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52
A dynamic bounding volume hierarchy for generalized collision detection
, 2006
"... In this paper, we propose a new dynamic and efficient bounding volume hierarchy for breakable objects undergoing structured and/or unstructured motion. Our object–space method is based on different ways to incrementally update the hierarchy during simulation by exploiting temporal coherence and lazy ..."
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Cited by 28 (2 self)
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In this paper, we propose a new dynamic and efficient bounding volume hierarchy for breakable objects undergoing structured and/or unstructured motion. Our object–space method is based on different ways to incrementally update the hierarchy during simulation by exploiting temporal coherence and lazy evaluation techniques. This leads to significant advantages in terms of execution speed. Furthermore, we also show how our method lends itself naturally for an adaptive low memory cost implementation, which may be of critical importance in some applications. Finally, we propose two different techniques for detecting selfintersections, one using our hierarchical data structure, and the other is an improved sortingbased method.
Towards small world emergence
 In Proceedings of 18th ACM Symposium on Parallelism in Algorithms and Architectures
, 2006
"... We investigate the problem of optimizing the routing performances of a virtual network by adding extra random links. Our asynchronous and distributed algorithm ensures, by adding a single extra link per node, that the resulting network is a navigable small world, i.e., in which greedy routing, using ..."
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Cited by 24 (3 self)
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We investigate the problem of optimizing the routing performances of a virtual network by adding extra random links. Our asynchronous and distributed algorithm ensures, by adding a single extra link per node, that the resulting network is a navigable small world, i.e., in which greedy routing, using the distance in the original network, computes paths of polylogarithmic length between any pair of nodes with probability 1 − O(1/n). Previously known small world augmentation processes require the global knowledge of the network and centralized computations, which is unrealistic for large decentralized networks. Our algorithm, based on a careful multilayer sampling of the nodes and the construction of a light overlay network, bypasses these limitations. For bounded growth graphs, i.e., graphs where, for any node u and any radius r the number of nodes within distance 2r from u is at most a constant times the number of nodes within distance r, our augmentation process proceeds with high probability in O(log n log D) communication rounds, with O(log n log D) messages of size O(log n) bits sent per node and requiring only O(log n log D) bit space in each node, where n is the number of nodes, and D the diameter. In particular, with the only knowledge of original distances, greedy routing computes,
An optimal dynamic spanner for doubling metric spaces
 In [KL04] [KR07] [Laa00] [Laa02] [Lee10] [LLKS85] [LP01] [Mit99] Proceedings of the 16th annual European symposium on Algorithms, ESA ’08
, 2008
"... For a set S of points in a metric space, a tspanner is a graph on the points of S such that between any pair of points there is a path in the spanner whose total length is at most t times the actual distance between the points. In this paper, we consider points residing in a metric space of doublin ..."
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Cited by 22 (6 self)
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For a set S of points in a metric space, a tspanner is a graph on the points of S such that between any pair of points there is a path in the spanner whose total length is at most t times the actual distance between the points. In this paper, we consider points residing in a metric space of doubling dimension λ, and show how to construct a dynamic (1+ε)spanner with constant degree and O(log n) update time (when λ and ε are taken as constants). Our update time is optimal up to a constant.
Improved algorithms for fully dynamic geometric spanners and geometric routing
 In ACM Symposium on Discrete Algorithms
, 2008
"... For a set S of points in R d, a tspanner is a sparse graph on the points of S such that between any pair of points there is a path in the spanner whose total length is at most t times the Euclidean distance between the points. In this paper, we show how to construct a (1 + ε)spanner with O(n/ε d) ..."
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Cited by 17 (11 self)
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For a set S of points in R d, a tspanner is a sparse graph on the points of S such that between any pair of points there is a path in the spanner whose total length is at most t times the Euclidean distance between the points. In this paper, we show how to construct a (1 + ε)spanner with O(n/ε d) edges and maximum degree O(1/ε d) in time O(n log n). A spanner with similar properties was previously presented in [6, 8]. However, using our new construction (coupled with several other innovations) we obtain new results for two fundamental problems for constant doubling dimension metrics: The first result is an essentially optimal compact routing scheme. In particular, we show how to perform routing with a stretch of 1 + ɛ, where the label size is ⌈log n ⌉ and the size of the table stored at each point is only O(log n/ε d). This routing problem was first considered by Peleg and Hassin [11], who presented a routing scheme in the plane. Later, Chan et al. [6] and Abraham et al. [1] considered this problem for doubling dimension metric spaces. Abraham et al. [1] were the first to present a (1 + ɛ) routing scheme where the label size depends solely on the number of points. In their scheme labels are of size of ⌈log n⌉, and each point stores a table of size O(log 2 n/ε d). In our routing scheme, we achieve routing tables of size O(log n/ε d), which is essentially the same size as a label (up to the factor of 1/ε d). The second and main result of this paper is the first fully dynamic geometric spanner with polylogarithmic update time for both insertions and deletions. We present an algorithm that allows points to be inserted into and deleted from S with an amortized update time of O(log 3 n).
