2 Search Results for "Yehuda, Itay"

Document
DOI: 10.4230/LIPIcs.SoCG.2021.41
Throwing a Sofa Through the Window

Authors: Dan Halperin, Micha Sharir, and Itay Yehuda

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

Abstract
We study several variants of the problem of moving a convex polytope K, with n edges, in three dimensions through a flat rectangular (and sometimes more general) window. Specifically: ii) We study variants where the motion is restricted to translations only, discuss situations where such a motion can be reduced to sliding (translation in a fixed direction), and present efficient algorithms for those variants, which run in time close to O(n^{8/3}). iii) We consider the case of a gate (an unbounded window with two parallel infinite edges), and show that K can pass through such a window, by any collision-free rigid motion, iff it can slide through it, an observation that leads to an efficient algorithm for this variant too. iv) We consider arbitrary compact convex windows, and show that if K can pass through such a window W (by any motion) then K can slide through a slab of width equal to the diameter of W. v) We show that if a purely translational motion for K through a rectangular window W exists, then K can also slide through W keeping the same orientation as in the translational motion. For a given fixed orientation of K we can determine in linear time whether K can translate (and hence slide) through W keeping the given orientation, and if so plan the motion, also in linear time. vi) We give an example of a polytope that cannot pass through a certain window by translations only, but can do so when rotations are allowed. vii) We study the case of a circular window W, and show that, for the regular tetrahedron K of edge length 1, there are two thresholds 1 > δ₁≈ 0.901388 > δ₂≈ 0.895611, such that (a) K can slide through W if the diameter d of W is ≥ 1, (b) K cannot slide through W but can pass through it by a purely translational motion when δ₁ ≤ d < 1, (c) K cannot pass through W by a purely translational motion but can do it when rotations are allowed when δ₂ ≤ d < δ₁, and (d) K cannot pass through W at all when d < δ₂. viii) Finally, we explore the general setup, where we want to plan a general motion (with all six degrees of freedom) for K through a rectangular window W, and present an efficient algorithm for this problem, with running time close to O(n⁴).
Cite as

Dan Halperin, Micha Sharir, and Itay Yehuda. Throwing a Sofa Through the Window. In 37th International Symposium on Computational Geometry (SoCG 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 189, pp. 41:1-41:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{halperin_et_al:LIPIcs.SoCG.2021.41,
  author =	{Halperin, Dan and Sharir, Micha and Yehuda, Itay},
  title =	{{Throwing a Sofa Through the Window}},
  booktitle =	{37th International Symposium on Computational Geometry (SoCG 2021)},
  pages =	{41:1--41:16},
  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.2021.41},
  URN =		{urn:nbn:de:0030-drops-138409},
  doi =		{10.4230/LIPIcs.SoCG.2021.41},
  annote =	{Keywords: Motion planning, Convex polytopes in 3D}
}
Document
DOI: 10.4230/LIPIcs.OPODIS.2019.20
Consensus in Equilibrium: Can One Against All Decide Fairly?

Authors: Itay Harel, Amit Jacob-Fanani, Moshe Sulamy, and Yehuda Afek

Published in: LIPIcs, Volume 153, 23rd International Conference on Principles of Distributed Systems (OPODIS 2019)

Abstract
Is there an equilibrium for distributed consensus when all agents except one collude to steer the decision value towards their preference? If an equilibrium exists, then an n-1 size coalition cannot do better by deviating from the algorithm, even if it prefers a different decision value. We show that an equilibrium exists under this condition only if the number of agents in the network is odd and the decision is binary (among two possible input values). That is, in this framework we provide a separation between binary and multi-valued consensus. Moreover, the input and output distribution must be uniform, regardless of the communication model (synchronous or asynchronous). Furthermore, we define a new problem - Resilient Input Sharing (RIS), and use it to find an iff condition for the (n-1)-resilient equilibrium for deterministic binary consensus, essentially showing that an equilibrium for deterministic consensus is equivalent to each agent learning all the other inputs in some strong sense. Finally, we note that (n-2)-resilient equilibrium for binary consensus is possible for any n. The case of (n-2)-resilient equilibrium for multi-valued consensus is left open.
Cite as

Itay Harel, Amit Jacob-Fanani, Moshe Sulamy, and Yehuda Afek. Consensus in Equilibrium: Can One Against All Decide Fairly?. In 23rd International Conference on Principles of Distributed Systems (OPODIS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 153, pp. 20:1-20:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

Copy BibTex To Clipboard

@InProceedings{harel_et_al:LIPIcs.OPODIS.2019.20,
  author =	{Harel, Itay and Jacob-Fanani, Amit and Sulamy, Moshe and Afek, Yehuda},
  title =	{{Consensus in Equilibrium: Can One Against All Decide Fairly?}},
  booktitle =	{23rd International Conference on Principles of Distributed Systems (OPODIS 2019)},
  pages =	{20:1--20:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-133-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{153},
  editor =	{Felber, Pascal and Friedman, Roy and Gilbert, Seth and Miller, Avery},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2019.20},
  URN =		{urn:nbn:de:0030-drops-118065},
  doi =		{10.4230/LIPIcs.OPODIS.2019.20},
  annote =	{Keywords: distributed computing, game theory, rational agents, consensus}
}
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