Icking, C., Klein, R., Ottmann, T. Priority Search Trees in Secondary Memory. GTCCS, 1987.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....of the query rectangle lies on the boundary of the data space. Arge et al. ASV99] design the external priority search tree that answers such queries optimally (i.e. logarithmic query cost and linear space consumption) Earlier, non optimal structures for RS and 3 sided queries can be found in [IKO87, KRVV96, RS94, SR95]. The first study on RS queries for moving objects [KGT99a] deals with only 1D data. Agarwal et al. AAE00] present several interesting results in the 2D space following the kinetic approach [BGH97] In particular, they show that if queries arrive in chronological order, a RS can be answered with ....

Icking, C., Klein, R., Ottmann, T. Priority Search Trees in Secondary Memory. GTCCS, 1987.

....search tree [McC] can all solve this problem well. Of these, the priority search tree solves a slightly more general problem (3 sided queries) with optimal query and update times and uses optimal storage. Many algorithms have been presented to solve this problem in secondary memory. These include [BlGa, BlGb, IKO]. The first I O optimal solution for this problem appeared in [KRV] KRV] reduces dynamic interval management to stabbing queries, which in turn reduce to a special case of 2 dimensional range searching called diagonal corner queries (see Figure 1) Diagonal corner queries can be answered in ....

....area) KKD, LOL] present solutions to the problem of indexing classes. However, their algorithms are based on heuristics and cannot guarantee good worst case performance. Previous attempts to answer 3 sided queries in secondary memory by implementing priority search trees in secondary memory [IKO, KRV] did not have optimal query times. IKO] uses optimal storage but answers queries in O(logn t=B) time. KRV] improves on this, answering queries in O(log B n log B t=B) time using optimal storage. Neither of them allow inserts and deletes from the data structure. We present a data structure ....

[Article contains additional citation context not shown here]

C. Icking, R. Klein, and T. Ottmann, Priority Search Trees in Secondary Memory (Extended Abstract), Lecture Notes In Computer Science #314, Springer-Verlag, 1988.

....dynamic case of three sided queries: organize a set of planar points, so that the points contained in a region of the form [x 1 , x 2 ] #, y] can be retrieved e#ciently. Because of its importance, the priority search tree has been the focus of many externalization attempts. Icking et al. IKO87] proposed a structure using optimal space, but with query cost O(log 2 n t B) I Os. The XPtree of [BG90] also uses optimal space, but the query cost is O(log B n t) I Os. Using path caching [RS94] the resulting structure has optimal query cost O(log B n t B) I Os, but requires non linear ....

Ch. Icking, R. Klein, and Th. Ottmann. Priority search trees in secondary memory. In Proc. Graph-Theoretic Concepts in Computer Science, LNCS 314, pages 84--93, 1987. 173

.... with the same bounds was described by Ramaswamy [36] In internal memory, the priority search tree of McCreight [31] can be used to answer more general queries than diagonal corner queries, namely 3 sided range queries, and a number of attempts have been made at externalizing this structure [15, 27, 38]. The structure by Icking et al. 27] uses optimal space but answers queries in O(log 2 N T=B) I Os. The structure by Blankenagel and G uting [15] also uses optimal space but answers queries in O(log B N T ) I Os. In both papers a number of non optimal dynamic versions of the structures are ....

.... Ramaswamy [36] In internal memory, the priority search tree of McCreight [31] can be used to answer more general queries than diagonal corner queries, namely 3 sided range queries, and a number of attempts have been made at externalizing this structure [15, 27, 38] The structure by Icking et al. [27] uses optimal space but answers queries in O(log 2 N T=B) I Os. The structure by Blankenagel and G uting [15] also uses optimal space but answers queries in O(log B N T ) I Os. In both papers a number of non optimal dynamic versions of the structures are also developed. Ramaswamy and ....

[Article contains additional citation context not shown here]

C. Icking, R. Klein, and T. Ottmann. Priority search trees in secondary memory. In Proc. Graph-Theoretic Concepts in Computer Science, LNCS 314, pages 84-93, 1987.

