M. H. Overmars. The Design of Dynamic Data Structures. Springer, 1983. Home/Search Document Not in Database Summary Related Articles Check |
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Space-Efficient Finger Search on Degree-Balanced Search.. - Blelloch, Maggs, Leung, Woo (2003) (3 citations) (Correct)
....treebased designs mentioned above, this O(n) extra storage requirement is a common trait. Our design is an attempt to avoid this O(n) storage requirement but at the same time retain the structural simplicity of balanced search trees. To this end, we base our design on degree balanced search trees [17] and we assume a compact k ary node with only (k 1) keys and k child pointers. Since any extra storage we need must be stored in some auxiliary data structures outside of the tree, our goal is to minimize the amount of auxiliary storage while supporting the finger search operation in worst case ....
M. H. Overmars. The Design of Dynamic Data Structures, pages 34--35. Number 156 in LNCS. SpringerVerlag, 1983.
Kinetic Medians and kd-Trees - Agarwal, Gao, Guibas (2002) (1 citation) (Correct)
....used in practice and several variants of them have been proposed [3, 7, 17] It is well known that a kd tree can answer a two dimensional orthogonal range query in O( # n k) time, where k is the number of points reported. Variants of kd trees that support insertions and deletions are studied in [18, 9]. No kinetic data structures are known for kd trees. Agarwal et al. 1] were the first to develop kinetic data structures for answering range searching queries on moving points. They developed a kinetic data structure that answers a two dimensional range query in O(log n k) time using O(n log ....
....whose proof is omitted. Theorem 4. Given an arrangement of n lines in the plane, we can compute a curve with C continuity which is a # approximate median level. The curve is determined by O(k # ) control points and is computed in O(k n log n # ) time. 3 Pseudo kd tree Overmars [18] proposed the pseudo kd tree as a dynamic data structure for range searching that admits e#cient insertion and deletion of points. Definition. A # pseudo kd tree is defined to be a binary tree created by alternately partitioning the points with vertical and horizontal lines, so that for each node ....
[Article contains additional citation context not shown here]
M. H. Overmars. The Design of Dynamic Data Structures, volume 156 of Lecture Notes Comput. Sci. Springer-Verlag, Heidelberg, West Germany, 1983.
Bkd-tree: A Dynamic Scalable kd-tree - Procopiuc, Agarwal, Arge, Vitter (2002) (2 citations) (Correct)
....approaches in terms of storage utilization and update time, while maintaining similar query performance. The main ingredients used in the design of the Bkd tree are an I O efficient KD B tree bulk loading algorithm and the so called logarithmic method for making a static data structure dynamic [8, 21]. Instead of maintaining one tree and dynamically rebalance it after an insertion, we maintain a set of static K D B trees and perform updates by rebuilding a carefully chosen set of the structures at regular intervals ( is the capacity of the memory buffer, in number of points) This way we ....
.... periodical rebuilding is of course that the update bound varies from update to update (thus the amortized result) However, queries can still be answered while an update (rebuilding) is being performed, and (at least theoretically) the update bound can be made worst case using additional storage [21]. While our Bkd tree has nice theoretical properties, the main contribution of this paper is a proof of its practical viability. We present the result of an extensive experimental study of the performance of the Bkd tree compared to the K D B tree using both real life (TIGER) and artificially ....
[Article contains additional citation context not shown here]
M. H. Overmars. The Design of Dynamic Data Structures, volume 156 of Lecture Notes Comput. Sci. Springer-Verlag, 1983.
LR-tree: a Logarithmic Decomposable Spatial Index Method - Bozanis, Nanopoulos.. (2003) (Correct)
.... main memory data structures: since it is easier to design data structures for static sets with good query time, there have been a number of efforts aimed at devising general methods for transforming static or semi dynamic data structures into dynamic ones for decomposable searching problems [9, 10, 11]. A searching problem is said to be decomposable if one can partition the input set into a set of disjoint subsets, perform the query on each subset independently and then easily compose the partial answers. The most useful geometric searching problems, like range searching, nearestneighbor ....
....Section 4 defines LR trees and presents the algorithms for queries and updates. Section 5 gives the performance study. Finally, Section 6 concludes our work. 2. A DYNAMIZATION TECHNIQUE FOR DECOMPOSABLE SEARCHING PROBLEMS In this section we will use the following notion of decomposability [9, 11]. DEFINITION 1. A searching problem P(q, S) on a set S with query q is called decomposable if and only if for any partition V = A,B ,S= A B, A =# of S and any query q , P(q, S) #(P(q, A) P(q, B) for some operator # computable in O(1) time. It follows promptly that, in order to ....
