Your team in charge of database administration was discussing different alternatives for indexing your organizations databases. Some tables in one database have very few insertions but they are used intensively by different services to check for information about items using the item_ID number. While many of your colleagues proposed using a tree index, you argued for a Hash index for these tables because it provides an average-case search cost of only slightly more than one disk I/O. The team leader agrees to adopt your solution but has asked you to write a short explanation for two questions:

a.How does Linear Hashing provide an average-case search cost of only slightly more than one disk I/O, given that overflow buckets are part of its data structure? (6 marks)

b.If a Linear Hashing index using Alternative (1) for data entries contains 10,000 records, with 10 records per page and an average storage utilization of 80 percent, what is the worst-case cost for an equality search? Under what conditions would this cost be the actual search cost? (6 marks)