Consider a tree-based index on some numeric attribute A of a relation R. If an index record (of the form <search-key, pointer>) is created for some of the values that appear in attribute A, then this index is sparse.
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 not all distinct values that appear in R.A also appear in index records, this index is sparse, otherwise it is calleddense.
A sparse index needs a way to access even the relation records with values that do not directly...