#### DMCA

## Optimization Techniques (1995)

### Citations

2713 | R-trees: A dynamic index structure for spatial searching
- GUTTMAN
- 1984
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Citation Context ...ons constitute an important class of user queries, they have not been studied extensively in spatial access methods. Query processing and optimization techniques have mainly focused on window queries =-=[Gutt84]-=-, topological relations of high resolution [Papa95b] and nearest neighbour queries [Rous95]. The main reason for this, is the lack of well-defined direction relations between actual objects. In Geogra... |

1243 | B.: ‘The R*-tree: An Efficient and Robust Access Method for Points and Rectangles
- Beckmann, Kriegel, et al.
- 1990
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Citation Context ...ctangles that correspond to lower level nodes. The fact that R-trees permit overlap among node entries sometimes leads to unsuccessful hits on the tree structure. The R+-tree [Sell87] and the R*-tree =-=[Beck90]-=- methods have been proposed to address the problem of performance degradation caused by the overlapping regions or excessive dead-space respectively. In order to retrieve objects that satisfy a direct... |

645 | Ubiquitous B-tree
- Comer
- 1979
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Citation Context ...ng factor of 4, i.e., each node contains at most four entries. 9are stored in a B-tree index of height h with L leaf nodes then the average cost C(r) for the retrieval of a constraint with range r is =-=[Come79]-=- C r h r L( ) = + ⋅ (1) In order to compute the expected cost C(r) for the retrieval of a constraint characterised by a range r we need to provide equations for the parameters of Eq. 1, namely h, L, r... |

585 | Nearest neighbor queries
- Roussopoulos, Kelley, et al.
- 1995
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Citation Context ...n spatial access methods. Query processing and optimization techniques have mainly focused on window queries [Gutt84], topological relations of high resolution [Papa95b] and nearest neighbour queries =-=[Rous95]-=-. The main reason for this, is the lack of well-defined direction relations between actual objects. In Geography, for example, although the linguistic terms used to describe the direction relation bet... |

428 |
The Art of Computer Programming, vol. 3: Sorting and Searching
- Knuth
- 1973
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Citation Context ...or the retrieval of direction relations includes the maintenance of a group of 4 alphanumeric indexes, such as B-trees. In particular, the implementation used in existing systems is the B+-tree index =-=[Knut73]-=- and, in this paper, we will think of B+-trees when we use the term B-trees. Each 8index corresponds to one of the four numbers: p'l-x, p'l-y, p'u-x, p'u-y, where p'l-x stands for the x-coordinate of ... |

428 | The K-D-B-tree: A search structure for large multidimensional dynamic indexes
- Robinson
- 1981
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Citation Context ... Retrieval of Direction Relations using KDB-trees The second solution for the retrieval of direction relations includes the maintenance of a group of 2 twodimensional point indexes, such as KDB-trees =-=[Robi81]-=-. The two indexes correspond to the MBR representative points p'l and p'u. KDB-trees, like B-trees, are multiway, height-balanced trees, which consist of leaf and intermediate nodes. Point data are st... |

341 | The R+-Tree: A Dynamic Index for MultiDimensional Objects
- Sellis, Roussopoulos, et al.
- 1987
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Citation Context ...gle which encloses all rectangles that correspond to lower level nodes. The fact that R-trees permit overlap among node entries sometimes leads to unsuccessful hits on the tree structure. The R+-tree =-=[Sell87]-=- and the R*-tree [Beck90] methods have been proposed to address the problem of performance degradation caused by the overlapping regions or excessive dead-space respectively. In order to retrieve obje... |

247 |
Reasoning about binary topological relations
- Egenhofer
- 1991
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Citation Context ...idence (e.g., overlap, disjoint), and distance relations (e.g., near, far). The above types of relations have been used in a wide range of topics, such as Spatial Query Languages [Papa95a], Reasoning =-=[Egen91]-=- and Consistency Checking Mechanisms [Grig95]. This paper describes implementations of direction relations in Spatial Database Management Systems (DBMS) and Geographical Information Systems (GIS). Des... |

172 | Qualitative Representation of Spatial Knowledge, Dissertation, Fakultät für Informatik der Technischen Universität - Hernández - 1994 |

162 | Beyond uniformity and independence: Analysis of R-trees using the concept of fractal dimension - Faloutsos, Kamel - 1994 |

131 | Qualitative spatial reasoning about distances and direction in geographic space - Frank - 1992 |

122 | Qualitative spatial reasoning: cardinal directions as an example - Frank - 1996 |

114 | Topological Relations in the World of Minimum Bounding Rectangles: A Study with R-Trees
- Papadias, Theodoridis, et al.
- 1995
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Citation Context ...they have not been studied extensively in spatial access methods. Query processing and optimization techniques have mainly focused on window queries [Gutt84], topological relations of high resolution =-=[Papa95b]-=- and nearest neighbour queries [Rous95]. The main reason for this, is the lack of well-defined direction relations between actual objects. In Geography, for example, although the linguistic terms used... |

