L. Arge. The bu#er tree: A new technique for optimal I/O-algorithms. In Proceedings of the Workshop on Algorithms and Data Structures, volume 955 of Lecture Notes in Computer Science, pages 334--345, 1995.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....can be done as a separate preprocessing step by e.g. sorting. For such an algorithm, the applicability of the method in a cache oblivious setting is linked to the degree of locality of the information needed in each merge step, a point we elaborate on in the beginning of Sect. 3. 4 Arge [2] introduced the bu#er tree an external memory data structure which, among other uses, also can be used to solve the orthogonal line segment intersection problem, batched range queries, and reporting pairwise rectangle intersection. It is an open question, if there exists an e#cient cache ....

....the rectangles. Since the pairwise rectangle intersection problem can be reduced to solving one orthogonal segment intersection reporting problem (reporting intersections of sides of rectangles) and one batched range searching problem (reporting rectangle corners within rectangles) as noted in [2, 10], the I O bound in Theorem 1 follows immediately. 3.7 All Nearest Neighbors Problem Given N points in the plane, compute for each point which other point is the closest. We solve the problem in two phases. After the first phase, each point p will be annotated by another point p 1 which is at ....

L. Arge. The bu#er tree: A new technique for optimal I/O-algorithms. In Proc. 4th Workshop on Algorithms and Data Structures (WADS), volume 955 of Lecture Notes in Computer Science, pages 334--345. Springer Verlag, Berlin, 1995.

....convenience log m n = max 1, log n) log m . Most notably I O e#cient algorithms have been developed for a large number of computational geometry [16] and graph problems [12] In [5] a general connection between the comparison complexity and the I O complexity of a given problem is shown, and in [4] alternative solutions for some of the problems in [12] and [16] are derived by developing and using dynamic external memory data structures. 1.3 Our Results In this paper, we combine and modify in novel ways several of the previously known techniques for designing e#cient algorithms for external ....

....structures. 1.3 Our Results In this paper, we combine and modify in novel ways several of the previously known techniques for designing e#cient algorithms for external memory. In particular we use the distribution sweeping and batched filtering paradigms of [16] the bu#er tree data structure of [4], and the deterministic distribution methods for parallel disks in [20] In addition we also develop a powerful new technique that can be regarded as a practical external memory version of batched fractional cascading on an external memory version of a segment tree. This enables us to improve ....

[Article contains additional citation context not shown here]

L. Arge. The bu#er tree: A new technique for optimal I/O-algorithms. In Proc. of 4th Workshop on Algorithms and Data Structures, 1995.

.... I O e#cient algorithms have been developed for a large number of computational geometry [3, 12] and graph problems [9] Also worth noticing in this context is [11] that addresses the problem of storing graphs in a paging environment, but not the problem of performing computation on them, and [2] where a number of external (batched) dynamic data structures are developed. Finally, it is demonstrated in [8, 19] that the results obtained in the mentioned papers are not only of theoretical but also of great practical interest. Some notes should be made about the typical bounds in the model. ....

....in question. Our solution to this problem is simple when a vertex is given a new label we inform all its immediate predecessors about it in a lazy way using a priority queue. Every time we give a vertex v a new label, we insert an element in the I O e#cient priority queue developed in [2] for each of the immediate predecessors of v. The elements in the priority queue are ordered according to level and vertex id of the receiving vertex, such that when we on a higher level want to know the new labels of sons of vertices on the level, we simply do deletemin operations on the queue ....

[Article contains additional citation context not shown here]

L. Arge: The Bu#er Tree: A New Technique for Optimal I/O-Algorithms. In Proc. of 4th Workshop on Algorithms and Data Structures, 1995.

....The intersection spatial join algorithms can be roughly divided into two categories: ones that use spatial index structures and ones that do not. Algorithms of [BKS93,HJR97] use spatial index structures such as R trees, R trees, R # trees. Interval B trees [ZSI99] and external segment trees [Arg95] can also be used. Algorithms without using index structures were reported in [PD96] LR96] and [APR 98,Vit98] PD96] and [LR96] used a partition based method, and [APR 98,Vit98] applied the distributes sweeping technique developed in [GTVV93] In [Rot91,SA97] spatial joins with a ....

....and Samet [HS98] developed a distance spatial join algorithm that uses R # tree like index structure and priority queue to compute tuples whose spatial attributes are within a given range. The worst case I O complexity of all above algorithms is unfortunately O(N 2 ) except that algorithms of [Arg95,APR 98,ZSI99] have a O(N logN k) I O complexity for intersection spatial join. Gunther [Gun93] proposed a general method using generalization trees as index structures for evaluating joins with many predicates including intersection, On Multi Way Spatial Joins with Direction Predicates 219 ....

L. Arge. The bu#er tree: A new technique for optimal I/O-algorithms. In Proc. Workshop on Algorithms and Data structures, 1995.

....previous results known were those of [13] which only work for the planar case and for K = 1. Also, in [3] it is shown that computing the closest pair of a point set requires sort(N) I Os, which implies the same lower bound for Problems 3 and 4. We extend the time forward processing technique of [1, 11] to certain types of incremental directed acyclic graphs that are generated on the y (Section 2) This together with standard external memory techniques is the main ingredient for developing external memory algorithms for the above problems. 1.3 Preliminaries For a given point set P , the ....

.... assigning constant size labels (v) to the nodes in V . For a node v, let (u 1 ; v) u k ; v) be all its inedges. Then (v) is a function of (u 1 ) u k ) and (v) The solution in [11] has certain limitations that are overcome by a priority queue based solution presented in [1], which uses the following lemma. Lemma 1 [1] Given a priority queue Q that allows insert and delete min operations, a sequence of N insert and delete min operations can be performed in O(sort(N) I Os using O(N=B) blocks of external memory, provided that Q is initially empty. Using this ....

