G. Blankenagel and R. H. Guting, "XP-Trees - External Priority Search Trees," FernUniversit at Hagen, Informatik--Bericht Nr. 92, 1990.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....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 ....

G. Blankenagel and R. H. Guting, "XP-Trees - External Priority Search Trees," FernUniversit at Hagen, Informatik--Bericht Nr. 92, 1990.

....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 space of O( log log B) disk blocks, and the update cost is O(log B n) amortized. Finally, Samoladas, and ....

G. Blankenagel and R. H. Guting. XP-trees---External priority search trees. Technical report, FernUniversitat Hagen, InformatikBericht Nr. 92, 1990.

....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 ....

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G. Blankenagel and R. H. Guting. XP-trees---External priority search trees. Technical report, FernUniversitat Hagen, Informatik-Bericht Nr. 92, 1990.

....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 ....

G. Blankenagel and R. H. Guting. XP-trees---External priority search trees. Technical report, FernUniversitat Hagen, Informatik-Bericht Nr. 92, 1990.

....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 ....

....2 B) In internal memory the priority search tree actually answers slightly more general queries than two sided queries, namely three sided two dimensional queries (Figure 3.8) in optimal query and update time using linear space. A number of attempts have been made to externalize this structure [27, 74, 110]. The structure in [74] uses linear space but answers queries in O(log 2 N t) I Os. The structure in [27] also uses linear 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. The structure in [110] was ....

[Article contains additional citation context not shown here]

G. Blankenagel and R. Guting. XP-trees --- External priority search trees. Technical report, FernUniversitat Hagen, Informatik-Bericht Nr. 92, 1990.

....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 ....

....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 transforming an 2 3 sided query 2 sided query diagonal corner query general 2 dimensional ....

[Article contains additional citation context not shown here]

G. Blankenagel and R. H. Guting. XP-trees---External priority search trees. Technical report, FernUniversitat Hagen, Informatik-Bericht Nr. 92, 1990. 22

....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 ....

....2 B) In internal memory the priority search tree actually answers slightly more general queries than two sided queries, namely three sided two dimensional queries (Figure 3.8) in optimal query and update time using linear space. A number of attempts have been made to externalize this structure [27, 74, 110]. The structure in [74] uses linear space but answers queries in O(log 2 N t) I Os. The structure in [27] also uses linear 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. The structure in [110] was ....

[Article contains additional citation context not shown here]

G. Blankenagel and R. Guting. XP-trees --- External priority search trees. Technical report, FernUniversitat Hagen, Informatik-Bericht Nr. 92, 1990.

....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 [8, 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 [8] 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 ....

....queries (Figure 1) in optimal query and update time using optimal space. A number of attempts have been made to externalize this structure, including [8, 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 [8] 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 transforming an efficient internal memory data structure into an I O efficient one is ....

[Article contains additional citation context not shown here]

G. Blankenagel and R. Guting. XP-trees --- External priority search trees. Technical report, FernUniversitat Hagen, Informatik-Bericht Nr. 92, 1990.

....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 approaches ....

G. Blankenagel & R. H. Guting, "XP-Trees -- External Priority Search Trees," FernUniversit at Hagen, Informatik--Bericht Nr. 92, 1990.

....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 approaches ....

G. Blankenagel and R. H. Guting, "XP-Trees - External Priority Search Trees," FernUniversit at Hagen, Informatik--Bericht Nr. 92, 1990.

....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 ....

....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) O(log B N T=B) O(log B N) amortized Our ....

G. Blankenagel and R. Guting. XP-trees --- External priority search trees. Technical report, FernUniversit at Hagen, Informatik-Bericht Nr. 92, 1990.

....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 ....

G. Blankenagel and R. H. Guting, "XP-Trees - External Priority Search Trees," FernUniversit at Hagen, Informatik--Bericht Nr. 92, 1990.

....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 approaches ....

G. Blankenagel and R. H. Guting, "XP-Trees -- External Priority Search Trees," FernUniversit at Hagen, Informatik--Bericht Nr. 92, 1990.

....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 ....

G. Blankenagel and R. H. GĻuting. XP-trees---External priority search trees. Technical report, FernUniversitĻat Hagen, Informatik-Bericht Nr. 92, 1990.

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