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The records may still be located directly for the primary attribute and indirection employed for secondary keys However, for symmetry, the system sketched in Fig 4-31 uses indirect referencing throughout Not all attributes need to have address spaces of equal length The goal le itself may have a pile or a sequential organization An insertion into a le using multiple pointer-lists will require changes to all pointer-lists in addition to the operation on the main le All entries for the same transformed value will have the same pointer-list address This increases the collision rate for attributes which are not unique When we dealt with simple direct les, whose records are stored by key values, we expected uniqueness Many other attributes in records will not have unique values The example of Fig 4-31 is hence atypical; you may wish to consider the pointer-list for sex = "male" Identical data attributes must lead to identical addresses in the the pointer-list space This problem can also be dealt with through the collisionhandling mechanism, but obviously attributes with poor partitioning power can overwhelm the mechanics of many solutions The result of the key-to-address transformation can no longer be uniform The use of over ow buckets rather than open addressing is now called for A popular database management system, adabas, uses the types of access presented here The pointer-lists may be prede ned and maintained, or created dynamically in response to transaction requests It also is possible to share a single pointer address space for several attributes by making this space appropriately larger and including the name, or another suitable identi er of the attribute itself, in the input to the address transformation function Figure 4-32 sketches this design using the symbols (I1 , I2 , I3 ) for attribute-type identi cation This method becomes especially interesting if the records have an irregular number of attributes, so that the individual pointer address spaces are of di erent sizes and possibly have dynamically varying length requirements The fact that no individual pointer-list areas have to be dimensioned and allocated reduces the amount of unused space while keeping the probability of exceeding the pointer space low A larger shared space can also reduce collisions due to clustering To verify that in case of a collision the correct pointer is picked, it is necessary that the pointer entry can be matched to its attribute name If this check is not made, problems will arise if two key values of di erent attributes are both identical and produce the same result from the address transformation An example would be a case where the health record number for John and the employee number assigned to Peter are identical and both happen to transform to the same address by di erent algorithms The author has come across a system where this case was not considered, but no access failure had ever been reported Transformations could be designed to avoid this possibility, but this restricts the choices available and limits the adaptability of this approach
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Shared Pointer-List A Common Transformation Procedure for Multiple Attributes A le using many attributes for access may need as many independent transformation routines The de nition and use of distinct routines can be avoided by transforming both the attribute name and value into an address within a single shared pointer-list The
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sketch in Fig 4-33 explains the catenation of the name and value strings prior to hashing A disadvantage of the simple scheme is that the pointer entry has to carry a long identi er for veri cation purposes The attribute name is better carried in abbreviated form The abbreviation might be a sequence number I, I = 1 a in a dictionary or schema for possible attributes, and this solution is illustrated The abbreviation has only to add enough information to the hashing algorithm to compensate for the increase in address space size The combined input to the hashing algorithm has to be kept as a key to test for collisions Another solution to the collision problem is to defer the recognition of collisions to the goal records The exact implementation will vary depending on the form of the goal records
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