Introduction to Algorithms: 6.006 Massachusetts Institute of Technology Instructors: Erik Demaine, Jason Ku, and Justin Solomon Lecture 13: Dijkstra’s Algorithm

Recall that Dijkstra’s algorithm finds the length of all the shortest paths in a directed graph with non-negative weights on the edges, from a source vertex s to every other vertex vi in the graph. We …

Last updated 1-28-2020 The problem solved is the single source min-weight paths problem for digraphs with no. negative edge weights. (Note: in the literature, the \weight" of an edge is often called \cost," …

We can keep the fringe in a linked list, and scan through it every time.

Dijkstra’s Algorithm–the following algorithm for finding single-source shortest paths in a weighted graph (directed or undirected) with no negative-weight edges:

8 Mathematical Proof that it Works It may (or may not) make intutive sense that Dijkstra's Algorithm does what it is claimed to do, but a proof is fairly straightforward. l and will not be updated later. It's th ed to …

1 Dijkstra's Algorithm ng Dijkstra's algorithm. The key idea, that Dijkstra will maintain as an invariant, is that 8t 2 V; the algorithm computes an estimate d[t] of the distance of t f