Crate toposort_scc

An implementation of Kahn’s algorithm for topological sorting and Kosaraju’s algorithm for strongly connected components.

This crate provides:

• an adjacency-list based graph data structure (IndexGraph)
• an implementation of a topological sorting algorithm that runs in O(V + E) time and O(V) additional space (Kahn’s algorithm)
• an implementation of an algorithm that finds the strongly connected components of a graph in O(V + E) time and O(V) additional space (Kosaraju’s algorithm)
• both algorithms are available either as single methods (.toposort() and .scc()) or as a combined method (.toposort_or_scc()) on IndexGraph

The id-arena feature adds an additional wrapper type (ArenaGraph) that allows topological sorting and finding of strongly connected components on arbitrary graph structures built with the id-arena crate by creating a proxy graph that is sorted and returning a list of indices into the original graph.

Example

This example creates an IndexGraph of the example graph from the Wikipedia page for Topological sorting.

A copy of the graph with cycles in it is created to demonstrate finding of strongly connected components.

use toposort_scc::IndexGraph;

let g = IndexGraph::from_adjacency_list(&vec![
    vec![3],
    vec![3, 4],
    vec![4, 7],
    vec![5, 6, 7],
    vec![6],
    vec![],
    vec![],
    vec![]
]);

let mut g2 = g.clone();
g2.add_edge(0, 0); // trivial cycle [0]
g2.add_edge(6, 2); // cycle [2, 4, 6]

assert_eq!(g.toposort_or_scc(), Ok(vec![0, 1, 2, 3, 4, 5, 7, 6]));
assert_eq!(g2.toposort_or_scc(), Err(vec![vec![0], vec![4, 2, 6]]));

Structs

ArenaGraph

An adjacency-list-based graph data structure wrapping an Arena from the id-arena crate.

ArenaGraphBuilder

A builder object that allows to easily add edges to a graph

IndexGraph

An adjacency-list-based graph data structure

IndexGraphBuilder

A builder object that allows to easily add edges to a graph

Vertex

A vertex in an IndexGraph