Shortest paths in a Euclidean graph

Taken by: Auguste Carmen Lunang Pomkam
Completed by: Auguste Carmen Lunang Pomkam

Finding the shortest path between two vertices in a weighted graph is a fundamental problem with numerous applications. There are of course classical algorithms for this problem like Dijkstra's Algorithm, but in many applications this algorithm is too slow, for example when we want to compute the best path between two cities in the graph of the roads of a whole country.

For this kind of problem, it is crucial to use the Euclidean property of the graph to design better algorithms. A classical approach is to use the A* search which uses an estimation on the minimal distance to minimize the search space in Dijkstra's algorithm. But if one is allowed to do some precomputations on the graph and to store some extra data, it is possible to answer any shortest path query between two points very efficiently.

The aim of the project is to understand and implements some of these algorithms.