A Practical Introduction to Data Structures and Algorithm Analysis

Sec. 9.4 Hashing 34954InsertDelete3210 .2 .4 .6 .8 1.0Figure 9.8 Growth of expected record accesses with α. The horizontal axis isthe value for α, the vertical axis is the expected number of accesses to the hashtable. Solid lines show the cost for “random” probing (a theoretical lower boundon the cost), while dashed lines show the cost for linear probing (a relatively poorcollision resolution strategy). The two leftmost lines show the cost for insertion(equivalently, unsuccessful search); the two rightmost lines show the cost for deletion(equivalently, successful search).full. Beyond that point performance will degrade rapidly. This requires that theimplementor have some idea of how many records are likely to be in the table atmaximum loading, and select the table size accordingly.You might notice that a recommendation to never let a hash table become morethan half full contradicts the disk-based space/time tradeoff principle, which strivesto minimize disk space to increase information density. Hashing represents an unusualsituation in that there is no benefit to be expected from locality of reference.In a sense, the hashing system implementor does everything possible to eliminatethe effects of locality of reference! Given the disk block containing the last recordaccessed, the chance of the next record access coming to the same disk block isno better than random chance in a well-designed hash system. This is because agood hashing implementation breaks up relationships between search keys. Insteadof improving performance by taking advantage of locality of reference, hashingtrades increased hash table space for an improved chance that the record will bein its home position. Thus, the more space available for the hash table, the moreefficient hashing should be.