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Multi-level indexes

Multi-level indexes in an index sequential file structure
Consider a bank with 100 million customers. They all have their own account number, which is an 8-digit number. Sometimes, the whole file holding the customers' details is accessed in batch processing mode, for example to print statements every month and sometimes individual records are retrieved, for example, when a customer has a query about their account. Because of this, the index sequential method of organising these records has been selected. The records are organised by putting the account numbers in sequential order. An index is then designed.  Imagine we didn't have an index, just one big sequential file. To find a particular account, you would go to the beginning of the file, and search one record after another until you either find the record or come to the end of the file. This is a simple system but with so many records it would take a long time. You could end up checking 100 million records before you found the one you wanted!

An index sequential file with one index level
Let's implement an index sequential file. To start with, let's just have one index. The account whose record we want to retrieve is account number 45843521. This is entered into the 'search' field. How is the record retrieved?

one index 
An index sequential file with one index.

In the system illustrated above, we have created an index. It is an index of the first two numbers in an account number. It starts with 00 then 01, 02, 03 up to 97, 98 and finally 99. If an account begins with e.g. 45, you go down the index to 45 and get the data held in that location. That data is the first memory address of a block of memory addresses where all the accounts begin with 45 - and the block in this example is 1000000 memory addresses long. You go to that memory address, and then start sequentially searching the block for the account number. You can do that because all of the accounts in that block from that memory location begin with 45. You don't have to search all the other account numbers that begin with 01 or 02 or 03 and so on. How has this helped? When we had just a sequential file, you may have had to check up to 100000000 records before you got to the one you wanted. With one index, you need to sequentially search the index (up to 100 comparisons) followed by a sequential search of 1000000 records. In the worse case, your program would have to make 1000100 comparisons before it found the requested record - a massive improvement on 100000000 records!

An index sequential file with two index levels
We can improve things further, however. After we have got to the place in memory where all accounts begin with 45, we could examine the next two numbers in an account and use this in another index. The first index pointed us to records that began with 45. The second index points us to records that begin with 4584. If we get to the block of addresses where every account begins with 4584, we can quickly find our target account using sequential searching. You can see this in the next diagram. The first index takes up to 100 comparisons. The second index will take up to a further 100 comparisons, a total of 200. The final sequential search will take only up to 10000 comparisons because the blocks being pointed to are now blocks of 10000 memory addresses! We have gone from having to search 100000000 records, to 1000100 records to 10200 records!

two indexes
An index sequential file with two indexes.

An index sequential file with three index levels
There is nothing stopping us adding a further index! Once we have got to the place where all accounts begin with 4584, we can check the next two digits by searching from that point sequentially. This will point us to an area in memory where all accounts begin with 458435. We then search that block of memory sequentially. This is shown below.

3 indexes 
An index sequential file with three indexes.

We can see how many comparisons are needed now before we find a record. We need up to 100 comparisons for the first index, 100 for the second index and 100 for the third index, a total of 300 comparisons. The blocks we will sequentially search to find an account only need to be 100 memory addresses long now. So now, we need only do up to 400 comparisons to find a record (or an average of 200 comparisons) - a far cry from 100 million!!

Another example of index sequential organisation
When a pupil joins the Noname University, they are allocated a unique ID code. The first two numbers of the code are based on the tutor that they have been allocated to. There are twelve tutors. The first has an ID of 01, the second 02 and so on up to 12. The third number in the student’s unique code is a 0 if the student is female and 1 if they are male. The next 2 digits are a code for the course they are on, from 01 to 15. The final two digits are a unique ID number, ranging from 01 to 99. An example of a code for somebody who was allocated tutor 6, is male, is doing course ID 15 and has the ID 40 is 0611540. We want to design an index sequential file structure so that we can retrieve records quickly. We will represent the structure using diagrams. How would we go about this? The first thing we need to do is have an index with 12 locations, for the twelve tutors. We need a first level index. The diagram would look like this:

1 index

Whenever we want to retrieve a record, we can now strip out the first two numbers in a student’s code and use it in a sequential search of our index. This will then point us to a block of memory where all students have that particular tutor. We can then search that block sequentially for any particular student. The worst-case scenario is searching for student 1211599. The first index will take 12 comparisons. Then searching the associated block will take 2970 comparisons, a total of 2982 comparisons. However, these blocks will still be large and will take time to search. (We might of course get lucky and need only 2 comparisons, if we were searching for student 0100101).

We can improve things by having a second index. After we have stripped out the first two numbers and searched for the right tutor, we can then strip out the third digit in the code and search sequentially for the right gender. This will then point us to blocks of memory where, in each block, students have a particular tutor and are a particular gender.

2 indexes

We can add another level for the course code to improve things even further, like this:

3 indexes

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