Dynamic programming is the algorithm design technique used in finding all pairs of shortest distances in a graph.

Explanation:
Dynamic programming is a technique that solves complex problems by breaking them down into overlapping subproblems and solving each subproblem only once, storing the results and reusing them to solve larger subproblems.

When finding all pairs of shortest distances in a graph, we need to find the shortest distance between every pair of vertices in the graph. This can be done efficiently using the Floyd-Warshall algorithm, which is based on dynamic programming.

The Floyd-Warshall algorithm uses a dynamic programming approach to compute the shortest distances between all pairs of vertices in a graph. It maintains a table, often called the distance matrix, where each entry represents the shortest distance between two vertices. The algorithm iteratively updates the entries of the distance matrix by considering all possible intermediate vertices.

The algorithm starts with an initial distance matrix, where the entry (i, j) represents the weight of the edge between vertices i and j, or infinity if there is no edge between them. Then, it considers each vertex k as a possible intermediate vertex and checks if the distance between vertices i and j can be minimized by including vertex k in the shortest path. If so, it updates the distance matrix accordingly.

By repeating this process for all vertices as intermediate vertices, the algorithm gradually computes the shortest distances between all pairs of vertices in the graph. At the end of the algorithm, the distance matrix contains the shortest distances between every pair of vertices.

In conclusion, dynamic programming is the algorithm design technique used in finding all pairs of shortest distances in a graph, as exemplified by the Floyd-Warshall algorithm.