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16
External Memory Data Structures
, 2001
"... In many massive dataset applications the data must be stored in space and query efficient data structures on external storage devices. Often the data needs to be changed dynamically. In this chapter we discuss recent advances in the development of provably worstcase efficient external memory dynami ..."
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Cited by 76 (32 self)
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In many massive dataset applications the data must be stored in space and query efficient data structures on external storage devices. Often the data needs to be changed dynamically. In this chapter we discuss recent advances in the development of provably worstcase efficient external memory dynamic data structures. We also briefly discuss some of the most popular external data structures used in practice.
Dynamic Trees and Dynamic Point Location
 In Proc. 23rd Annu. ACM Sympos. Theory Comput
, 1991
"... This paper describes new methods for maintaining a pointlocation data structure for a dynamicallychanging monotone subdivision S. The main approach is based on the maintenance of two interlaced spanning trees, one for S and one for the graphtheoretic planar dual of S. Queries are answered by using ..."
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Cited by 46 (9 self)
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This paper describes new methods for maintaining a pointlocation data structure for a dynamicallychanging monotone subdivision S. The main approach is based on the maintenance of two interlaced spanning trees, one for S and one for the graphtheoretic planar dual of S. Queries are answered by using a centroid decomposition of the dual tree to drive searches in the primal tree. These trees are maintained via the linkcut trees structure of Sleator and Tarjan, leading to a scheme that achieves vertex insertion/deletion in O(log n) time, insertion/deletion of kedge monotone chains in O(log n + k) time, and answers queries in O(log 2 n) time, with O(n) space, where n is the current size of subdivision S. The techniques described also allow for the dual operations expand and contract to be implemented in O(log n) time, leading to an improved method for spatial pointlocation in a 3dimensional convex subdivision. In addition, the interlacedtree approach is applied to online pointlo...
FULLY DYNAMIC POINT LOCATION IN A MONOTONE SUBDIVISION
, 1989
"... In this paper a dynamic technique for locating a point in a monotone planar subdivision, whose current number of vertices is n, is presented. The (complete set of) update operations are insertion of a point on an edge and of a chain of edges between two vertices, and their reverse operations. The d ..."
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Cited by 23 (7 self)
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In this paper a dynamic technique for locating a point in a monotone planar subdivision, whose current number of vertices is n, is presented. The (complete set of) update operations are insertion of a point on an edge and of a chain of edges between two vertices, and their reverse operations. The data structure uses space O(n). The query time is O(log n), the time for insertion/deletion of a point is O(log n), and the time for insertion/deletion of a chain with k edges is O(log n + k), all worstcase. The technique is conceptually a special case of the chain method of Lee and Preparata and uses the same query algorithm. The emergence of full dynamic capabilities is afforded by a subtle choice of the chain set (separators), which induces a total order on the set of regions of the planar subdivision.
New Results on Binary Space Partitions in the Plane
 COMPUT. GEOM. THEORY APPL
, 1994
"... We prove the existence of linear size binary space partitions for sets of objects in the plane under certain conditions that are often satisfied in practical situations. In particular, we construct linear size binary space partitions for sets of fat objects, for sets of line segments where the ra ..."
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Cited by 20 (7 self)
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We prove the existence of linear size binary space partitions for sets of objects in the plane under certain conditions that are often satisfied in practical situations. In particular, we construct linear size binary space partitions for sets of fat objects, for sets of line segments where the ratio between the lengths of the longest and shortest segment is bounded by a constant, and for homothetic objects. For all cases we also show how to turn the existence proofs into efficient algorithms.
A Unified Approach to Dynamic Point Location, Ray Shooting, and Shortest Paths in Planar Maps
, 1992
"... We describe a new technique for dynamically maintaining the trapezoidal decomposition of a connected planar map M with 7 ~ vertices, and apply it to the development of a unified dynamic data structure that supports pointlocation, rayshooting, and shortestpath queries in M. The space requirement i ..."
