Multi-device MQTT network in Raspberry Pi - Time & Space Complexity

Time Complexity: Multi-device MQTT network

O(n)

Understanding Time Complexity

When many Raspberry Pi devices send messages using MQTT, we want to know how the time to process messages grows as more devices join.

We ask: How does adding more devices affect the work the network does?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

import paho.mqtt.client as mqtt

clients = []

for i in range(n):
    client = mqtt.Client(f"device_{i}")
    client.connect("broker.local")
    client.loop_start()
    clients.append(client)

for client in clients:
    client.publish("sensor/data", "message")

This code connects n devices to an MQTT broker and each device sends one message.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Looping over n devices to connect and send messages.
• How many times: Each loop runs n times, once per device.

How Execution Grows With Input

As the number of devices n grows, the total work grows roughly the same way.

Input Size (n)	Approx. Operations
10	About 20 operations (connect + publish per device)
100	About 200 operations
1000	About 2000 operations

Pattern observation: Doubling devices roughly doubles the work needed.

Final Time Complexity

Time Complexity: O(n)

This means the time to connect and send messages grows directly with the number of devices.

Common Mistake

[X] Wrong: "Adding more devices won't affect the time much because messages are sent independently."

[OK] Correct: Each device adds its own connection and message sending steps, so total work adds up linearly.

Interview Connect

Understanding how work grows with devices helps you design scalable IoT systems and shows you can think about performance in real networks.

Self-Check

What if each device sends m messages instead of one? How would the time complexity change?