[Article contains additional citation context not shown here]
Overmars, M. H. (1983) The Design of Dynamic Data Structures. Springer, Berlin.
Low Latency Photon Mapping Using Block Hashing - Ma, McCool (2002) (4 citations) (Correct)
....the kNN and AkNN problems. Christensen described an iterative traversal method for a heap based kd tree used in photon mapping [37] and claimed a 25 performance improvement, under ideal conditions, over the recursive method. Vanco et al. 70] devised a scheme that employs a pseudo kd tree [52] with hash tables as leaf nodes, the latter helping to limit the number of candidates examined at each leaf node. Havran [27] analysed a novel memory mapping method designed to improve spatial locality of data stored in binary trees, thus speeding up tree traversal algorithms. Sample et al. 62] ....
Mark H. Overmars. The design of dynamic data structures. Springer-Verlag, Berlin, 1983. 2.2
Semi-Online Maintenance of Geometric Optima and Measures - Chan (2003) (Correct)
....in Section 8, including improved time bounds for Klee s measure problem [26] in the case of 4 dimensional unit hypercubes, and for the minimum diameter spanning tree problem, which are of independent interest. 2 The strategy for semi online dynamization The most common dynamization strategy [5, 24, 25] is based on decomposing a set of objects into subsets, solving the problem on each subset, and combining the answers. An update a ects only a small number of subsets and thus can be eciently handled. Unfortunately, this simple approach is not viable for any of our problems, because they are not ....
....O(b ) time. The total time for n updates is therefore e O( n=b) n n (b ) 2 = 1 ) 1) if we set the parameter b n = 1 ) This proves an amortized time bound of e O(n ) If the application insists on a worst case time bound, a well known modi cation (e.g. see [24, 25]) is required: spread the work of rebuilding the data structure for S evenly over the next b=2 updates. The data structure for S is available for the j th update whenever j mod b b=2. A similar shifted version of S and S can deal with the other case j mod b b=2. 2 All our e orts are now ....
[Article contains additional citation context not shown here]
M. H. Overmars, The Design of Dynamic Data Structures, Lect. Notes in Comput. Sci., vol. 156, Springer-Verlag, Heidelberg, 1983.
Implementing I/O-Efficient Data Structures Using TPIE - Arge, Procopiuc, Vitter (2002) (1 citation) (Correct)
....are widely used indexing data structures for spatial data. The TPIE implementation uses the insertion heuristics proposed by Beckmann et al. 10] their variant is called the R tree) and various bulk loading procedures. More details are given in [6, 7] Logarithmic method. The logarithmic method [16] is a generic dynamization method. Given a static index with certain properties, it produces a dynamic structure consisting of a set of smaller static indexes of geometrically increasing sizes. We implemented the external memory versions of this method, as proposed by Arge and Vahrenhold [8] and ....
M. H. Overmars. The Design of Dynamic Data Structures, volume 156 of Lecture Notes Comput. Sci. Springer-Verlag, Heidelberg, West Germany, 1983.
Efficient Aggregation over Objects with Extent (Extended Abstract) - Zhang, al. (2002) (7 citations) (Correct)
....to range sum. Furthermore, the data structure is rather complex to implement in practice. Note that the ECDF tree and the range tree are both static and internal memory structures. To dynamize a static data structure some standard techniques can be used [12] For example, the global rebuilding [24] or the logarithmic method [8] To externalize an internal memory data structure, a widely used method is to augment it with block access capabilities [34] Range Sum for Data Cubes and Point Data. The data cube range sum problem addresses the following query: given a d dimensional array A and a ....
M. H. Overmars, \The Design of Dynamic Data Structures ", LNCS 156, 1983.
Concatenavble Segment Trees - van Kreveld, al. (1988) (Correct)
....with each node there is an associated structure that stores some set of objects. Splitting then normally means rebuilding such associated struc tures, which takes too much time. Hence, more sophisticated techniques are required. In this paper we devise such a method for segment trees (see [3, 4, 8, 9, 11, 14]) This variant of the structure we design works efficiently and might be useful in a number of geometric applications (it was recently used for solving some robotics problem Is] Segment trees are used to store intervals on a line. Such intervals might overlap. When splitting a segment tree we ....
