Publish-subscribe architecture in IOT Protocols - Time & Space Complexity

Time Complexity: Publish-subscribe architecture

O(n)

Understanding Time Complexity

We want to understand how the work done by a publish-subscribe system grows as more devices or messages are involved.

How does the system handle more subscribers or more messages efficiently?

Scenario Under Consideration

Analyze the time complexity of the following publish-subscribe message dispatch code.

// Pseudocode for message dispatch in publish-subscribe
function publish(topic, message) {
  subscribers = getSubscribers(topic);
  for each subscriber in subscribers {
    sendMessage(subscriber, message);
  }
}
    

This code sends a message to all subscribers of a given topic.

Identify Repeating Operations

Look for repeated actions that take most time.

• Primary operation: Loop over all subscribers to send messages.
• How many times: Once for each subscriber subscribed to the topic.

How Execution Grows With Input

As the number of subscribers grows, the number of send operations grows the same way.

Input Size (subscribers)	Approx. Operations (sendMessage calls)
10	10
100	100
1000	1000

Pattern observation: The work grows directly with the number of subscribers.

Final Time Complexity

Time Complexity: O(n)

This means the time to send messages grows linearly with the number of subscribers.

Common Mistake

[X] Wrong: "Sending one message to a topic always takes the same time, no matter how many subscribers there are."

[OK] Correct: Each subscriber must receive the message, so more subscribers mean more send operations and more time.

Interview Connect

Understanding how message dispatch scales helps you design systems that handle many devices smoothly. This skill shows you can think about system growth and efficiency.

Self-Check

What if the system cached messages and sent them in batches? How would that change the time complexity?