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Tulio Halperin Donghi, Révolution et guerre. Formation d'une élite dirigeante dans l'Argentine Créole

2014
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Lectures
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Formation d'une élite dirigeante

doi:10.4000/lectures.16226
fatcat:svwk3yemuza4xbgmjdn5qkfihm
*dans*l'Argentine créole Texte intégral 1 Donghi Tulio*Halperin*, Revolución y guerra, formación de una elite dirigente en la Argentina Crioll (...) 2 Donghi Tulio*Halperin*... Tulio*Halperin*Donghi, Révolution et guerre. ...##
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Space-Aware Reconfiguration
[article]

2020
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arXiv
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pre-print

We consider the problem of reconfiguring a set of physical objects into a desired target configuration, a typical (sub)task in robotics and automation, arising in product assembly, packaging, stocking store shelves, and more. In this paper we address a variant, which we call space-aware reconfiguration, where the goal is to minimize the physical space needed for the reconfiguration, while obeying constraints on the allowable collision-free motions of the objects. Since for given start and

arXiv:2006.04402v2
fatcat:rsmmreffwjgazdqb6vdbudirsy
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... configurations, reconfiguration may be impossible, we translate the entire target configuration rigidly into a location that admits a valid sequence of moves, where each object moves in turn just once, along a straight line, from its starting to its target location, so that the overall physical space required by the start, all intermediate, and target configurations for all the objects is minimized. We investigate two variants of space-aware reconfiguration for the often examined setting of n unit discs in the plane, depending on whether the discs are distinguishable (labeled) or indistinguishable (unlabeled). For the labeled case, we propose a representation of size O(n^4) of the space of all feasible initial rigid translations, and use it to find, in O(n^6) time, a shortest valid translation, or one that minimizes the enclosing disc or axis-aligned rectangle of both the start and target configurations. For the significantly harder unlabeled case, we show that for almost every direction, there exists a translation in this direction that makes the problem feasible. We use this to devise heuristic solutions, where we optimize the translation under stricter notions of feasibility. We present an implementation of such a heuristic, which solves unlabeled instances with hundreds of discs in seconds.##
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Deconstructing Approximate Offsets
[article]

2011
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arXiv
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pre-print

We consider the offset-deconstruction problem: Given a polygonal shape Q with n vertices, can it be expressed, up to a tolerance \eps in Hausdorff distance, as the Minkowski sum of another polygonal shape P with a disk of fixed radius? If it does, we also seek a preferably simple-looking solution P; then, P's offset constitutes an accurate, vertex-reduced, and smoothened approximation of Q. We give an O(n log n)-time exact decision algorithm that handles any polygonal shape, assuming the

arXiv:1109.2158v1
fatcat:pdcmaafkrfb7pjvx4lvob7g3tq
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... M model of computation. A variant of the algorithm, which we have implemented using CGAL, is based on rational arithmetic and answers the same deconstruction problem up to an uncertainty parameter \delta; its running time additionally depends on \delta. If the input shape is found to be approximable, this algorithm also computes an approximate solution for the problem. It also allows us to solve parameter-optimization problems induced by the offset-deconstruction problem. For convex shapes, the complexity of the exact decision algorithm drops to O(n), which is also the time required to compute a solution P with at most one more vertex than a vertex-minimal one.##
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Iterated snap rounding

2002
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Computational geometry
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Snap rounding is a well known method for converting arbitrary-precision arrangements of segments into a fixedprecision representation. We point out that in a snap-rounded arrangement, the distance between a vertex and a non-incident edge can be extremely small compared with the width of a pixel in the grid used for rounding. We propose and analyze an augmented procedure, iterated snap rounding, which rounds the arrangement such that each vertex is at least half-the-width-of-a-pixel away from

doi:10.1016/s0925-7721(01)00064-5
fatcat:zs24mky5wjdo3lgllnrzetj74e
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... non-incident edge. Iterated snap rounding preserves the topology of the original arrangement in the same sense that the original scheme does. However, the guaranteed quality of the approximation degrades. Thus each scheme may be suitable in different situations. We describe an implementation of both schemes. In our implementation we substitute an intricate data structure for segment/pixel intersection that is used to obtain good worst-case resource bounds for iterated snap rounding by a simple and effective data structure which is a cluster of kd-trees. Finally, we present rounding examples obtained with the implementation.##
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Deconstructing Approximate Offsets