....Department of Computer Science, University of Aarhus, Denmark and I.N.R.I.A. Sophia Antipolis, France. Email: jsv cs.duke.edu. 1 Introduction There has recently been much effort toward developing worst case I O efficient external memory data structures for range searching in two dimensions [1, 2, 4, 8, 12, 13, 20, 26, 28, 29]. In their pioneering work, Kanellakis et al. 13] showed that the problem of indexing in new data models (such as constraint, temporal, and object models) can be reduced to special cases of twodimensional indexing. Refer to Figure 1) In particular they identified the 3 sided range searching ....

....solutions exist for other special cases of two dimensional range searching. The priority search tree [16] for example can be used to answer 3 sided range queries in optimal query and update time using linear space. A number of attempts have been made to externalize priority search trees, including [4, 12, 13, 20], but all previous attempts have been nonoptimal. The structure in [12] uses optimal space, but answers queries in O(log N t) I Os. The structure of [4] also uses optimal space, but answers queries in O(log B N T ) I Os. In both these papers, a number of nonoptimal dynamic versions of the ....

[Article contains additional citation context not shown here]

C. Icking, R. Klein, and T. Ottmann. Priority search trees in secondary memory. In Proc. Graph-Theoretic Concepts in Computer Science, LNCS 314, pages 84-- 93, 1987.

....B we lose when charging the construction of a structure of size B i to only B i Gamma1 objects is offset by the 1=B factor in the construction bound. Deletions can also be handled I O efficiently using a global rebuilding idea. 4. 2 Optimal dynamic structure Following several earlier attempts [101, 127, 141, 43, 98], Arge et al. 26] developed an optimal dynamic structure for the 3 sided planar range searching problem. The structure is an external version of the internal memory priority search tree structure [113] The external priority search tree consists of a base B tree on the x coordinates of the N ....

C. Icking, R. Klein, and T. Ottmann. Priority search trees in secondary memory. In Proc. Graph-Theoretic Concepts in Computer Science, LNCS 314, pages 84--93, 1987.

....papers also deal with fundamental problems such as permutation, sorting and matrix transposition. The problem of implementing various classes of permutations has been addressed in [47, 48, 50] More recently researchers have moved on to more specialized problems in the computational geometry [11, 15, 34, 40, 67, 74, 79, 110, 121, 130, 137], graph [12, 40, 42, 97] and string areas [44, 56, 57] As already mentioned the number of I O operations needed to read the entire input is N=B and for convenience we call this quotient n. We use the term scanning to describe the fundamental primitive of reading (or writing) all elements in a ....

....problems. A number of researchers have considered the design of worst case efficient external memory on line data structures, mainly for the range searching problem. While B trees [21, 51, 82] efficiently support range searching in one dimension they are inefficient in higher dimensions. In [27, 74, 79, 110, 121, 130] data structures for (special cases of) two and three dimensional range searching are developed. In [Interval] we develop an optimal on line data structure for the equally important problem of dynamic interval management. This problem is a special case of two dimensional range searching with ....

[Article contains additional citation context not shown here]

C. Icking, R. Klein, and T. Ottmann. Priority search trees in secondary memory. In Proc. Graph-Theoretic Concepts in Computer Science, LNCS 314, pages 84--93, 1987.

....The priority search tree [27] for example can be used to answer slightly more general queries than diagonal corner queries, namely 3 sided range queries (Figure 1) in optimal query and update time using optimal space. A number of attempts have been made to externalize this structure, including [9, 21, 35], but they are all non optimal. The structure in [21] uses optimal space but answers queries in O(log 2 N T=B) I Os. The structure in [9] also uses optimal space but answers queries in O(log B N T ) I Os. In both papers a number of non optimal dynamic versions of the structures are also ....

....answer slightly more general queries than diagonal corner queries, namely 3 sided range queries (Figure 1) in optimal query and update time using optimal space. A number of attempts have been made to externalize this structure, including [9, 21, 35] but they are all non optimal. The structure in [21] uses optimal space but answers queries in O(log 2 N T=B) I Os. The structure in [9] also uses optimal space but answers queries in O(log B N T ) I Os. In both papers a number of non optimal dynamic versions of the structures are also developed. In [35] a technique called path caching for ....

[Article contains additional citation context not shown here]

C. Icking, R. Klein, and T. Ottmann. Priority search trees in secondary memory. In Proc. Graph-Theoretic Concepts in Computer Science, LNCS 314, pages 84--93, 1987.

