G. Blankenagel and R. H. Guting, "External Segment Trees," FernUniversitat Hagen, Informatik --Bericht, 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 ....

....O( log B log log B) and performs updates in O(log B n log B) time. In addition to these data structures, path caching can also be applied to other main memory data structures to obtain optimal query times at the expense of small space overheads. By doing this, we improve on the bounds of [BlGb] for implementing segment trees in secondary memory. To summarize, we present a simple technique called path caching that can be used to transform many in core data structures to efficient secondary storage structures. We show how to use path caching to implement priority search trees in ....

G. Blankenagel and R. H. Guting, "External Segment Trees," FernUniversitat Hagen, Informatik --Bericht, 1990.

....(e.g. 24, 25, 13, 1, 9] Finally, in Section 5 we discuss how to use the ideas utilized in our external interval tree to develop an external segment tree using O( N=B) log B N) space. This improves upon previously known external segment tree structures, which use O( N=B) log 2 N) disk blocks [14, 38]. 2 External memory interval tree with xed endpoint set In this section we present our external interval tree structure assuming that the endpoints of the intervals stored in the structure belong to a xed set E of size N . We also assume that the internal memory is capable of holding O(B) ....

....in O(1) I Os. The structure can be constructed in O(K=B) I Os. 5 External segment tree In this section we sketch how the ideas used in the external interval tree can also be used to develop an external segment tree like structure with a better space bound than previously known such structures [14, 38]. In internal memory, a segment tree consists of a binary base tree with intervals stored in secondary structures of interval nodes like in the interval tree. Unlike in the interval tree, an interval can be stored in secondary structures of up to two nodes on each level of the base tree. More ....

G. Blankenagel and R. Guting. External segment trees. Algorithmica, 12:498-532, 1994.

....database applications. These data structures have been developed to deal with extended objects with a dimensionality greater than one and they are not specialized for one dimensional objects resp. intervals. On the other hand there are specialized data structures like the external segment tree [5] which are rather complicated to integrate into a DBMS. However, the problem of ecient management and query processing of one dimensional intervals is an interesting question, because B Trees and other common access methods of commercial RDBMS cannot handle them eciently. From now on we call one ....

Blankenagel, G. and H. Guting (1994); External Segment Trees. Algorithmica 12(6) (pp. 498-532)

....As discussed in [79] an optimal structure for this problem leads to an optimal solution to the interval management problem. The segment tree structure solves the stabbing query problem in internal memory and some attempts have been made to externalizing this structure in an on line setting [28, 110]. They all use O(n log 2 n) blocks of external memory and the best of them [110] is static and answers queries in the optimal O(log B n t) I Os. In [Interval] we use our ideas from [Buffer] Section 3.2.2) to develop an on line version of the segment tree with the improved space bound O(n log B n) ....

....and that very recently a static structure for 3 dimensional queries has been developed in [130] The segment tree [23] can also be used to solve the stabbing query problem, but even in internal memory it uses more than linear space. Some attempts have been made to externalizing this structure [28, 110] and they all use O( N=B) log 2 N) blocks of external memory. The best of them [110] is static and answers queries in the optimal O(log B N T=B) I Os. 1.2 Overview of our results Our main results in this paper is an optimal external memory data structure for the stabbing query problem. As ....

[Article contains additional citation context not shown here]

G. Blankenagel and R. Guting. External segment trees. Algorithmica, 12:498--532, 1994.

....and that very recently a static structure for 3 dimensional queries has been developed in [43] The segment tree [6] can also be used to solve the stabbing query problem, but even in internal memory it uses more than linear space. Some attempts have been made to externalizing this structure [8, 35] and they all use O( N=B) log 2 N) blocks of external memory. The best of them [35] is static and answers queries in the optimal O(log B N T=B) I Os. 1.2 Overview of our results Our main results in this paper is an optimal external memory data structure for the stabbing query problem. As ....

....bound of the internal interval tree, but our method is much simpler. Finally, in Section 5 we discuss how to use the ideas behind our external interval tree to develop an external version of the segment tree with space bound O( N=B) log B N ) This improves upon previously known data structures [8, 35], which use O( N=B) log 2 N) blocks of external memory. Our structure has worst case optimal query and update I O bounds, whereas the other known structures are only query optimal in the static case. Fixing B to a constant yields an internalmemory segment tree (without the fixed endpoint set ....

[Article contains additional citation context not shown here]

G. Blankenagel and R. Guting. External segment trees. Algorithmica, 12:498--532, 1994.

....As discussed in [79] an optimal structure for this problem leads to an optimal solution to the interval management problem. The segment tree structure solves the stabbing query problem in internal memory and some attempts have been made to externalizing this structure in an on line setting [28, 110]. They all use O(n log 2 n) blocks of external memory and the best of them [110] is static and answers queries in the optimal O(log B n t) I Os. In [Interval] we use our ideas from [Bu#er] Section 3.2.2) to develop an on line version of the segment tree with the improved space bound O(n log B n) ....

