Open file cache in Nginx - Time & Space Complexity

Time Complexity: Open file cache

O(n)

Understanding Time Complexity

We want to understand how the time to access files changes when using nginx's open file cache.

Specifically, how does caching affect the number of file operations as requests increase?

Scenario Under Consideration

Analyze the time complexity of the following nginx configuration snippet.

open_file_cache max=1000 inactive=20s;
open_file_cache_valid 30s;
open_file_cache_min_uses 2;
open_file_cache_errors on;

location /static/ {
    root /var/www/html;
}
    

This configuration enables caching of open file descriptors for static files to reduce file system checks.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Checking and opening files on each request.
• How many times: Once per file request, but caching reduces repeated opens.

How Execution Grows With Input

As the number of file requests grows, the cache helps avoid repeated file opens.

Input Size (n)	Approx. Operations
10	About 10 file checks, fewer opens due to cache
100	About 100 file checks, many served from cache
1000	About 1000 file checks, most file opens avoided by cache

Pattern observation: The number of actual file opens grows slower than requests because cache reuse saves work.

Final Time Complexity

Time Complexity: O(n)

This means the work grows linearly with requests, but caching reduces the cost per request.

Common Mistake

[X] Wrong: "Caching makes file access constant time regardless of requests."

[OK] Correct: Cache helps reduce repeated opens but each new file still requires a check and open.

Interview Connect

Understanding how caching affects operation counts shows you can reason about performance in real systems.

Self-Check

"What if the cache size max is set to a very small number? How would the time complexity change?"