....papers also deal with fundamental problems such as permutation, sorting and matrix transposition. The problem of implementing various classes of permutations has been addressed in [47, 48, 50] More recently researchers have moved on to more specialized problems in the computational geometry [11, 15, 34, 40, 67, 74, 79, 110, 121, 130, 137], graph [12, 40, 42, 97] and string areas [44, 56, 57] As already mentioned the number of I O operations needed to read the entire input is N B and for convenience we call this quotient n. We use the term scanning to describe the fundamental primitive of reading (or writing) all elements in a ....

....problems. A number of researchers have considered the design of worst case e#cient external memory on line data structures, mainly for the range searching problem. While B trees [21, 51, 82] e#ciently support range searching in one dimension they are ine#cient in higher dimensions. In [27, 74, 79, 110, 121, 130] data structures for (special cases of) two and three dimensional range searching are developed. In [Interval] we develop an optimal on line data structure for the equally important problem of dynamic interval management. This problem is a special case of two dimensional range searching with ....

[Article contains additional citation context not shown here]

C. Icking, R. Klein, and T. Ottmann. Priority search trees in secondary memory. In Proc. Graph-Theoretic Concepts in Computer Science, LNCS 314, pages 84--93, 1987.

.... tree can answer 3 sided queries (and therefore, 2 sided queries as well) in core in time O(logn t) using storage O(n) with a worst case update time of O(log n) Previous attempts to answer 2 and 3 sided queries in secondary memory by implementing priority search trees in secondary memory [17,19] did not have optimal query times. 17] uses optimal storage but answers queries in O(logn t=B) time. 19] improves on this, answering queries in O(log B n log B t=B) time using optimal storage. Neither of them allow inserts and deletes from the data structure. In [27] we presented a data ....

....therefore, 2 sided queries as well) in core in time O(logn t) using storage O(n) with a worst case update time of O(log n) Previous attempts to answer 2 and 3 sided queries in secondary memory by implementing priority search trees in secondary memory [17,19] did not have optimal query times. [17] uses optimal storage but answers queries in O(logn t=B) time. 19] improves on this, answering queries in O(log B n log B t=B) time using optimal storage. Neither of them allow inserts and deletes from the data structure. In [27] we presented a data structure to solve this problem using a ....

C. Icking, R. Klein, and T. Ottmann, Priority Search Trees in Secondary Memory (Extended Abstract), Lecture Notes In Computer Science #314, Springer-Verlag, 1988.

....where a data structure is built on an input set of intervals and then queried (or updated) in an on line fashion. That is, the results of a query have to be returned before the next query is processed. This problem has been extensively studied both in main memory [5,7,8,17] and secondary storage [4,14,16,19,25]. In particular, 4] recently resolved the open problem of whether it is possible to build a dynamic, worst case optimal data structure for this problem. However, directly applying the on line intersection algorithm to this problem results in a running time of O(N log B n t) I O s which is a ....

C. Icking, R. Klein & T. Ottmann, Priority Search Trees in Secondary Memory (Extended Abstract), Lecture Notes In Computer Science #314, Springer-Verlag, 1988.

....search tree does the best because it solves the interval management problem in optimal time and space, and provides an optimal worst case update time as well. There have been several pieces of work done by researchers to implement these data structures in secondary memory. These works include [18], 5] 6] 18] contains a claimed optimal solution for implementing static priority search trees in secondary memory. Unfor12 tunately, the [18] static solution has static query time O(log 2 n t=B) instead of O(log B n t=B) and the claimed optimal solution is incorrect. None of the other ....

....does the best because it solves the interval management problem in optimal time and space, and provides an optimal worst case update time as well. There have been several pieces of work done by researchers to implement these data structures in secondary memory. These works include [18] 5] 6] [18] contains a claimed optimal solution for implementing static priority search trees in secondary memory. Unfor12 tunately, the [18] static solution has static query time O(log 2 n t=B) instead of O(log B n t=B) and the claimed optimal solution is incorrect. None of the other approaches solve the ....

[Article contains additional citation context not shown here]

C. Icking, R. Klein & T. Ottmann, Priority Search Trees in Secondary Memory (Extended Abstract), Lecture Notes In Computer Science #314, Springer-Verlag, 1988.

