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Considering indexed allocation with a single-level index block, what is the space complexity overhead compared to contiguous allocation, and why might candidates underestimate it?

medium🪤 Complexity Trap Q6 of Q15
Operating Systems - File Allocation Methods - Contiguous, Linked, Indexed
Considering indexed allocation with a single-level index block, what is the space complexity overhead compared to contiguous allocation, and why might candidates underestimate it?
AO(n), because an index block stores pointers for each file block; candidates often ignore this auxiliary space.
BO(1), since only one index block is used regardless of file size.
CO(log n), due to hierarchical indexing structures.
DO(n^2), because each pointer requires additional metadata.
Step-by-Step Solution
Solution:

  1. Step 1: Understand indexed allocation space use

    Indexed allocation requires an index block storing pointers to all file blocks.

  2. Step 2: Analyze space overhead

    Index block size grows linearly with file size, so overhead is O(n).

  3. Step 3: Compare to contiguous allocation

    Contiguous allocation has no extra pointer overhead, so less auxiliary space.

  4. Step 4: Address misconception

    Candidates may think index block is fixed size or negligible, underestimating overhead.

  5. Final Answer:

    Option A -> Option A

  6. Quick Check:

    Index block size scales linearly with file blocks -> O(n) overhead [OK]
Quick Trick: Indexed allocation uses linear extra space for pointers [OK]
Common Mistakes:
MISTAKES
  • Assuming index block size is constant
  • Confusing indexing overhead with linked allocation
  • Overestimating overhead as quadratic
Trap Explanation:
PITFALL
  • Candidates often overlook auxiliary space for index blocks, thinking it's constant.
Interviewer Note:
CONTEXT
  • Evaluates understanding of space overhead trade-offs in allocation methods.
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