Faulttolerant spanners for general graphs
 in STOC’09, 2009
"... The paper concerns graph spanners that are resistant to vertex or edge failures. Given a weighted undirected nvertex graph G = (V,E) and an integer k ≥ 1, the subgraph H = (V,E′), E ′ ⊆ E, is a spanner of stretch k (or, a kspanner) of G if δH(u, v) ≤ k · δG(u, v) for every u, v ∈ V, where δG′(u ..."
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Cited by 17 (4 self)
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The paper concerns graph spanners that are resistant to vertex or edge failures. Given a weighted undirected nvertex graph G = (V,E) and an integer k ≥ 1, the subgraph H = (V,E′), E ′ ⊆ E, is a spanner of stretch k (or, a kspanner) of G if δH(u, v) ≤ k · δG(u, v) for every u, v ∈ V, where δG′(u, v) denotes the distance between u and v in G Graph spanners were extensively studied since their introduction over two decades ago. It is known how to efficiently construct a (2k−1)spanner of size O(n1+1/k), and this sizestretch tradeoff is conjectured to be tight. The notion of fault tolerant spanners was introduced a decade ago in the geometric setting [Levcopoulos et al., STOC’98]. A subgraph H is an fvertex fault tolerant kspanner of the graph G if for any set F ⊆ V of size at most f and any pair of vertices u, v ∈ V \ F, the distances in H satisfy δH\F (u, v) ≤ k · δG\F (u, v). Levcopoulos et al. presented an efficient algorithm that given a set S of n points in Rd, constructs an fvertex fault tolerant geometric (1+)spanner for S, that is, a sparse graph H such that for every set F ⊆ S of size f and any pair of points u, v ∈ S \F, δH\F (u, v) ≤ (1+)uv, where uv  is the Euclidean distance between u and v. A fault tolerant geometric spanner with optimal maximum degree and total weight was presented in [Czumaj & Zhao, SoCG’03]. This paper also raised as an open problem the question whether it is possible to obtain a fault tolerant spanner for an arbitrary undirected weighted graph. The current paper answers this question in the affirmative, presenting an fvertex fault tolerant (2k−1)spanner of size
Subspace SelfCollision Culling
"... We show how to greatly accelerate selfcollision detection (SCD) for reduced deformable models. Given a triangle mesh and a set of deformation modes, our method precomputes Subspace SelfCollision Culling (SSCC) certificates which, if satisfied, prove the absence of selfcollisions for large parts o ..."
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Cited by 14 (1 self)
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We show how to greatly accelerate selfcollision detection (SCD) for reduced deformable models. Given a triangle mesh and a set of deformation modes, our method precomputes Subspace SelfCollision Culling (SSCC) certificates which, if satisfied, prove the absence of selfcollisions for large parts of the model. At runtime, bounding volume hierarchies augmented with our certificates can aggressively cull overlap tests and reduce hierarchy updates. Our method supports both discrete and continuous SCD, can handle complex geometry, and makes no assumptions about geometric smoothness or normal bounds. It is particularly effective for simulations with modest subspace deformations, where it can often verify the absence of selfcollisions in constant time. Our certificates enable low amortized costs, in time and across many objects in multibody dynamics simulations. Finally, SSCC is effective enough to support selfcollision tests at audio rates, which we demonstrate by producing the first sound simulations of clattering objects.
Fast Adaptive Shape Matching Deformations
, 2008
"... We present a new shapematching deformation model that allows for efficient handling of topological changes and dynamic adaptive selection of levels of detail. Similar to the recently presented Fast Lattice Shape Matching (FLSM), we compute the position of simulation nodes by convolution of rigid sh ..."
