Suppose that a static hash file initially has 600 buckets in the primary area and that records are inserted that create an overflow area of 600 buckets. If we reorganize the hash file, we can assume that the overflow is eliminated. If the cost of reorganizing the file is the cost of the bucket transfers (reading and writing al of the buckets) and the only periodic file operation is the fetch operation, then how many times would we have to perform a fetch (successfully) to make the reorganization cost-effective? That is, the reorganization cost and subsequent search cost are less than the search cost before reorganization. Assume s=16, rd=8.3 ms, btt=1 ms.

What will be an ideal response?

Primary Area = 600 buckets
Secondary Area (Overflow) = 600 buckets
Total reorganization cost = Buckets Read & Buckets Written for (600 & 600) +
1200 = 2400 buckets = 2400 (1 ms) = 2400 ms
Let X = number of random fetches from the file.
Average Search time per fetch = time to access (1 + 1/2) buckets where 50% of
time we need to access the overflow bucket.
Access time for one bucket access = (S + r + btt)
= 16 + 8.3 + 0-8
= 25.1 ms
Time with reorganization for the X fetches
= 2400 + X (25.1) ms
Time without reorganization for X fetches = X (25.1) (1 + 1/2) ms
= 1.5 * X * (25.1) ms.
Hence, 2400 + X (25.1) < (25.1) * (1.5X)
2374.9/ 12.55 < X
Hence, 189.23 < X
If we make at least 190 fetches, the reorganization is worthwhile.