....the so called point databases . For such databases, which typically contain N points on the plane, several external memory data structures have been developed. Those data structures are characterized by an I O complexity for search and update operations comparable to the internal memory results [11, 14, 19, 21]. Compared to the point database case, much less work has been carried out for the so called segment databases which represent a more general case. A segment database stores in secondary storage N non crossing but possibly touching plane segments (for brevity, called NCT segments) Segment ....

....in the same half plane with respect to such line. Thus, the main contributions of the paper can be summarized as follows (proofs of the proposed results are presented in [4] 1. We propose a data structure to store and query line based segments, based on priority search trees (PST for short) [7, 11], similar to the internal memory data structure proposed in [6] The proposed data structure is then extended with the P range technique presented in [21] to reduce time complexity. 2. We propose two approaches to the problem of VS queries: In the first approach, the first level structure is ....

[Article contains additional citation context not shown here]

C. Icking, R. Klein, and T. Ottmann. Priority Search Trees in Secondary Memory. In LNCS 314: Proc. of the Int. Workshop on Graph-Theoretic Concepts in Computer Science, pages 84--93, 1988.

....search tree does the best because it solves the interval management problem in optimal time and space, and provides an optimal worst case update time as well. There have been several pieces of work done by researchers to implement these data structures in secondary memory. These works include [16], 5] 4] 16] contains a claimed optimal solution for implementing static priority search trees in secondary memory. Unfortunately, the [16] static solution has static query time O(log 2 n t=B) instead of O(log B n t=B) and the claimed optimal solution is incorrect. None of the other ....

....does the best because it solves the interval management problem in optimal time and space, and provides an optimal worst case update time as well. There have been several pieces of work done by researchers to implement these data structures in secondary memory. These works include [16] 5] 4] [16] contains a claimed optimal solution for implementing static priority search trees in secondary memory. Unfortunately, the [16] static solution has static query time O(log 2 n t=B) instead of O(log B n t=B) and the claimed optimal solution is incorrect. None of the other approaches solve the ....

[Article contains additional citation context not shown here]

C. Icking, R. Klein, and T. Ottmann, Priority Search Trees in Secondary Memory (Extended Abstract), Lecture Notes In Computer Science #314, Springer-Verlag, 1988.

....searching. The priority search tree [7] for example can be used to answer slightly more general queries than diagonal corner queries, namely 3 sided range queries, in optimal query and update time using optimal space. A number of attempts have been made to externalize this structure, including [3, 5, 8], but they are all non optimal. In [8] a technique called path caching for transforming an efficient internalmemory data structure into an I O efficient one is developed. Using this technique on the priority search tree results in a structure that can be used to answer 2 sided queries, which are ....

....of Aarhus, Aarhus, Denmark. Email: large cs.duke.edu y Supported in part by the National Science Foundation under grant CCR 9522047 and by the U.S. Army Research Office under grant DAAH4 93 G 0076. Email: jsv cs.duke.edu Space (blocks) Query I O bound Update I O bound Priority search tree [5] O(N=B) O(log 2 N T=B) XP tree [3] O(N=B) O(log B N T ) Metablock tree [6] O(N=B) O(log B N T=B) O(log B N (log B N) 2 =B) amortized (inserts only) P range tree [9] O(N=B) O(log B N T=B IL (B) O(log B N (log B N) 2 =B) amortized Path Caching [8] O( N=B) log 2 log 2 B) ....

C. Icking, R. Klein, and T. Ottmann. Priority search trees in secondary memory. In Proc. GraphTheoretic Concepts in Computer Science, LNCS 314, pages 84--93, 1987.

....but so far this generalization has not shown any particular advantage that makes it useful. In this paper we present a new generalization of the SBB tree that represents a b trees where a = 2 k and b = 2 k 1 for any positive integer k. This generalized structure, denoted an SBB(k) tree (in [9] it is referred to as a red h black tree) inherits the good properties of the SBB tree with respect to space efficiency, need of only a constant number of restructurings and simplicity of the algorithms. Moreover, it has the advantage of being of low height, l (1 1 k ) log(n 1) m . These ....

C. Icking, R. Klein, and T. Ottmann. Priority search trees in secondary memory. In Graphtheoretic Concepts in Computer Science (WG '87), Staffelstein, LNCS 314, pages 84--93, 1987.

