# What is APSP problem?

## What is APSP problem?

The all-pairs shortest paths (APSP) problem is to find shortest paths between all pairs of vertices in a graph. There is a simple form for the solution that records a minimal amount of information needed to lookup distances along shortest paths as well as reconstruct the shortest paths.

**What is APSP in DAA?**

A central problem in algorithmic graph theory is the shortest path problem. Hereby, the problem of finding the shortest path between every pair of nodes is known as all-pair-shortest-paths (APSP) problem.

### What is the formula for all pair shortest path?

The all pair shortest path algorithm is also known as Floyd-Warshall algorithm is used to find all pair shortest path problem from a given weighted graph. As a result of this algorithm, it will generate a matrix, which will represent the minimum distance from any node to all other nodes in the graph.

**Who discover all pairs shortest path algo?**

The Floyd Warshall Algorithm is for solving the All Pairs Shortest Path problem. The problem is to find shortest distances between every pair of vertices in a given edge weighted directed Graph. Try It!

#### What is the time complexity of Apsp *?

The complexity is O(mn+ n^2 \ln n). The Floyd–Warshall algorithm for directed graphs with arbitrary weights.

**What is an intermediate vertex?**

A vertex between the source and the sink.

## What is the difference between single source shortest path and all pair shortest path?

The single-source shortest-path problem requires that we find the shortest path from a single vertex to all other vertices in a graph. The all-pairs shortest-path problem requires that we find the shortest path between all pairs of vertices in a graph.

**Is Floyd warshall greedy?**

The Floyd-Warshall algorithm takes into account all possible routes so that there are some routes are displayed while the greedy algorithm checks every node that is passed to select the shortest route (Local Optimum) so that the time needed in searching is faster.

### What is transitive closure in DAA?

Transitive Closure it the reachability matrix to reach from vertex u to vertex v of a graph. One graph is given, we have to find a vertex v which is reachable from another vertex u, for all vertex pairs (u, v).