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Cited by 13 (2 self)
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We present a new shapematching deformation model that allows for efficient handling of topological changes and dynamic adaptive selection of levels of detail. Similar to the recently presented Fast Lattice Shape Matching (FLSM), we compute the position of simulation nodes by convolution of rigid shape matching operators on many overlapping regions, but we rely instead on octreebased hierarchical sampling and an intervalbased region definition. Our approach enjoys the efficiency and robustness of shapematching deformation models, and the same algorithmic simplicity and linear cost as FLSM, but it eliminates its dense sampling requirements. Our method can handle adaptive spatial discretizations, allowing the simulation of more degrees of freedom in arbitrary regions of interest at little additional cost. The method is also versatile, as it can simulate elastic and plastic deformation, it can handle cuts interactively, and it reuses the underlying data structures for efficient handling of (self)collisions. All this makes it especially useful for interactive applications such as videogames.
Distributed proximity maintenance in ad hoc mobile networks
, 2005
"... We present an efficient distributed data structure, called the DSPANNER, for maintaining proximity information among communicating mobile nodes. The DSPANNER is a kinetic sparse graph spanner on the nodes that allows each node to quickly determine which other nodes are within a given distance of ..."
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Cited by 9 (2 self)
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We present an efficient distributed data structure, called the DSPANNER, for maintaining proximity information among communicating mobile nodes. The DSPANNER is a kinetic sparse graph spanner on the nodes that allows each node to quickly determine which other nodes are within a given distance of itself, to estimate an approximate nearest neighbor, and to perform a variety of other proximity related tasks. A lightweight and fully distributed implementation is possible, in that maintenance of the proximity information only requires each node to exchange a modest number of messages with a small number of mostly neighboring nodes. The structure is based on distance information between communicating nodes that can be derived using ranging or localization methods and requires no additional shared infrastructure other than an underlying communication network. Its modest requirements make it scalable to networks with large numbers of nodes.
Distancesensitive routing and information brokerage in sensor networks
 in IEEE International Conference on Distributed Computing in Sensor System (DCOSS’06
, 2006
"... Abstract — In a sensor network information from multiple nodes must usually be aggregated in order to accomplish a certain task. A natural way to view this information gathering is in terms of interactions between nodes that are producers of information, e.g., those that have collected data, detecte ..."
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Cited by 9 (2 self)
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Abstract — In a sensor network information from multiple nodes must usually be aggregated in order to accomplish a certain task. A natural way to view this information gathering is in terms of interactions between nodes that are producers of information, e.g., those that have collected data, detected events, etc., and nodes that are consumers of information, i.e., nodes that seek data of certain types. Our overall goal in this paper is to construct efficient schemes allowing consumer and producer nodes to discover each other so that the desired information can be sent quickly to those who seek it. Here, efficiency is an issue for both the producers (limiting the redundancy of where information is stored) as well as the consumers (keeping the query time low). We introduce the notion of distancesensitive information brokerage and provide schemes for efficiently bringing together information producers and consumers at a cost proportional to the separation between them—even though the consumers do not know the locations of the producers they seek. Our algorithms rely purely on the communication topology of the sensor network and do not require any geographic location information. In the process we introduce a new routing scheme that is of interest in its own right because it provides constantfactor approximations to the optimal paths. We give theoretical proofs of the efficiency of our scheme, as well as experimental results that further demonstrate its performance and suggest its practicality even for large scale sensor networks. I.
Optimal Euclidean spanners: really short, thin and lanky
 BenGurion University
, 2012
"... The degree, the (hop)diameter, and the weight are the most basic and wellstudied parameters of geometric spanners. In a seminal STOC’95 paper, titled“Euclidean spanners: short, thin and lanky”, Arya et al. [2] devised a construction of Euclidean (1 + ɛ)spanners that achieves constant degree, diam ..."
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Cited by 7 (5 self)
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The degree, the (hop)diameter, and the weight are the most basic and wellstudied parameters of geometric spanners. In a seminal STOC’95 paper, titled“Euclidean spanners: short, thin and lanky”, Arya et al. [2] devised a construction of Euclidean (1 + ɛ)spanners that achieves constant degree, diameter O(log n), weight O(log 2 n) · ω(MST), and has running time O(n · log n). This construction applies to npoint constantdimensional Euclidean spaces. Moreover, Arya et al. conjectured that the weight bound can be improved by a logarithmic factor, without increasing the degree and the diameter of the spanner, and within the same running time. This conjecture of Arya et al. became one of the most central open problems in the area of Euclidean spanners. Nevertheless, the only progress since 1995 towards its resolution was achieved in the lower bounds front: Any spanner with