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18
Mobiscopes for human spaces
 IEEE Pervasive Computing
, 2007
"... The proliferation of affordable mobile devices with processing and sensing capabilities, together with the rapid growth in ubiquitous network connectivity, herald an era of Mobiscopes; networked sensing applications that rely on multiple mobile sensors to accomplish global tasks. These distributed s ..."
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Cited by 57 (7 self)
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The proliferation of affordable mobile devices with processing and sensing capabilities, together with the rapid growth in ubiquitous network connectivity, herald an era of Mobiscopes; networked sensing applications that rely on multiple mobile sensors to accomplish global tasks. These distributed sensing systems extend the model of traditional sensor networks, introducing challenges in data management, data integrity, privacy, and network system design. While several applications that fit the above description exist in prior literature, they provide tailored onetime solutions to what essentially is the same set of problems. It is time to work towards a general architecture that identifies common challenges and provides a generalizable methodology for the design of future Mobiscopes. Towards that end, this paper surveys a variety of current and emerging mobile, networked, sensing applications; articulates their common challenges; and provides architectural guidelines and design directions for this important
Compressing kinetic data from sensor networks
, 2009
"... We introduce a framework for storing and processing kinetic data observed by sensor networks. These sensor networks generate vast quantities of data, which motivates a significant need for data compression. We are given a set of sensors, each of which continuously monitors some region of space. We ..."
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Cited by 4 (3 self)
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We introduce a framework for storing and processing kinetic data observed by sensor networks. These sensor networks generate vast quantities of data, which motivates a significant need for data compression. We are given a set of sensors, each of which continuously monitors some region of space. We are interested in the kinetic data generated by a finite set of objects moving through space, as observed by these sensors. Our model relies purely on sensor observations; it allows points to move freely and requires no advance notification of motion plans. Sensor outputs are represented as random processes, where nearby sensors may be statistically dependent. We model the local nature of sensor networks by assuming that two sensor outputs are statistically dependent only if the two sensors are among the k nearest neighbors of each other. We present an algorithm for the lossless compression of the data produced by the network. We show that, under the statistical dependence and locality assumptions of our framework, asymptotically this compression algorithm encodes the data to within a constant factor of the informationtheoretic lower bound optimum dictated by the joint entropy of the system.
Approximation Algorithm for the Kinetic Robust KCenter Problem
, 2009
"... Two complications frequently arise in realworld applications, motion and the contamination of data by outliers. We consider a fundamental clustering problem, the kcenter problem, within the context of these two issues. We are given a finite point set S of size n and an integer k. In the standard k ..."
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Cited by 4 (3 self)
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Two complications frequently arise in realworld applications, motion and the contamination of data by outliers. We consider a fundamental clustering problem, the kcenter problem, within the context of these two issues. We are given a finite point set S of size n and an integer k. In the standard kcenter problem, the objective is to compute a set of k center points to minimize the maximum distance from any point of S to its closest center, or equivalently, the smallest radius such that S can be covered by k disks of this radius. In the discrete kcenter problem the disk centers are drawn from the points of S, and in the absolute kcenter problem the disk centers are unrestricted. We generalize this problem in two ways. First, we assume that points are in continuous motion, and the objective is to maintain a solution over time. Second, we assume that some given robustness parameter 0 < t ≤ 1 is given, and the objective is to compute the smallest radius such that there exist k disks of this radius that cover at least ⌈tn ⌉ points of S. We present a kinetic data structure (in the KDS framework) that maintains a (3 + ε)approximation for the robust discrete kcenter problem and a (4 + ε)approximation for the robust absolute kcenter problem, both under the assumption that k is a constant. We also improve on a previous 8approximation for the nonrobust discrete kinetic kcenter problem, for arbitrary k, and show that our data structure achieves a (4 + ε)approximation. All these results hold in any metric space of constant doubling dimension, which includes Euclidean space of constant dimension.
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 4 (0 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.
Maintaining Nets and Net Trees under Incremental Motion ⋆
"... Abstract. The problem of maintaining geometric structures for points in motion has been well studied over the years. Much theoretical work to date has been based on the assumption that point motion is continuous and predictable, but in practice, motion is typically presented incrementally in discret ..."
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Cited by 3 (1 self)
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Abstract. The problem of maintaining geometric structures for points in motion has been well studied over the years. Much theoretical work to date has been based on the assumption that point motion is continuous and predictable, but in practice, motion is typically presented incrementally in discrete time steps and may not be predictable. We consider the problem of maintaining a data structure for a set of points undergoing such incremental motion. We present a simple online model in which two agents cooperate to maintain the structure. One defines the data structure and provides a collection of certificates, which guarantee the structure’s correctness. The other checks that the motion over time satisfies these certificates and notifies the first agent of any violations. We present efficient online algorithms for maintaining both nets and net trees for a point set undergoing incremental motion in a space of constant dimension. We analyze our algorithms ’ efficiencies by bounding their competitive ratios relative to an optimal algorithm. We prove a constant factor competitive ratio for maintaining a slack form of nets, and our competitive ratio for net trees is proportional to the square of the tree’s height. 1
Maintaining Approximate Minimum Steiner Tree and kcenter for Mobile Agents in a Sensor Network
"... Abstract—We study the problem of maintaining group communication between m mobile agents, tracked and helped by n static networked sensors. We develop algorithms to maintain a O(lg n)approximation to the minimum Steiner tree of the mobile agents such that the maintenance message cost is on average ..."