....The segment tree is a one dimeusional data structure used for solving many two dimeusional problems, such as finding rectangle intersections and finding the contour of the union of rectangles. It was introduced by Bentley in 1977 [3] see 2 [a:x) b:y) Figure 1: Insertion in a segment tree also [4, 8, 9, 11, 14]) Suppose n segments (intervals) al. hi] a2: bi] an: bn ] on the real line are given. Segments may intersect or overlap, and left and right endpoints of two segments may be equal. We sort all different endpoints, obtaining an ordered sequence x, x2, x, where rn 2n. These endpoints ....
Overmars, M.H., The design of dynamic data structures, Lect. Notes in Comp. Science Vol. 156, Springer-Verlag, 1983.
Divided k-d Trees - van Kreveld, Overmars (1988) (2 citations) Self-citation (Overmars) (Correct)
....to build. Proof. Follows from lemmas 1, 2 and 5. 2. 3 Worst case bounds The amortized insertion and deletion time bounds of theorem 1 can be changed into worst case time bounds with the general technique of global rebuilding, introduced by Overmars and van Leeuwen in [11] also described in [10]. We will not describe the technique here, but we will give the theorem that we use to obtain worst case time bounds. Theorem 2 Given a tree T representing n points with rebuilding time bounded by O(n log n) that allows for weak insertions and for weak deletions, we can dynamize it into a ....
Overmars, M.H., The design of dynamic data structures, Lect. Notes in Comp. Science 156, Springer-Verlag, Heidelberg, 1983.
Dynamizing Static Algorithms, with Applications to.. - Acar, Blelloch.. (2003) (Correct)
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M. H. Overmars. The Design of Dynamic Data Structures. Springer, 1983.
Space-Ecient Finger Search on Degree-Balanced Search Trees - Guy Blelloch Bruce (Correct)
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M. H. Overmars. The Design of Dynamic Data Structures, pages 34--35. Number 156 in LNCS. SpringerVerlag, 1983.
Remembrance of Streams Past: Overload-Sensitive.. - Chandrasekaran, Franklin (2004) (1 citation) (Correct)
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M. Overmars: "The design of dynamic data structures". LNCS 1983
Remembrance of Streams Past: - Overload-Sensitive Management Of (2004) (Correct)
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M. Overmars: "The design of dynamic data structures". LNCS 1983
A Dynamic Separator Algorithm - Deganit Armon John (1993) (1 citation) (Correct)
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M. Overmars. The design of dynamic data structures. Lecture Notes in Computer Science, 156, Springer-Verlag, 1983.
Dynamizing Static Algorithms, with Applications to.. - Acar, Blelloch.. (2004) (Correct)
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M. H. Overmars. The Design of Dynamic Data Structures. Springer, 1983.
Fully-dynamic orthogonal range reporting on RAM - Mortensen (2003) (Correct)
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Mark H. Overmars. The Design of Dynamic Data Structures. Springer, 1983.
Dynamizing Static Algorithms, with Applications to.. - Acar, Blelloch.. (2003) (Correct)
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M. H. Overmars. The Design of Dynamic Data Structures. Springer, 1983.
Indexing Problems in Spatiotemporal Databases - Kollios (2000) (Correct)
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M.H. Overmars. The Design of Dynamic Data Structures. LNCS vol. 156, SpringerVerlag, Heidelberg, West Germany, 1983.
Dynamic Planar Convex Hull Operations in Near-Logarithmic.. - Chan (2000) (17 citations) (Correct)
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M. H. Overmars. The Design of Dynamic Data Structures. Lect. Notes in Comput. Sci., vol. 156, Springer-Verlag, 1983.
Active Libraries and Universal Languages - Veldhuizen (2004) (1 citation) (Correct)
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M. H. Overmars. The Design of Dynamic Data Structures. Springer, Berlin, 1983. ISBN 3-540-12330-X.
Cache-Oblivious B-Trees - Bender, Demaine, Farach-Colton (2000) (25 citations) (Correct)
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M. H. Overmars. The Design of Dynamic Data Structures, LNCS 156. Springer-Verlag, 1983.
Title Page - Submitted Pods' Paper (Correct)
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M. H. Overmars, \The Design of Dynamic Data Structures", LNCS 156, 1983.
Aggregation Computation over Complex Objects - Zhang (2002) (2 citations) (Correct)
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M. H. Overmars, "The Design of Dynamic Data Structures", LNCS 156, 1983.
Connected Component and Simple Polygon - Pankaj (1994) (Correct)
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Overmars, M. H., The Design of Dynamic Data Structures, Lect. Notes on Comp. Science 156, Springer-Verlag, Berlin, 1983.
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