Tutorials

Every tutorial is a Julia script whose code runs when this site is built, so the outputs on each page are PATHPACK.jl's own. Each one has a notebook download under its title, and all of them run as is in a Codespace.

New to PATHPACK.jl? Start with Get Started, then Road Networks and One Graph, Many Questions.

The Basics

Tutorial	What it shows	Semiring
Road Networks	Every travel time on a street grid, the most central intersection, and rows from a factorization	MinPlus
One Graph, Many Questions	One landscape, three questions: cheapest route, worst barrier, where a random walk goes	MinPlus, MinMax, PlusProd
Shortest and Widest Paths	A small directed graph, all pairs and single-source queries	MinPlus, MaxMin
Factorize Once, Query Many Times	mlu and triangular solves: some rows or columns without the whole matrix	MinPlus

Other Questions, Same Call

Tutorial	What it shows	Semiring
Longest Paths and Schedules	Earliest start times and the critical path of a project	MaxPlus
Most Reliable Routes	The route most likely to work when links fail	MaxProd
Bandwidth and Widest Paths	The largest capacity between every pair of nodes	MaxMin, MinMax
Access Audits	Who can read which files on a Linux file system, by any route, and the leak a bind mount opens	OrAnd

Applications

Tutorial	What it shows	Semiring
Exact Diffusion for GNNs	Personalized PageRank diffusion, the matrix PyTorch Geometric's GDC computes	PlusProd
Isomap and Manifold Learning	Unrolling a swiss roll from the distances of its nearest-neighbour graph	MinPlus
Distances on Surfaces	Distances along a folded surface, for spatial null models of brain maps	MinPlus

Scaling Up

Page	What it shows
GPUs, One or Many	apsp_gpu on one GPU and on several, plans, and keeping results on the device
Performance Guide	Threads, orderings, element types and when to use a GPU
Benchmarks	PATHPACK.jl against GPU codes, graph libraries and the tools of each field