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52
Data structures for mobile data
 JOURNAL OF ALGORITHMS
, 1997
"... A kinetic data structure (KDS) maintains an attribute of interest in a system of geometric objects undergoing continuous motion. In this paper we develop a conceptual framework for kinetic data structures, propose a number of criteria for the quality of such structures, and describe a number of fund ..."
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Cited by 270 (57 self)
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A kinetic data structure (KDS) maintains an attribute of interest in a system of geometric objects undergoing continuous motion. In this paper we develop a conceptual framework for kinetic data structures, propose a number of criteria for the quality of such structures, and describe a number of fundamental techniques for their design. We illustrate these general concepts by presenting kinetic data structures for maintaining the convex hull and the closest pair of moving points in the plane; these structures behavewell according to the proposed quality criteria for KDSs.
Indexing moving points
, 2003
"... We propose three indexing schemes for storing a set S of N points in the plane, each moving along a linear trajectory, so that any query of the following form can be answered quickly: Given a rectangle R and a real value t; report all K points of S that lie inside R at time t: We first present an in ..."
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Cited by 193 (13 self)
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We propose three indexing schemes for storing a set S of N points in the plane, each moving along a linear trajectory, so that any query of the following form can be answered quickly: Given a rectangle R and a real value t; report all K points of S that lie inside R at time t: We first present an indexing structure that, for any given constant e> 0; uses OðN=BÞ disk blocks and answers a query in OððN=BÞ 1=2þe þ K=BÞ I/Os, where B is the block size. It can also report all the points of S that lie inside R during a given time interval. A point can be inserted or deleted, or the trajectory of a point can be changed, in Oðlog 2 B NÞ I/Os. Next, we present a general approach that improves the query time if the queries arrive in chronological order, by allowing the index to evolve over time. We obtain a tradeoff between the query time and the number of times the index needs to be updated as the points move. We also describe an indexing scheme in which the number of I/Os required to answer a query depends monotonically on the difference between the query time stamp t and the current time. Finally, we develop an efficient indexing scheme to answer approximate
Kinetic Data Structures  A State of the Art Report
, 1998
"... ... In this paper we present a general framework for addressing such problems and the tools for designing and analyzing relevant algorithms, which we call kinetic data structures. We discuss kinetic data structures for a variety of fundamental geometric problems, such as the maintenance of convex hu ..."
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Cited by 103 (29 self)
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... In this paper we present a general framework for addressing such problems and the tools for designing and analyzing relevant algorithms, which we call kinetic data structures. We discuss kinetic data structures for a variety of fundamental geometric problems, such as the maintenance of convex hulls, Voronoi and Delaunay diagrams, closest pairs, and intersection and visibility problems. We also briefly address the issues that arise in implementing such structures robustly and efficiently. The resulting techniques satisfy three desirable properties: (1) they exploit the continuity of the motion of the objects to gain efficiency, (2) the number of events processed by the algorithms is close to the minimum necessary in the worst case, and (3) any object may change its `flight plan' at any moment with a low cost update to the simulation data structures. For computer applications dealing with motion in the physical world, kinetic data structures lead to simulation performance unattainable by other means. In addition, they raise fundamentally new combinatorial and algorithmic questions whose study may prove fruitful for other disciplines as well.
Discrete Mobile Centers
 Discrete and Computational Geometry
, 2001
"... We propose a new randomized algorithm for maintaining a set of clusters among moving nodes in the plane. Given a specified cluster radius, our algorithm selects and maintains a variable subset of the nodes as cluster centers. This subset has the property that (1) balls of the given radius centered a ..."
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Cited by 97 (14 self)
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We propose a new randomized algorithm for maintaining a set of clusters among moving nodes in the plane. Given a specified cluster radius, our algorithm selects and maintains a variable subset of the nodes as cluster centers. This subset has the property that (1) balls of the given radius centered at the chosen nodes cover all the others and (2) the number of centers selected is a constantfactor approximation of the minimum possible. As the nodes move, an eventbased kinetic data structure updates the clustering as necessary. This kinetic data structure is shown to be responsive, efficient, local, and compact. The produced cover is also smooth, in the sense that wholesale cluster rearrangements are avoided. The algorithm can be implemented without exact knowledge of the node positions, if each node is able to sense its distance to other nodes up to the cluster radius. Such a kinetic clustering can be used in numerous applications where mobile devices must be interconnected into an adhoc network to collaboratively perform some tasks. 1
Deformable free space tilings for kinetic collision detection
 International Journal of Robotics Research
, 2000
"... We present kinetic data structures for detecting collisions between a set of polygons that are not only moving continuously but whose shapes can also change continuously with time. We construct a planar subdivision of the common exterior of the polygons, called a pseudotriangulation, that certifies ..."
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Cited by 76 (12 self)
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We present kinetic data structures for detecting collisions between a set of polygons that are not only moving continuously but whose shapes can also change continuously with time. We construct a planar subdivision of the common exterior of the polygons, called a pseudotriangulation, that certifies their disjointness. We show different schemes for maintaining pseudotriangulations as a kinetic data structure, and we analyze their performance. Specifically, we first describe an algorithm for maintaining a pseudotriangulation of a point set, and show that the pseudotriangulation changes only quadratically many times if points move along algebraic arcs of constant degree. We then describe an algorithm for maintaining a pseudotriangulation of a set of convex polygons. Finally, we extend our algorithm to maintaining a pseudotriangulation of a set of simple polygons.
