## A Mathematical Model For Optimal Indexing In Object-Oriented Databases

### BibTeX

@MISC{Shidlovsky_amathematical,

author = {Boris Shidlovsky and Elisa Bertino},

title = {A Mathematical Model For Optimal Indexing In Object-Oriented Databases},

year = {}

}

### OpenURL

### Abstract

A generalized approach to the problem of optimal indexing structures for navigation along inheritance and aggregation hierarchies in object-oriented database systems is proposed. The approach is based on two main ideas. First, we use the notion of indexing graphs for providing an abstract view of the indexing relationships among classes in the hierarchies. Second, we propose a mapping schema which reflects an indexing graph into B-tree-like data structures and develop the cost model for the basic workload operations. This reduces the query optimization and optimal indexing problems to standard shortest paths and nonlinear integer programming problems. We detect the exponential complexity of the obtained optimization problem and give an efficient approximation method for the selection of nearly optimal indexing structure. 1

### Citations

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(Show Context)
Citation Context ... searching and exploited data structures studied in computational geometry. Most techniques for indexing an aggregation hierarchy [BeKi89, BG93, Ber94, BeFo95] originate from the join index structure =-=[Val87]-=-. Typically, an indexing structure for an aggregation hierarchy associates the values of nested attributes with the objects in the leading classes of the hierarchy [BeKi89]. For fast evaluation of nes... |

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(Show Context)
Citation Context ...rom the join index structure [Val87]. Typically, an indexing structure for an aggregation hierarchy associates the values of nested attributes with the objects in the leading classes of the hierarchy =-=[BeKi89]-=-. For fast evaluation of nested predicate, path-index and nested-index [BG93, BeFo95] support object instantiations along an entire hierarchy. Such solution has a rather poor performance for update op... |

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(Show Context)
Citation Context ...are executed. As a result, a method combining the advantages of both CHand H-trees has been proposed in [KiMo94]. A different approach to the problem has been proposed by Kanellakis, Ramaswamy at al. =-=[KaRa94]-=-. They reduced the indexing a simple class attribute to external dynamic 2dimensional range searching and exploited data structures studied in computational geometry. Most techniques for indexing an a... |

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(Show Context)
Citation Context ... ; h vr ); where BB(k; n; h) is the cost of retrieving a number k of keys during the batched scanning of a B + -tree of height h with a total number of n keys. It is formulated by using Yao's formula =-=[Yao77] as f-=-ollows: BB(k; n; h) = h X l=1 Y (k; n l ; n) = h X l=1 n l \Delta " 1 \Gamma k\Gamma1 Y i=0 n \Gamma n n l \Gamma i n \Gamma i # : Then, the cost of the leaf records access is LV (i; v r ) = ae Y... |

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(Show Context)
Citation Context ...e domain of another class. The most intensively studied query type was indexing an inheritance hierarchy against a simple attribute [KKD89, LOL92, KiMo94, KaRa94]. The class-hierarchy index (CHindex) =-=[KKD89]-=- is based on B + -trees and maintains a single index for all classes in the inheritance hierarchy. The CHindex efficiently performs match point operations, but is not optimal for range queries. Conver... |

38 | Join index hierarchies for supporting efficient navigations on object-oriented databases
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(Show Context)
Citation Context ...timal indexing structure for each of fragments [Ber94]. The problem of the optimal indexing structure for both downward and upward navigation along a hierarchy has been first addressed by Xie and Han =-=[XiHa94]-=-. Their approach consists of building a hierarchy of join indices, thus transforming a sequence of navigation steps into a simple search in an appropriate join index. In this work we model the optimal... |

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(Show Context)
Citation Context ... + -trees and maintains a single index for all classes in the inheritance hierarchy. The CHindex efficiently performs match point operations, but is not optimal for range queries. Conversely, H-index =-=[LOL92]-=- efficiently performs range operations and reads more pages than CH-index when match point queries are executed. As a result, a method combining the advantages of both CHand H-trees has been proposed ... |

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15 | Indexing multiple sets
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(Show Context)
Citation Context ...ficiently performs range operations and reads more pages than CH-index when match point queries are executed. As a result, a method combining the advantages of both CHand H-trees has been proposed in =-=[KiMo94]-=-. A different approach to the problem has been proposed by Kanellakis, Ramaswamy at al. [KaRa94]. They reduced the indexing a simple class attribute to external dynamic 2dimensional range searching an... |

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(Show Context)
Citation Context ... Such complexity is too large to be solved by precise methods. To give an approximated solution, we use a method that is an integer analogy of the multidimensional steepest descent for real functions =-=[BS79]-=-. The integer steepest descent is an iteration method. On the j-th iteration, a new IIG named X j is constructed. The IIG is chosen from a list of candidates built from X j \Gamma1 obtained from the p... |

2 |
Index configuration
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(Show Context)
Citation Context ...ther poor performance for update operations, and it has thus been proposed to split the aggregation hierarchy into several fragments and determine the optimal indexing structure for each of fragments =-=[Ber94]-=-. The problem of the optimal indexing structure for both downward and upward navigation along a hierarchy has been first addressed by Xie and Han [XiHa94]. Their approach consists of building a hierar... |