[Article contains additional citation context not shown here]

L. Arge. The buer tree: A new technique for optimal I/O-algorithms. Proc. WADS'95, LNCS 955, pp. 334-345, 1995.

.... all nearest neighbors for a set of N points in the plane, dominance problems, and other geometric problems in the plane are discussed in [2, 3, 7, 13, 20] General line segment intersection problems have been studied in [6] For lower bounds on computational geometry problems in EM see [5] See [4] for bu er trees, priority queues, and their applications. Overview. In Sect. 2, we discuss our solution to the batched range counting problem. In Sect. 3, we use the solution for a special case of this problem to compute K th order graphs for point sets in d dimensions. We also discuss how to ....

....B (1) r ; B (k 1) r , in order to deal with the extra dimension. That is algorithm B consists of phases A (1) p ; B (1) r ; A (2) p ; B (2) r ; A (k 1) p ; B (k 1) r ; A (k) p . We solve the search problem to be addressed by phase B (i) r using a bu er tree [4] of degree p m c and algorithm A (i) r . The bu er tree is built over the coordinates of the points in P in the d th dimension. Queries are ltered from the root of the tree to the leaves. At every level, each query q is answered w.r.t. the maximal multislab spanned by q. A point is colored ....

L. Arge. The buer tree: A new technique for optimal I/O-algorithms. Proc. WADS, pp. 334-345, 1995.

No context found.

L. Arge. The bu#er tree: A new technique for optimal I/O-algorithms. In Proceedings of the Workshop on Algorithms and Data Structures, volume 955 of Lecture Notes in Computer Science, pages 334--345, 1995.

....in O(log B N) I Os. While trivially performing a sequence of N given updates on a (modified as well as unmodified) persistent B tree takes O(N log B N) I Os, it has been shown how the N updates can be performed in O( N I Os (the sorting bound) on a normal (unmodified) persistent B tree [25, 3, 6]. In the modified B tree case, the lack of a total order seems to prevent us from performing the updates in this much smaller number of I Os. In fact, the existence of such a fast algorithm would immediately lead to a semi dynamic insert e#cient vertical ray shooting structure using the external ....

L. Arge. The bu#er tree: A new technique for optimal I/O-algorithms. In Proc. Workshop on Algorithms and Data Structures, LNCS 955, pages 334--345, 1995.

No context found.

L. Arge. The buer tree: A new technique for optimal I/O-algorithms. In Proc. Workshop on Algorithms and Data Structures, LNCS 955, pages 334-345, 1995.

....need to increase the fanout of the base tree to decrease its height to O(log B N ) This creates several problems. The main idea behind our successful externalization of the structure, as compared with previous attempts [15, 38] is that we use a fan out of B instead of B, following ideas from [5, 10]. The external interval tree on a set of intervals I with endpoints in a xed set E of size N is de ned as follows. We assume without loss of generality that the endpoints of the intervals in I are distinct and that jEj = B for some i 0) The base tree T is a perfectly balanced ....

L. Arge. The buer tree: A new technique for optimal I/O-algorithms. In Proc. Workshop on Algorithms and Data Structures, LNCS 955, pages 334-345, 1995.

....To sort optimally we need a data structure supporting the relevant ) memory transfers. Note that for reasonable values of N , M , and B, this term is less than 1 and we can therefore only obtain this bound in an amortized sense. To obtain such a bound, Arge developed the bu er tree technique [8]. The main idea in this technique is to perform operations in a lazy (or batched) Problem Our cache oblivious result Previous best cache aware result Priority queue ) O( 8] List ranking O(sort(V ) O(sort(V ) 19, 8] Tree algorithms O(sort(V ) O(sort(V ) Directed BFS and DFS ....

....only obtain this bound in an amortized sense. To obtain such a bound, Arge developed the bu er tree technique [8] The main idea in this technique is to perform operations in a lazy (or batched) Problem Our cache oblivious result Previous best cache aware result Priority queue ) O( [8] List ranking O(sort(V ) O(sort(V ) 19, 8] Tree algorithms O(sort(V ) O(sort(V ) Directed BFS and DFS O( V E=B) log 2 V sort(E) O( V E=B) log 2 V sort(E) 18] O(V BM Undirected BFS O(V sort(E) O(V sort(E) 30] Minimal spanning forest O(sort(E) log 2 log 2 V ) ....

[Article contains additional citation context not shown here]

L. Arge. The buer tree: A new technique for optimal I/O-algorithms. In Proc. Workshop on Algorithms and Data Structures, LNCS 955, pages 334-345, 1995.

....extract min operations on the priority queue. We can see that for each cell in the grid we perform at most a constant number of insert and extract min operations, resulting in a total of O(N) operations in total. The amortized I O cost of a priority queue operation is O( 1 B log M B N B ) [2, 5], so the sweep uses O N B log M B N B =O sort(N) I Os. After the sweep determines the labels of each cell, we sort them by grid position to obtain the grid of watershed labels. The full paper discusses how to find the boundaries between watersheds and how to generate and label the ....

L. Arge. The bu#er tree: A new technique for optimal I/O-algorithms. In Proc. Workshop on Algorithms and Data Structures, LNCS 955, pages 334--345, 1995.

No context found.

L. Arge. The bu#er tree: A new technique for optimal I/O-algorithms. In Proc. 4th Workshop on Algorithms and Data Structures (WADS), volume 955 of Lecture Notes in Computer Science, pages 334--345. Springer Verlag, Berlin, 1995.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC