Randomness in Distributed Interactive Proofs

Authors: Pedro Montealegre, Diego Ramírez-Romero, and Ivan Rapaport

Published in: LIPIcs, Volume 181, 31st International Symposium on Algorithms and Computation (ISAAC 2020)

Abstract
In distributed interactive proofs, the nodes of a graph G interact with a powerful but untrustable prover who tries to convince them, in a small number of rounds and through short messages, that G satisfies some property. This series of interactions is followed by a phase of distributed verification, which may be either deterministic or randomized, where nodes exchange messages with their neighbors. The nature of this last verification round defines the two types of interactive protocols. We say that the protocol is of Arthur-Merlin type if the verification round is deterministic. We say that the protocol is of Merlin-Arthur type if, in the verification round, the nodes are allowed to use a fresh set of random bits. In the original model introduced by Kol, Oshman, and Saxena [PODC 2018], the randomness was private in the sense that each node had only access to an individual source of random coins. Crescenzi, Fraigniaud, and Paz [DISC 2019] initiated the study of the impact of shared randomness (the situation where the coin tosses are visible to all nodes) in the distributed interactive model. In this work, we continue that research line by showing that the impact of the two forms of randomness is very different depending on whether we are considering Arthur-Merlin protocols or Merlin-Arthur protocols. While private randomness gives more power to the first type of protocols, shared randomness provides more power to the second. Our results also connect shared randomness in distributed interactive proofs with distributed verification, and new lower bounds are obtained.
Cite as

Pedro Montealegre, Diego Ramírez-Romero, and Ivan Rapaport. Shared vs Private Randomness in Distributed Interactive Proofs. In 31st International Symposium on Algorithms and Computation (ISAAC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 181, pp. 51:1-51:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{montealegre_et_al:LIPIcs.ISAAC.2020.51,
  author =	{Montealegre, Pedro and Ram{\'\i}rez-Romero, Diego and Rapaport, Ivan},
  title =	{{Shared vs Private Randomness in Distributed Interactive Proofs}},
  booktitle =	{31st International Symposium on Algorithms and Computation (ISAAC 2020)},
  pages =	{51:1--51:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-173-3},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{181},
  editor =	{Cao, Yixin and Cheng, Siu-Wing and Li, Minming},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2020.51},
  URN =		{urn:nbn:de:0030-drops-133959},
  doi =		{10.4230/LIPIcs.ISAAC.2020.51},
  annote =	{Keywords: Distributed interactive proofs, Distributed verification, Shared randomness, Private randomness}
}
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