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Cited by 1 (1 self)
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Abstract—We study the problem of maintaining group communication between m mobile agents, tracked and helped by n static networked sensors. We develop algorithms to maintain a O(lg n)approximation to the minimum Steiner tree of the mobile agents such that the maintenance message cost is on average O(lg n) per each hop an agent moves. The key idea is to extract a ‘hierarchical wellseparated tree (HST) ’ on the sensor nodes such that the tree distance approximates the sensor network hop distance by a factor of O(lg n). We then prove that maintaining the subtree of the mobile agents on the HST uses logarithmic messages per hop movement. With the HST we can also maintain O(lg n) approximate kcenter for the mobile agents with the same message cost. Both the minimum Steiner tree and the kcenter problems are NPhard and our algorithms are the first efficient algorithms for maintaining approximate solutions in a distributed setting. I.
Algorithms for Calculating Statistical Properties of Moving Points
"... Robust statistics and kinetic data structures are two frequently studied theoretical areas with practical motivations. The former topic is the study of statistical estimators that are robust to data outliers. The latter topic is the study of data structures for calculations on moving point sets. The ..."
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Robust statistics and kinetic data structures are two frequently studied theoretical areas with practical motivations. The former topic is the study of statistical estimators that are robust to data outliers. The latter topic is the study of data structures for calculations on moving point sets. The combination of these two areas has not previously been studied. In studying this intersection, we consider these problems in the context of both an established kinetic framework (called KDS) that relies on advance point motion information and calculates properties continuously and a new sensorbased framework that uses discrete point observations. Using the KDS model, we present an approximation algorithm for the kinetic robust kcenter problem, a clustering problem that requires k clusters but allows some outlying points to remain unclustered. For many practical problems that inspired the exploration into robustness, the KDS model is inapplicable due to the point motion restrictions and the advance flight plans required. Working towards a solution to the kinetic robust kcenter problem on a framework that allows unrestricted point motion, we present a new framework for kinetic data that allows calculations on moving points via sensorrecorded observations. This new framework is one
Kinetic Maintenance of Mobile kCentres on Trees ⋆
"... Given a set P of points (clients) on a weighted tree T, a kcentre of P corresponds to a set of k points (facilities) on T such that the maximum graph distance between any client and its nearest facility is minimized. We consider the mobile kcentre problem on trees. Let C denote a set of n mobile c ..."
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Given a set P of points (clients) on a weighted tree T, a kcentre of P corresponds to a set of k points (facilities) on T such that the maximum graph distance between any client and its nearest facility is minimized. We consider the mobile kcentre problem on trees. Let C denote a set of n mobile clients, each of which follows a continuous trajectory on a weighted tree T. We establish tight bounds on the maximum relative velocity of the 1centre and 2centre of C. When each client in C moves with linear motion along a path on T, the motions of the corresponding 1centre and 2centre are piecewise linear; we derive a tight combinatorial bound of Θ(n) on the complexity of the motion of the 1centre and corresponding bounds of O(n 2 α(n)) and Ω(n 2) for a 2centre, where α(n) denotes the inverse Ackermann function. We describe efficient algorithms for calculating the trajectories of the 1centre and 2centre of C: the 1centre can be found in optimal time O(n log n) and a 2centre can be found in time O(n 2 log n). These algorithms lend themselves to implementation within the framework of kinetic data structures. Finally, we examine properties of the mobile 1centre on graphs and describe an optimal unitvelocity
Robust, Efficient, and Accurate Contact Algorithms
"... Robust, efficient, and accurate contact response remains a challenging problem in the simulation of deformable materials. Contact models should robustly handle contact between geometry by preventing interpenetrations. This should be accomplished while respecting natural laws in order to maintain phy ..."
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Robust, efficient, and accurate contact response remains a challenging problem in the simulation of deformable materials. Contact models should robustly handle contact between geometry by preventing interpenetrations. This should be accomplished while respecting natural laws in order to maintain physical correctness. We simultaneously desire to achieve these criteria as efficiently as possible to minimize simulation runtimes. Many methods exist that partially achieve these properties, but none yet fully attain all three. This thesis investigates existing methodologies with respect to these attributes, and proposes a novel algorithm for the simulation of deformable materials that demonstrate them all. This new method is analyzed and optimized, paving the way for future work in this simplified but