Understanding all-pair shortest path problem

The all-pair shortest path problem is the natural extension of the single source shortest path problem and is also a very common problem that can be modeled as a graph. To understand the problem better, let's look at an example of how we face it and how we require an efficient solution.

Logistics Services

Consider a large e-commerce company with multiple warehouses storing the goods it sells. Delivering goods from a warehouse depletes its inventory, and the company has to ensure items are restocked. The inventory is often rebalanced by moving items from one warehouse to another. However, to save logistics costs, the company would want to move items from the nearest warehouse with excess stock.

This problem can be modeled as a graph in which each node represents a warehouse and an edge represents the transportation link between them, where the weight of the edges is the transport cost.