A Note on Two Problems in Connexion with Graphs

Dijkstra's three-page paper asks how to find the shortest route through a weighted network without listing every possible path. Read it to see how a growing settled frontier, one tentative distance per reachable node, and a smallest-first choice turn a global route question into a sequence of local commitments.

Reading focus: How settled, frontier, and unseen node sets separate distances that are final from routes that are only the best found so far. Why inspecting the newest settled node can shorten a neighbour's tentative route, and why the smallest tentative total is the next safe commitment. Why non-negative edge weights protect that greedy commitment, how direction-dependent costs still fit, and why minimum spanning trees solve a different problem.

Numerische Mathematik 1959. E. W. Dijkstra. 30 min read, very easy difficulty.