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The addition of indirection via pointers, as introduced in Sec 4-6-2, can remove the record placement restrictions at additional access cost The use of a pointer-list, as sketched in Fig 4-33, is applied to the previous problem as shown in Fig 4-41 Now multiple indirect paths to the goal records are possible There now also is freedom in record placement, which can be exploited to improve the locality of rings, so that retrieval of members will be fast The collision-handling mechanism can take several forms Open addressing was preferred when records were not linked In the ring structure, additional pointer chains can be considered but may require much maintenance A compromise using open addressing is to use the pointer-list for le-type veri cation and the goal record for record category and key identi cation No key eld is provided in the pointer-list This becomes feasible when the pointer-list is shared by many rings Most collisions will be recognized in the list, and can be resolved there A collision which is detected when the goal record is accessed will require a continuation of the open addressing search through the pointer-list The structures de ned in such a system lend themselves well to some of the more formal information-retrieval methodologies We will present a generalized view of such access in the next section
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4-7-5 Multiattribute Ring Access In a ring structure with intersecting rings, as symbolically presented in Fig 4-42, the records of the ring category Available skills represent the association of Employees and Skills Let the number of Employees be ne and the total number of distinct Skills be ns The associative level can be viewed either as ns rings, one for every skill, with ring sizes according to the number of employees which have that skill, ne(s); or as ne rings, one for every employee with ring sizes according to the number of skills which an employee has ns(e) The number of records in the association Available skills na is then
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If rapid access to the individual members of the association is desired, direct access can be provided using as key the catenation of the two parent values There can be multiple associations between two parent types; in the gure a second association is called Training In general, there can be any number of associations between two sets of data elements In order to generalize this aspect, a third parent, say Expertise Level, can be considered to be the header of the set {Training, Available Skill, Craftsman, Teacher, }, that is, all the associations made between Employees and Skills The three-way symmetric concept is indicated in Fig 4-43 The rings for which this parent provides the header records will link all records for Training, Available Skill, Craftsman, Teacher, etc
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Sec 4-7
Options of the Complex Ring Organization
Implementation of a Fundamental Data Structure The associative structure of three elements represents the basic unit to carry information It also forms a minimal record as de ned in Sec 3-1 To identify a record in such an association, three arguments are required; in a programming language implementation of such associations (leap-type data structures) these three are called Object, Attribute, and Value, as shown in Table 4-4
Table 4-4 Name
General Associations in leap or
Sym Function O A V Example Employee Skill Type Expertise Level, Training, etc
Object or Attribute or Value or
Key Goal-attribute name Goal-attribute value
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Given this structure, seven type of questions can be asked as in Table 4-5
Table 4-5
Fundamental Queries in Data Triplets
Example based on Fig 4-42 Does Jones have Welding as an Available skill Which Employees have Welding as an Available skill Which Employees relate to Welding and how expertly Does Jones relate to Welding and how expertly What Employees have which Skills Available Jones has which Skills Available To which Skills is Jones related and how expertly
# 1 2 3 4 5 6 7
Format A ( O )= V A ( )= V A ( )= A ( O )= ( )= V ( O )= V ( O )=
The rst query can have only the response true or false Multiple responses will be given, in general, for the other queries; for instance, the last query (7) may have as response three triplets: Welding(Jones) = Available skill Machining(Jones) = Training Painting(Jones) = Available skill If semantic considerations are disregarded, it can be seen that any of the three elds can take on any of the three roles Triplet structures as presented here are used in applications where complex relationships have to be accessed rapidly, for instance, in graphics and in robot operation Thses systems can typically keep all of their data in core memory Triplets are di cult to map to external storage, since the records are small and the access paths unpredictable Locality can be hard to achieve so that the amount of data obtained per block access is small When rings have to be followed in order to retrieve a subset, there is the possibility that the rings will cross many block boundaries, so that the objective of rapid access is not achieved Good locality can be achieved, as presented in Sec 3-6, for all rings relative to one parent by placing all member records of a ring within a block If this is done in respect to Skill type , then queries of type 1, 2, 3, and 4 can be answered rapidly Direct access can identify the block for a speci c argument value of A, and then the position within the block can be obtained by in-core direct accessing for O or V to nd headers for these subrings, or by direct in-core accessing using the catenation of O&V to locate individual records Implementations of leap-type structures have used redundancy in order to provide equivalent access for queries with unknown values of A; a copy of the le is organized based on O or V The hash for query type 1 does not have to be supported in the second le These structures have not had goal attributes appended to their records, but this is, of course, possible The goal parts may be best kept remote, so that the locality of the primary access structure remains high Collisions also have to be resolved appropriately; this is achieved by use of additional chains from header and member records
Sec 4-8 4-8
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