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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 81 (36 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 (11 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...
I/OEfficient Dynamic Planar Point Location
"... We present the first provably I/Oefficient dynamic data structure for point location in a general planar subdivision. Our structure uses O(N/B) disk blocks to store a subdivision of size N , where B is the disk block size. Queries can be answered in ... I/Os in the worstcase, and insertions and de ..."
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Cited by 29 (17 self)
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We present the first provably I/Oefficient dynamic data structure for point location in a general planar subdivision. Our structure uses O(N/B) disk blocks to store a subdivision of size N , where B is the disk block size. Queries can be answered in ... I/Os in the worstcase, and insertions and deletions can be performed in ... and ... I/Os amortized, respectively. Previously, an I/Oefficient dynamic point location structure was only known for monotone subdivisions. Part of our data structure...
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.
I/OEfficient Dynamic Point Location in Monotone Planar Subdivisions (Extended Abstract)
"... We present an efficient externalmemory dynamic data structure for point location in monotone planar subdivisions. Our data structure uses O(N=B) disk blocks to store a monotone subdivision of size N, where B is the size of a disk block. It supports queries in O(log2B N) I/Os (worstcase) and upda ..."
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Cited by 20 (15 self)
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We present an efficient externalmemory dynamic data structure for point location in monotone planar subdivisions. Our data structure uses O(N=B) disk blocks to store a monotone subdivision of size N, where B is the size of a disk block. It supports queries in O(log2B N) I/Os (worstcase) and updates in O(log2B N) I/Os (amortized). We also
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 19 (6 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.
Dynamization of the Trapezoid Method for Planar Point Location in Monotone Subdivisions
 INTERNATIONAL JOURNAL OF COMPUTATIONAL GEOMETRY AND APPLICATIONS
, 1992
"... 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. Poi ..."
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Cited by 16 (5 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(logn) time, while updates take O(log² n) time (amortized for vertex insertion/deletion and worstcase for the others). 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 and O we ar ..."
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Cited by 7 (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.
Efficient Algorithms for Exact Motion Planning amidst Fat Obstacles
, 1993
"... The complexity of exact motion planning algorithms highly depends on the complexity of the robot's free space, i.e., the set of all collisionfree placements of the robot. Theoretically, the complexity of the free space can be very high. In practice, the complexity of the free space tends to be much ..."
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Cited by 6 (0 self)
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The complexity of exact motion planning algorithms highly depends on the complexity of the robot's free space, i.e., the set of all collisionfree placements of the robot. Theoretically, the complexity of the free space can be very high. In practice, the complexity of the free space tends to be much smaller. We show that, under some realistic assumptions, the complexity of the free space of a robot moving amidst fat obstacles is linear in the number of obstacles. The complexity results lead to efficient algorithms for motion planning amidst fat obstacles: we show that the O(n 5 ) motion planning algorithm by Schwartz and Sharir runs in O(n 2 ) time if the obstacles are fat. Finally, we modify the algorithm to improve the running time to O(n log 2 n). 1 Introduction Autonomous robots are one of the ultimate goals in the field of robotics. An autonomous robot must accept highlevel descriptions of tasks and execute these tasks without further intervention from its environment. An...
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.