Consider a tree-based index on some numeric attribute A of a relation R. This index is called dense if every search-key value of attribute A in relation R also appears in the index. Hence, for every search-key value x in A, there is an index record of the form <x, pointer>, where pointer points to the first record (if many such exist) in relation R that has R.A = x.
Tree-based indices are built on numeric attributes and maintain an order among the indexed search-key values. Hence, they provide efficient access to the records of a relation by attribute value. Consider, for example, an index built on attribute A of relation R. The leaf pages of the index contain index-records of the form <search-key, pointer>, where search-key corresponds to a value from the indexed attribute A and pointer points to the respective record in the indexed relation R with that attribute value. If all distinct values that appear in R.A also appear in index records, this index is dense;...