2012
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Discrete & Computational Geometry
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We consider the offset-deconstruction problem: Given a polygonal shape Q with n vertices, can it be expressed, up to a tolerance ε in Hausdorff distance, as the Minkowski sum of another polygonal shape P with a disk of fixed radius? If it does, we also seek a preferably simple-looking solution shape P ; then, P 's offset constitutes an accurate, vertexreduced, and smoothened approximation of Q. We give an O(n log n)-time exact decision algorithm that handles any polygonal shape, assuming the

doi:10.1007/s00454-012-9441-5
fatcat:5eigl7y5znhijleudzu3lug5ky
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... l-RAM model of computation. An alternative algorithm, based purely on rational arithmetic, answers the same deconstruction problem, up to an uncertainty parameter δ, and its running time depends on the parameter δ (in addition to the other input parameters: n, ε and the radius of the disk). If the input shape is found to be approximable, the rational-arithmetic algorithm also computes an approximate solution shape for the problem. For convex shapes, the complexity of the exact decision algorithm drops to O(n), which is also the time required to compute a solution shape P with at most one more vertex than a vertex-minimal one. Our study is motivated by applications from two different domains. However, since the offset operation has numerous uses, we anticipate that the reverse question that we study here will be still more broadly applicable. We present results obtained with our implementation of the rational-arithmetic algorithm.##
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On Two-Handed Planar Assembly Partitioning
[article]

2020
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arXiv
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pre-print

[9]

arXiv:2009.12369v1
fatcat:jehazma3sncylabksgomlayaa4
*Dan**Halperin*, Jean-Claude Latombe, and Randall H Wilson. A general framework for assembly planning: The motion space approach. ... [7] Tzvika Geft, Aviv Tamar, Ken Goldberg, and*Dan**Halperin*. Robust 2D assembly sequencing via geometric planning with learned scores. ...##
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Sensory Regimes of Effective Distributed Searching without Leaders
[article]

2019
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arXiv
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pre-print

Collective animal movement fascinates children and scientists alike. One of the most commonly given explanations for collective animal movement is improved foraging. Animals are hypothesized to gain from searching for food in groups. Here, we use a computer simulation to analyze how moving in a group assists searching for food. We use a well-established collective movement model that only assumes local interactions between individuals without any leadership, in order to examine the benefits of

arXiv:1904.02895v1
fatcat:quuh2uydwfcx3fpxqwvk6gnzmq
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... roup searching. We focus on how the sensory abilities of the simulated individuals, and specifically their ability to detect food and to follow neighbours, influence searching dynamics and searching performance. We show that local interactions between neighbors are sufficient for the formation of groups, which search more efficiently than independently moving individuals. Once a member of a group finds food, this information diffuses through the group and results in a convergence of up to 85\% of group members on the food. Interestingly, this convergence behavior can emerge from the local interactions between group members without a need to explicitly define it. In order to understand the principles underlying the group's performance, we perturb many of the model's basic parameters, including its social, environmental and sensory parameters. We test a wide range of biological-plausible sensory regimes, relevant to different species and different sensory modalities and examine how they effect group-foraging performance. This thorough analysis of model parameters allows for the generalization of our results to a wide range of organisms, which rely on different sensory modalities, explaining why they move and forage in groups.##
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Refined Hardness of Distance-Optimal Multi-Agent Path Finding
[article]

2022
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arXiv
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pre-print

We study the computational complexity of multi-agent path finding (MAPF). Given a graph G and a set of agents, each having a start and target vertex, the goal is to find collision-free paths minimizing the total distance traveled. To better understand the source of difficulty of the problem, we aim to study the simplest and least constrained graph class for which it remains hard. To this end, we restrict G to be a 2D grid, which is a ubiquitous abstraction, as it conveniently allows for

arXiv:2203.07416v1
fatcat:jo2fgd3f2jf6rlpy6s5rmasugm
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... well-structured environments (e.g., warehouses). Previous hardness results considered highly constrained 2D grids having only one vertex unoccupied by an agent, while the most restricted hardness result that allowed multiple empty vertices was for (non-grid) planar graphs. We therefore refine previous results by simultaneously considering both 2D grids and multiple empty vertices. We show that even in this case distance-optimal MAPF remains NP-hard, which settles an open problem posed by Banfi et al. (2017). We present a reduction directly from 3-SAT using simple gadgets, making our proof arguably more informative than previous work in terms of potential progress towards positive results. Furthermore, our reduction is the first linear one for the case where G is planar, appearing nearly four decades after the first related result. This allows us to go a step further and exploit the Exponential Time Hypothesis (ETH) to obtain an exponential lower bound for the running time of the problem. Finally, as a stepping stone towards our main results, we prove the NP-hardness of the monotone case, in which agents move one by one with no intermediate stops.##
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Sampling-based bottleneck pathfinding with applications to Frechet matching
[article]

2016
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arXiv
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pre-print

A different approach was taken by Janson and Pavone who introduced the FMT* algorithm [26] , which was later refined by Salzman and

arXiv:1607.02770v1
fatcat:j25lbdxderaa7cvurg4zowoqiy
*Halperin*[39] . ...##
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Optimized Synthesis of Snapping Fixtures
[article]

2020
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arXiv
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pre-print

