## INDEXING OF MULTIDIMENSIONAL DISCRETE DATA SPACES AND HYBRID EXTENSIONS (2009)

Citations: | 1 - 0 self |

### BibTeX

@MISC{Chen09indexingof,

author = {Changqing Chen},

title = {INDEXING OF MULTIDIMENSIONAL DISCRETE DATA SPACES AND HYBRID EXTENSIONS },

year = {2009}

}

### OpenURL

### Abstract

In this thesis various indexing techniques are developed and evaluated to support efficient queries in different vector data spaces. Various indexing techniques have been introduced for the (ordered) Continuous Data Space (CDS) and the Non-ordered Discrete Data Space (NDDS). All these techniques rely on special properties of the CDS or the NDDS to optimize data accesses and storage in their corresponding structures. Besides conventional exact match queries, the similarity queries and the box queries are two types of fundamental operations widely supported by modern indexing techniques. A box query is different from a similarity query in that the box query in multidimensional spaces tries to look up indexed data which meet query conditions on each and every dimension. The difference between similarity queries and box queriessuggests that indexing techniques which work well for similarity queries may not necessarily support efficient box queries. In this thesis, we propose the BoND-tree, a new indexing technique designed for supporting box queries in an NDDS. Both our theoretical analysis and experimental results demonstrate that the new heuristics proposed for the BoND-tree improve the performance of box queries in an NDDS significantly. The Hybrid

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Citation Context ...ime. And it forces reinsertion of indexed vectors to reorganize tree structure and reduce overlap among sibling nodes. Other examples of data-partitioning methods include the SS- tree[102], the X-tree=-=[14]-=-, the R+-tree[93], the SR-tree[57] and the TV-tree[52]. All of them try to address certain properties in CDSs indexing. For example, the SS-tree uses bounding spheres to partition the indexed space. A... |

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Citation Context ...ause they cannot support queries on multidimensional indexing keys. For the reason provided in section 1.3, in-memory indexing techniques like the k-d tree[12] (multidimensional search tree), quadtree=-=[88]-=- and grid file[72] are also excluded from our discussion. We start our discussion with related work on indexing techniques in the metric space[25, 59, 111]. Since the vector space is a special case of... |

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Citation Context ...ace at query time (through the triangle inequality property). Many indexing schemes have been developed to support similarity queries in the metric space. Some typical ones are the vantage-point tree =-=[109, 50]-=-, the generalizedhyperplane tree (GHT) [96], the multi-vantage-point tree (MVPT)[18] and the balanced monotonous bisector tree (MBT)[36]. All these techniques use one or more reference points (vantage... |

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Citation Context ...of the NDDS Indexing of the NDDS is a relatively new topic. In this section we introduce existing indexing techniques proposed for the NDDS. The first technique to be introduced is the bitmap indexing=-=[74, 73]-=-, an indexing scheme widely supported by many commercial DBMSs such as Oracle and DB2. Then we review typical string indexing methods popular in areas such as data mining and information retrieval. Tw... |

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Citation Context ...xisting indexing schemes for the CDS cannot be directly applied to the NDDS. Traditional string indexing techniques such as Tries and its derivatives (e.g., the suffix tree and the ternary search tree=-=[11, 31]-=-) could be applied to discrete data when the vectors to be indexed could be treated as strings. However, as we have mentioned in section 2.3.2, they are in-memory indexing structures which could not b... |

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Citation Context ... the HDS, which involve features from both the CDS and the NDDS. One way to apply these techniques in the HDS is to transform data from one space to the other. An example is the discretization method =-=[39, 61]-=-, which is used to transform continuous attributes to discrete ones through certain supervised (e.g., using the Chi-square-based criteria[95, 17] or the entropy-based criteria[103, 38]) or unsupervise... |

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Citation Context ...ace at query time (through the triangle inequality property). Many indexing schemes have been developed to support similarity queries in the metric space. Some typical ones are the vantage-point tree =-=[109, 50]-=-, the generalizedhyperplane tree (GHT) [96], the multi-vantage-point tree (MVPT)[18] and the balanced monotonous bisector tree (MBT)[36]. All these techniques use one or more reference points (vantage... |

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Citation Context ... k-d tree[12] (multidimensional search tree), quadtree[88] and grid file[72] are also excluded from our discussion. We start our discussion with related work on indexing techniques in the metric space=-=[25, 59, 111]-=-. Since the vector space is a special case of the metric space, theoretically all metric space indexing methods could be applied to the vector space. However, for the same reason (the metric space is ... |

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Citation Context ...rted by modern database indexing techniques. In practice these two queries frequently occur on database systems, and have become important criteria for evaluating the efficiency of indexing techniques=-=[94]-=-. Similarity queries are used to search indexed data points which are ’similar’ to a given query vector. They are important query types because they could be applied to retrieve information that canno... |

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Citation Context ...tual data regions idea in the LSDh tree (a space-partitioning approach) is actually the minimum bounding rectangle idea from data-partitioning approaches. In this section we introduce the hybrid-tree =-=[22]-=-, an indexing methods which combines concepts in both data-partitioning and space-partitioning approaches to achieve better query performances. The hybrid-tree is more close to space-partitioning meth... |

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Citation Context ... an indexing structure lead to deterioration of space utilization. 2.2.2 Space-partitioning Approaches in the CDS Typical space-partitioning methods of the CDS include the K-D-B tree[82], the LSD tree=-=[49]-=- and the LSD h tree[48]. The K-D-B tree is a combination of the K-D tree[10](multidimensional binary search tree) and the B-tree[8] (1-dimensional multiway search tree). As a memory-based multidimensi... |

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Citation Context ...whose time complexity is proportional to the search time[51]. However, Trie-related structures are memory-based which prevents them from being allied to large scale data sets[1, 32]. The Prefix B-tree=-=[6]-=- and the String B-tree[40] are disk-based indexing methods derived from the B-tree family[100, 75] (e.g., the B-tree, the B*-tree and the B+-tree). Records in the Prefix B-tree are organized based on ... |

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Citation Context ...rection). For example, the discretization method could transform continuous data to discrete data. A number of discretization techniques have been proposed to convert continuous data to discrete data =-=[21, 43, 64]-=-. Although these techniques could be applied to HDSs indexing, the semantics of the original data are changed during the transformation process. For example, we can categorize network user as ’normal’... |

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Citation Context ...imes people want to build indexing trees quickly and discard them after performing a limited number of queries. In such cases, the BoND-tree could be generated using algorithms introduced in [60] and =-=[85]-=-, which provide approximate solutions with guaranteed closeness to the optimal solution with much less time complexity and system resource requirements. We illustrate the BoND-tree splitting algorithm... |

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Citation Context ...ure could be used for exact matching or prefix matching (i.e., find all indexed strings prefixed by a given query string) by simply following the path corresponding to the query string. A suffix tree =-=[101, 69]-=- is a suffix Trie structure which saves all possible suffixes of indexed strings. Unary nodes (nodes with only one child) are compressed to improve space utilization. Suffix-trees could answer exact a... |