Raising Roofs, Crashing Cycles, and Playing Pool: Applications of a Data Structure for Finding Pairwise Interactions
 In Proc. 14th Annu. ACM Sympos. Comput. Geom
, 1998
"... The straight skeleton of a polygon is a variant of the medial axis, introduced by Aichholzer et al., defined by a shrinking process in which each edge of the polygon moves inward at a fixed rate. We construct the straight skeleton of an ngon with r reflex vertices in time O(n 1+" +n 8=11+& ..."
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Cited by 59 (1 self)
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The straight skeleton of a polygon is a variant of the medial axis, introduced by Aichholzer et al., defined by a shrinking process in which each edge of the polygon moves inward at a fixed rate. We construct the straight skeleton of an ngon with r reflex vertices in time O(n 1+" +n 8=11+" r 9=11+" ), for any fixed " ? 0, improving the previous best upper bound of O(nr log n). Our algorithm simulates the sequence of collisions between edges and vertices during the shrinking process, using a technique of Eppstein for maintaining extrema of binary functions to reduce the problem of finding successive interactions to two dynamic range query problems: (1) maintain a changing set of triangles in IR 3 and answer queries asking which triangle would be first hit by a query ray, and (2) maintain a changing set of rays in IR 3 and answer queries asking for the lowest intersection of any ray with a query triangle. We also exploit a novel characterization of the straight skeleton as a ...
Communication in Disconnected Adhoc Networks Using Message Relay
, 2003
"... this paper we explore the possibility of changing the host trajectories in order to facilitate communication. We show how information about the motion of the destination host can be used to determine how messages can be sent to this host by cooperating intermediate hosts. Given an adhoc network of ..."
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Cited by 44 (1 self)
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this paper we explore the possibility of changing the host trajectories in order to facilitate communication. We show how information about the motion of the destination host can be used to determine how messages can be sent to this host by cooperating intermediate hosts. Given an adhoc network of mobile computers where the trajectory of each node is approximately known, we would like to develop an algorithm for computing a trajectory for sending a message from host A to host B by recruiting intermediate hosts to help. In our context, recruiting means asking intermediate hosts to change their trajectory in order to complete a routing path between hosts A and B. We would like to minimize the trajectory modifications while getting the message across as fast as possible
Parametric and Kinetic Minimum Spanning Trees
"... We consider the parametric minimum spanning treeproblem, in which we are given a graph with edge weights that are linear functions of a parameter * and wish tocompute the sequence of minimum spanning trees generated as * varies. We also consider the kinetic minimumspanning tree problem, in which * r ..."
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Cited by 34 (9 self)
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We consider the parametric minimum spanning treeproblem, in which we are given a graph with edge weights that are linear functions of a parameter * and wish tocompute the sequence of minimum spanning trees generated as * varies. We also consider the kinetic minimumspanning tree problem, in which * represents time and the graph is subject in addition to changes such as edge insertions, deletions, and modifications of the weight functions as time progresses. We solve both problems in time O(n2=3 log4=3 n) per combinatorial change in the tree (or randomized O(n2=3 log n) per change). Our time bounds reduce to O(n1=2 log3=2 n) per change (O(n1=2 log n) randomized) for planar graphs or other minorclosed families of graphs, and O(n1=4 log3=2 n) per change (O(n1=4 log n) randomized) for planar graphs with weight changes but no insertions or deletions.
Asynchronous contact mechanics
"... We develop a method for reliable simulation of elastica in complex contact scenarios. Our focus is on firmly establishing three parameterindependent guarantees: that simulations of wellposed problems (a) have no interpenetrations, (b) obey causality, momentum and energyconservation laws, and (c ..."
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Cited by 30 (8 self)
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We develop a method for reliable simulation of elastica in complex contact scenarios. Our focus is on firmly establishing three parameterindependent guarantees: that simulations of wellposed problems (a) have no interpenetrations, (b) obey causality, momentum and energyconservation laws, and (c) complete in finite time. We achieve these guarantees through a novel synthesis of asynchronous variational integrators, kinetic data structures, and a discretization of the contact barrier potential by an infinite sum of nested quadratic potentials. In a series of two and threedimensional examples, we illustrate that this method more easily handles challenging problems involving complex contact geometries, sharp features, and sliding during extremely tight contact.
Buddy Tracking  Efficient Proximity Detection Among Mobile Friends
, 2004
"... Global positioning systems (GPS) and mobile phone networks are making it possible to track individual users with an increasing accuracy. It is natural to ask whether one can use this information to maintain social networks. Here each user wishes to be informed whenever one of a list of other users, ..."
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Cited by 27 (1 self)
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Global positioning systems (GPS) and mobile phone networks are making it possible to track individual users with an increasing accuracy. It is natural to ask whether one can use this information to maintain social networks. Here each user wishes to be informed whenever one of a list of other users, called the user's friends, appears in the user's vicinity. In contrast to more traditional positioning based algorithms, the computation here depends not only on the user's own position on a static map, but also on the dynamic position of the user's friends. Hence it requires both communication and computation resources. The computation can be carried out either between the individual users in a peertopeer fashion or by centralized servers where computation and data can be collected at one central location. In the peertopeer model, a novel algorithm for minimizing the number of location update messages between pairs of friends is presented. We also present an efficient algorithm for the centralized model, based on region hierarchy and quadtrees. The paper provides an analysis of the two algorithms, compares them with a naive approach, and evaluates them using the IBM City Simulator system.