Proxy cache basics in Nginx - Time & Space Complexity

Time Complexity: Proxy cache basics

O(1)

Understanding Time Complexity

When using nginx as a proxy cache, it is important to understand how the time to serve requests changes as more cached items are stored.

We want to know how the caching process scales when handling many requests and cache entries.

Scenario Under Consideration

Analyze the time complexity of the following nginx proxy cache configuration snippet.

proxy_cache_path /data/nginx/cache levels=1:2 keys_zone=my_cache:10m max_size=1g inactive=60m;

server {
    location / {
        proxy_cache my_cache;
        proxy_pass http://backend;
        proxy_cache_valid 200 302 10m;
    }
}

This snippet sets up a proxy cache with a specific directory structure and cache zone, then uses it to cache responses from a backend server.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Searching the cache directory structure for a matching cached file.
• How many times: Once per incoming request to check if a cached response exists.

How Execution Grows With Input

As the number of cached items grows, nginx looks up cached files using a directory hierarchy to keep lookups fast.

Input Size (n)	Approx. Operations
10	Few file lookups in shallow directories
100	More lookups but still quick due to directory levels
1000	Still efficient because of structured cache levels

Pattern observation: Lookup time grows slowly because the cache is organized to avoid searching many files in one place.

Final Time Complexity

Time Complexity: O(1)

This means nginx can find cached responses quickly regardless of how many items are stored, thanks to its directory structure.

Common Mistake

[X] Wrong: "The cache lookup time grows linearly as more items are cached."

[OK] Correct: nginx uses a multi-level directory structure to avoid scanning large directories, so lookup stays fast even with many cached files.

Interview Connect

Understanding how nginx proxy cache scales helps you explain real-world caching performance and shows you can reason about system efficiency.

Self-Check

"What if we removed the 'levels' directive and stored all cached files in one directory? How would the time complexity change?"