....search tree [McC] can all solve this problem well. Of these, the priority search tree solves a slightly more general problem (3 sided queries) with optimal query and update times and uses optimal storage. Many algorithms have been presented to solve this problem in secondary memory. These include [BlGa, BlGb, IKO]. The first I O optimal solution for this problem appeared in [KRV] KRV] reduces dynamic interval management to stabbing queries, which in turn reduce to a special case of 2 dimensional range searching called diagonal corner queries (see Figure 1) Diagonal corner queries can be answered in ....

....this area) KKD, LOL] present solutions to the problem of indexing classes. However, their algorithms are based on heuristics and cannot guarantee good worst case performance. Previous attempts to answer 3 sided queries in secondary memory by implementing priority search trees in secondary memory [IKO, KRV] did not have optimal query times. IKO] uses optimal storage but answers queries in O(logn t=B) time. KRV] improves on this, answering queries in O(log B n log B t=B) time using optimal storage. Neither of them allow inserts and deletes from the data structure. We present a data structure ....

[Article contains additional citation context not shown here]

C. Icking, R. Klein, and T. Ottmann, Priority Search Trees in Secondary Memory (Extended Abstract), Lecture Notes In Computer Science #314, Springer-Verlag, 1988.

....search tree does the best because it solves the interval management problem in optimal time and space, and provides an optimal worst case update time as well. There have been several pieces of work done by researchers to implement these data structures in secondary memory. These works include [17], 5] 6] 17] contains a claimed optimal solution for implementing static priority search trees in secondary memory. Unfortunately, the [17] static solution has static query time O(log 2 n t=B) instead of O(log B n t=B) and the claimed optimal solution is incorrect. None of the other ....

....does the best because it solves the interval management problem in optimal time and space, and provides an optimal worst case update time as well. There have been several pieces of work done by researchers to implement these data structures in secondary memory. These works include [17] 5] 6] [17] contains a claimed optimal solution for implementing static priority search trees in secondary memory. Unfortunately, the [17] static solution has static query time O(log 2 n t=B) instead of O(log B n t=B) and the claimed optimal solution is incorrect. None of the other approaches solve the ....

[Article contains additional citation context not shown here]

C. Icking, R. Klein, and T. Ottmann, Priority Search Trees in Secondary Memory (Extended Abstract), Lecture Notes In Computer Science #314, Springer-Verlag, 1988.

....to the research papers for a discussion of this. For completeness it should be mentioned that recently a number of researchers have considered the design of worst case efficient external memory on line data structures, mainly for (special cases of) two and three dimensional range searching [20, 25, 59, 61, 78, 84, 93]. While B trees [22, 37, 65] efficiently support range searching in one dimension they are inefficient in higher dimensions. Similarly the many sophisticated internal memory data structures for range searching are not efficient when mapped to external memory. This has lead to the development of a ....

C. Icking, R. Klein, and T. Ottmann. Priority search trees in secondary memory. In Proc. Graph-Theoretic Concepts in Computer Science, LNCS 314, pages 84--93, 1987.

....2 n t) and update time O(log 2 n) which are all optimal. It is open whether dynamic interval management on secondary storage can be achieved optimally in O(n=B) pages, dynamic query I O time O(log B n t=B) and update time O(log B n) Note that, various suboptimal solutions are proposed in [IKO], for a slightly more general problem, as well as a claimed optimal static solution. Unfortunately, the [IKO] static solution has static query time O(log 2 n t=B) instead of O(log B n t=B) and the claimed optimal solution is incorrect. In this paper we provide an optimal static solution for ....

....on secondary storage can be achieved optimally in O(n=B) pages, dynamic query I O time O(log B n t=B) and update time O(log B n) Note that, various suboptimal solutions are proposed in [IKO] for a slightly more general problem, as well as a claimed optimal static solution. Unfortunately, the [IKO] static solution has static query time O(log 2 n t=B) instead of O(log B n t=B) and the claimed optimal solution is incorrect. In this paper we provide an optimal static solution for external dynamic interval management. This static solution is quite involved, but it achieves the optimal space ....

[Article contains additional citation context not shown here]

C. Icking, R. Klein, and T. Ottmann, Priority Search Trees in Secondary Memory (Extended Abstract), Lecture Notes In Computer Science #314, Springer-Verlag, 1988.

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