84 | Topological inference
- Grigni, Papadias, et al.
- 1995
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Citation Context ...e relations (e.g., near, far). The above types of relations have been used in a wide range of topics, such as Spatial Query Languages [Papa95a], Reasoning [Egen91] and Consistency Checking Mechanisms =-=[Grig95]-=-. This paper describes implementations of direction relations in Spatial Database Management Systems (DBMS) and Geographical Information Systems (GIS). Despite the fact that direction relations consti... |

80 | Qualitative representation f spatial knowledge in two-dimensional space - Papadias, Sellis - 1994 |

69 |
Analysis of object oriented spatial access methods
- Faloutos, Sellis, et al.
- 1987
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Citation Context ... entries and nj,x.nj,y is the average node size at level j (the root is assumed at level j=h and the leaf-nodes at level j=1). The expression for computing the height h of the R-tree (or KDB-tree) is =-=[Falo87]-=- h N c mc m = + ⋅ ⋅1 log , (6) the expected number of nodes Nj at level j is ( )N N c m j j= ⋅ (7) and the average node sizes nj,x and nj,y are given by ( )n n Nj x j y j, ,= = 1 12 (8) Using... |

66 | Towards an analysis of range query performance - Pagel, Six, et al. - 1993 |

55 | On random 2–3 trees - Yao - 1978 |

30 | A pictorial query-by-example language
- Papadias, Sellis
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Citation Context ...neighbourhood and incidence (e.g., overlap, disjoint), and distance relations (e.g., near, far). The above types of relations have been used in a wide range of topics, such as Spatial Query Languages =-=[Papa95a]-=-, Reasoning [Egen91] and Consistency Checking Mechanisms [Grig95]. This paper describes implementations of direction relations in Spatial Database Management Systems (DBMS) and Geographical Informatio... |

26 | Range Queries Involving Spatial Relations: A Performance Analysis
- Theodoridis, Papadias
- 1995
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Citation Context ...submitted to the 12th IEEE International Conference on Data Engineering [Theo95a]. Some parts of the performance analysis appear in the Proceedings of the 2nd Conference on Spatial Information Theory =-=[Theo95c]-=-. Yannis Theodoridis and Timos Sellis were partially supported by the Department of Research and Technology of Greece (PENED’91) and by the European Commission under the ESPRIT Basic Research project ... |

19 | The retrieval of direction relations using R-trees
- Papadias, Theodoridis, et al.
- 1994
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Citation Context ...north and weak_north_east. For the rest of the relations all retrieved MBRs correspond to objects that satisfy the query. Details about the retrieval of direction relations using MBRs can be found in =-=[Papa94b]-=-. In the next sections we will show how the above results can be applied to indexing techniques available in commercial DBMSs. 3. RETRIEVAL OF DIRECTION RELATIONS The retrieval of direction relations ... |

13 | Constraint-Based Reasoning in Geographic Databases: The Case of Symbolic Arrays - Papadias, Frank, et al. - 1994 |

6 |
B+ Trees and Indexed Sequential Files: A Performance Comparison
- Batory
- 1981
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Citation Context ... Suppose now that m is the maximum number of entries in a B-tree node, c is the average capacity of a node, and N is the total number of keys stored in the leaf nodes. We have the following equations =-=[Bato81]-=- for the average h and L values in order to use them in Eq. 1: h N m c m= + 1 log . (2) L N c m= ⋅ (3) What remains in order to have a complete expression for Eq. 1 is the value of parameter ... |

5 | On the Performance Analysis of Multi-dimensional R-tree-based Data Structures", submitted for publication
- Theodoridis, Sellis
- 1995
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Citation Context ...aightforward as the KDB-tree one (Eq. 8). If Nj is the number of nodes at level j, and dj is the density3 of these nodes then the average node sizes nj,x and nj,y are given by the following equations =-=[Theo95b]-=-: ( )n n D Nj x j y j j, ,= = 12 (10) wheres( ) ( )D D c m j j = + − ⋅ − 1 11 1 2 1 2 2 (11) and N N c m j j = ⋅ −1 (12) Therefore, Dj and Nj can be computed recursively using D0 and N... |

3 |
Supporting Direction Relations in Spatial Database Systems", submitted for publication
- unknown authors
- 1995
(Show Context)
Citation Context ...ion Relations, Range Queries, Data Structures, Performance Analysis, Query Optimisation. A short version of this paper has been submitted to the 12th IEEE International Conference on Data Engineering =-=[Theo95a]-=-. Some parts of the performance analysis appear in the Proceedings of the 2nd Conference on Spatial Information Theory [Theo95c]. Yannis Theodoridis and Timos Sellis were partially supported by the De... |