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Cited by 20 (6 self)
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We describe a new technique for dynamically maintaining the trapezoidal decomposition of a connected planar map M with 7 ~ vertices, and apply it to the development of a unified dynamic data structure that supports pointlocation, rayshooting, and shortestpath queries in M. The space requirement is O(nlog n). Pointlocation queries take time O(log 7~). Rayshooting and shortestpath queries take time O(log3 TZ) (plus O(k) time if the k edges of the shortest path are reported in addition to its length). Updates consist of insertions and deletions of vertices and edges, and take O(log3 n) time (amortized for vertex updates).
Dynamization of the Trapezoid Method for Planar Point Location
, 1991
"... We present a fully dynamic data structure for point location in a monotone subdivision, based on the trapezoid method. The operations supported are insertion and deletion of vertices and edges, and horizontal translation of vertices. Let n be the current number of vertices of the subdivision. Point ..."
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Cited by 15 (4 self)
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We present a fully dynamic data structure for point location in a monotone subdivision, based on the trapezoid method. The operations supported are insertion and deletion of vertices and edges, and horizontal translation of vertices. Let n be the current number of vertices of the subdivision. Point location queries take O(log n) time, while updates take O(log2 n) time. The space requirement is O(n log n). This is the first fully dynamic point location data structure for monotone subdivisions that achieves optimal query time.
A General Approach to Dominance in the Plane
 Journal of Algorithms
, 1988
"... Given two points p and q and a set of points 0 in the plane, p is said to dominate q with respect to O if p dominates q and there is no o O such that p dominates o and o dominates q. In other words, O is a set of obstacles that might block the "rectangular view" from p to q. Given sets P a ..."
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Cited by 9 (2 self)
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Given two points p and q and a set of points 0 in the plane, p is said to dominate q with respect to O if p dominates q and there is no o O such that p dominates o and o dominates q. In other words, O is a set of obstacles that might block the "rectangular view" from p to q. Given sets P and O we are interested in determining all pairs (p, q) P x P such that p dominates q with respect to O. This generalizes hotions of direct dominance and rectangular visibility that have been studied before. An algorithm is presented that solves the problem in optimal time O(nlogn k), where n is the size of P U O and k is the number of answers. A second problem asks to store the sets P and O such that queries of the form "given a query point q, compute all points p in P, such that q dominates p with respect to O" can be answered efficiently. A static structure is devised with a query time of O(logn k) using O(nlo 2 n) storage. Using a different approach, we devise a fully dynamic structure in which queries cost O(log 2 n k) time.
H.," Efficient Algorithms for Exact Motion Planning amidst Fat Obstacles
 IEEE int. Conf. on Robotics and Automation
, 1993
"... ..."
Dynamic Partition Trees
 IN SCANDAWIAN WORKSHOP ON ALGORITHMS THEORY
, 1989
"... In this paper we study dynamic variants of conjugation trees and related structures that have recently been introduced for performing various types of queries on sets of points and line segments, like halfplanar range searching, shooting, intersection queries, etc. For most of these types of que ..."
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Cited by 1 (0 self)
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In this paper we study dynamic variants of conjugation trees and related structures that have recently been introduced for performing various types of queries on sets of points and line segments, like halfplanar range searching, shooting, intersection queries, etc. For most of these types of queries dynamic structures are obtained with an amortized update time of O(log 2 n) (or less) with only minor increases in the query times. As an application of the method we obtain an outputsensitive method for hidden surface removal in a set of n triangles that runs in time O(n. kls,(l+v) 1 log n) where k is the size of the visibility map obtained.
Computation of the Axial View of a Set of lsothetic Palrallelepipeds
, 1990
"... We present a new technique to display a scene of threedimensional isothetic parallelepipeds (3Drectangles), viewed from infinity along one of the coordinate axes (axial view). In this situation, there always exists a topological sorting of the 3Drectangles based on the relation of occlusion (a do ..."
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We present a new technique to display a scene of threedimensional isothetic parallelepipeds (3Drectangles), viewed from infinity along one of the coordinate axes (axial view). In this situation, there always exists a topological sorting of the 3Drectangles based on the relation of occlusion (a dominance relation). The arising total order is used to generate the axial view, where the twodimensional view of each 3Drectangle is incrementally added, starting from the closest 3Drectangle. The proposed scenesensitiue algorithm runs in time O(N logzN + d log N), where N is the number of 3Drectangles and d is the number of edges of the display. This improves over the previously best known technique based on the same approach.