Fixtures for constraining the movement of parts have been extensively investigated in robotics, since they are essential for using robots in automated manufacturing. This paper deals with the design and optimized synthesis of a special type of fixtures, which we call snapping fixtures. Given a polyhedral workpiece P with n vertices and of constant genus, which we need to hold, a snapping fixture is a semi-rigid polyhedron G, made of a palm and several fingers, such that when P and G are well

arXiv:1909.05953v2
fatcat:amqqfhtqsbg5zn4bn7hy565d74
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... arated, we can push P toward G, slightly bending the fingers of G on the way (exploiting its mild flexibility), and obtain a configuration, where G is back in its original shape and P and G are inseparable as rigid bodies. We prove the minimal closure conditions under which such fixtures can hold parts, using Helly's theorem. We then introduce an algorithm running in O(n^3) time that produces a snapping fixture, minimizing the number of fingers and optimizing additional objectives, if a snapping fixture exists. We also provide an efficient and robust implementation of a simpler version of the algorithm, which produces the fixture model to be 3D printed and runs in O(n^4) time. We describe two applications with different optimization criteria: Fixtures to hold add-ons for drones, where we aim to make the fixture as lightweight as possible, and small-scale fixtures to hold precious stones in jewelry, where we aim to maximize the exposure of the stones, namely minimize the obscuring of the workpiece by the fixture.##
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Motion Planning for Multiple Unit-Ball Robots in R^d
[article]

2018
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arXiv
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pre-print

Similarly to the labeled problem, the unlabeled problem was also shown to be computationally intractable; Solovey and

arXiv:1807.05428v1
fatcat:mjj7nfuzn5hzrfqxkesnucho3q
*Halperin*[31] proved it to be PSPACE-hard for unit-square robots amidst polygonal ...##
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Sparsification of Motion-Planning Roadmaps by Edge Contraction
[article]

2012
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arXiv
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pre-print

We present Roadmap Sparsification by Edge Contraction (RSEC), a simple and effective algorithm for reducing the size of a motion-planning roadmap. The algorithm exhibits minimal effect on the quality of paths that can be extracted from the new roadmap. The primitive operation used by RSEC is edge contraction - the contraction of a roadmap edge to a single vertex and the connection of the new vertex to the neighboring vertices of the contracted edge. For certain scenarios, we compress more than

arXiv:1209.4463v1
fatcat:a65332piznbxflkmgqhafrl7fq
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... 8% of the edges and vertices at the cost of degradation of average shortest path length by at most 2%.##
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Throwing a Sofa Through the Window
[article]

2021
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arXiv
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pre-print

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: ∙ 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). ∙ We consider the case of a 'gate' (an unbounded

arXiv:2102.04262v2
fatcat:m74j67y2jzatjgaytupatizg4e
## more »

... dow with two parallel infinite edges), and show that K can pass through such a window, by any collision-free rigid motion, if and only if it can slide through it. ∙ 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 gate of width equal to the diameter of W. ∙ 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 > δ_1≈ 0.901388 > δ_2≈ 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 δ_1≤ d < 1, (c) K cannot pass through W by a purely translational motion but can do it when rotations are allowed when δ_2 ≤ d < δ_1, and (d) K cannot pass through W at all when d < δ_2. ∙ 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(n^4).##
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Spheres, molecules, and hidden surface removal

1998
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Computational geometry
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We devise techniques to manipulate a collection of loosely interpenetrating spheres in three-dimensional space. Our study is motivated by the representation and manipulation of molecular configurations, modeled by a collection of spheres. We analyze the sphere model and point to properties that make it more easy to manipulate than an arbitrary collection of spheres. For this special sphere model we present efficient algorithms for computing its union boundary and for hidden surface removal. The

doi:10.1016/s0925-7721(98)00023-6
fatcat:axprckr2ozfw5abkcbuwccda3m
## more »

... efficiency and practicality of our approach are demonstrated by experiments on actual molecule data. . 3 A radius r and a center c induce a ball B = {p I d(p, c) ~< r} and a sphere S = {p I d(p, c) = r}, where d(pl, P2) is the Euclidean distance between the points Pl and P2 in 3-space. Throughout the text we will refer to spheres and balls interchangeably. In some cases the term 'ball' is more appropriate than 'sphere', but we use the latter to comply with prevailing terminology in molecular biology. 0925-7721/98/$ -see front matter##
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The Offset Filtration of Convex Objects
[article]

2015
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arXiv
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pre-print

We consider offsets of a union of convex objects. We aim for a filtration, a sequence of nested cell complexes, that captures the topological evolution of the offsets for increasing radii. We describe methods to compute a filtration based on the Voronoi partition with respect to the given convex objects. We prove that, in two and three dimensions, the size of the filtration is proportional to the size of the Voronoi diagram. Our algorithm runs in Θ(n n) in the 2-dimensional case and in expected

arXiv:1407.6132v2
fatcat:g4bszkdffbfn3c7vuso22zg65m
## more »

... time O(n^3 + ϵ), for any ϵ > 0, in the 3-dimensional case. Our approach is inspired by alpha-complexes for point sets, but requires more involved machinery and analysis primarily since Voronoi regions of general convex objects do not form a good cover. We show by experiments that our approach results in a similarly fast and topologically more stable method for computing a filtration compared to approximating the input by point samples.
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