....and that very recently a static structure for 3 dimensional queries has been developed in [130] The segment tree [23] can also be used to solve the stabbing query problem, but even in internal memory it uses more than linear space. Some attempts have been made to externalizing this structure [28, 110] and they all use O( N B) log 2 N) blocks of external memory. The best of them [110] is static and answers queries in the optimal O(log B N T B) I Os. 1.2 Overview of our results Our main results in this paper is an optimal external memory data structure for the stabbing query problem. As ....

[Article contains additional citation context not shown here]

G. Blankenagel and R. Guting. External segment trees. Algorithmica, 12:498--532, 1994.

....applications dealing with polyline objects. Approximating a polyline, even it is has been cut into smaller pieces, by a rectangle is not efficent since most of the rectangle space is lost. Some classical SAMs have been adapted to polylines [Sam90b] Examples of SAMs dedicated to line segments are [Jag90a, KS91, BG94]. In the Moving objects applications[SWCD97, WXCJ98, KGT99] a point is following a fixed trajectory (e.g. belonging to a road network) or a free line trajectory in the plane. A typical query is: report the objects inside a rectangle within a given time interval . Moving applications are just ....

G. Blankenagel and R. H. Gueting. External Segment Trees. Algorithmica, 12:498--532, 1994.

....B N (log B N ) 2 B) amortized Path Caching [35] O( N B) log 2 log 2 B) O(log B N T B) O(log B N ) amortized Our Result O(N B) O(log B N T B) O(log B N ) Figure 2. Comparison of our data structure for stabbing queries with previous data structures. made to externalizing this structure [9, 35] and they all use O( N B) log 2 N ) blocks of external memory. The best of them [35] is static and answers queries in the optimal O(log B N T B) I Os. 1.2. Overview of our results Our main results in this paper is an optimal externalmemory data structure for the stabbing query problem. As ....

....bound of the internal interval tree, but our method is much simpler. Finally, in Section 4 we discuss how to use the ideas behind our external interval tree to develop an external version of the segment tree with space bound O( N B) log B N ) This improves upon previously known data structures [9, 35], which use O( N B) log 2 N ) blocks of external memory. Our structure has worst case optimal query and update I O bounds, whereas the other known structures are only query optimal in the static case. Fixing B to a constant yields an internal memory segment tree (without the fixed endpoint set ....

[Article contains additional citation context not shown here]

G. Blankenagel and R. Guting. External segment trees. Algorithmica, 12:498--532, 1994.

....log log B) disk blocks of storage. In addition to these data structures, path caching can also be applied to other main memory data structures like the segment tree and interval tree to obtain optimal query times at the expense of small space overheads. By doing this, we improve on the bounds of [6] for implementing segment trees in secondary memory. 6 1.5 Experimental Work The actual use of a data structure in a database depends on many factors. Most of the data structures considered here have good worst case bounds, but asymptotic bounds by themselves are not enough proof that a data ....

....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 solve ....

G. Blankenagel & R. H. Guting, "External Segment Trees," FernUniversitat Hagen, Informatik--Bericht, 1990. 103

....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 solve ....

G. Blankenagel and R. H. Guting, "External Segment Trees," FernUniversitat Hagen, Informatik --Bericht, 1990.

.... structure) ii) investigating the effect of cache structures; iii) designing a benchmarking data set against which previously proposed structures could be evaluated and compared and; iv) investigating whether the overlapping approach could be used with other range indexing structures (e.g. BG94] Acknowledgments Jefferson R. O. Silva (972147 dcc.unicamp.br) was supported by FAPESP (Process 97 11205 8) Mario A. Nascimento was partially supported by CNPq (Process 300208 97 9) and is also a researcher with Embrapa (mario cnptia.embrapa.br) This research was developed as part of ....

G. Blankenagel and R. H. Guting. External segment trees. Algorithmica, 12(6):490--532, 1994.

....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 ....

....O( n B log B log log B) and performs updates in O(log B n log 2 B) time. In addition to these data structures, path caching can also be applied to other main memory data structures to obtain optimal query times at the expense of small space overheads. By doing this, we improve on the bounds of [BlGb] for implementing segment trees in secondary memory. To summarize, we present a simple technique called path caching that can be used to transform many in core data structures to efficient secondary storage structures. We show how to use path caching to implement priority search trees in secondary ....

G. Blankenagel and R. H. Guting, "External Segment Trees," FernUniversitat Hagen, Informatik --Bericht, 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 solve ....

G. Blankenagel and R. H. Guting, "External Segment Trees," FernUniversitat Hagen, Informatik --Bericht, 1990.

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