Introduction:
The Unix file system is a widely used file system in Unix-like operating systems. It manages the allocation of data blocks for storing file data efficiently. When dealing with very large files, it becomes crucial to optimize the allocation strategy to minimize fragmentation and improve performance. In the Unix file system, the data blocks of a very large file are allocated using an extension of indexed allocation.

Indexed Allocation:
Indexed allocation is a file allocation method where a separate index block is used to store pointers to the data blocks of a file. Each index block contains a fixed number of pointers, and each pointer points to a data block. This technique allows quick access to any data block in the file by following the pointers in the index blocks.

Limitations of Indexed Allocation:
While indexed allocation is efficient for small to moderate-sized files, it may not be suitable for very large files due to the following limitations:

1. Memory Overhead: In indexed allocation, an index block is required for every fixed number of data blocks. For very large files, this can lead to a significant amount of memory overhead, as a large number of index blocks need to be allocated.

2. Sequential Access: Since indexed allocation relies on following pointers to access data blocks, it is not efficient for sequential access of large files. The overhead of traversing the index blocks and following the pointers can degrade performance.

3. Fragmentation: Indexed allocation can also suffer from internal fragmentation. If a file does not occupy a complete data block, the remaining space in the block is wasted.

Extension of Indexed Allocation:
To overcome the limitations of indexed allocation for very large files, an extension of indexed allocation is used. In this approach, multiple levels of index blocks are used to create a hierarchical structure.

1. First-Level Index Blocks: The first-level index blocks point to second-level index blocks.

2. Second-Level Index Blocks: The second-level index blocks point to third-level index blocks.

3. Third-Level Index Blocks: The third-level index blocks finally point to the data blocks of the file.

By using multiple levels of index blocks, it becomes possible to allocate and manage the data blocks of very large files efficiently. This hierarchical structure allows for better organization of the index blocks and reduces memory overhead. It also enables faster access to data blocks by reducing the number of levels that need to be traversed.

Therefore, the data blocks of a very large file in the Unix file system are allocated using an extension of indexed allocation to optimize performance and minimize fragmentation.