How can I solve the travelling salesman problem using rust and petgraph?

Question

I have a parser from my raw input to a petgraph::UnGraph structure. I need to find the shortest path that visits all nodes. I found algo::dijkstra, but from what I understood, Dijkstra would only give me the shortest path connecting two specific nodes.

Is there a function in the petgraph library that offers a way to solve the travelling salesman problem easily, or will I need to implement a solver myself? I browsed the documentation, but couldn't find anything, but maybe it's just my limited experience with graph algorithms.

Answer 1

I've been playing with petgraph for a little while and took your question as a challenge. I find petgraph very powerful, but like many complex systems it is hard to understand and the documentation doesn't give enough examples.
For example what is the diffence between an EdgeReference and an EdgeIndex?
If I have an EdgeReference how do I get an EdgeIndex?
If have an EdgeIndex how do I get the NodeIndexs it connects?
Anyway I created a crude TSP solver using petgraph as a starting point for you. Please note that it is minimally tested, ni_to_n is unneeded, but I left it in case it is useful to you, and many improvements are crying out to be made. But, it should give you some idea how you might take an Ungraph<String, u32> (nodes are city names and edge weights are u32 distances) and get to an approximate TSP solution.
My basic strategy is to use petgraph's min_spanning_tree() then to create a cycle.
See the comments below for more.

I hope this is useful, if you improve it, please post!

use petgraph::algo::min_spanning_tree;
use petgraph::data::FromElements;
use petgraph::graph::{EdgeIndex, NodeIndex, UnGraph};
use std::collections::{HashMap, HashSet, VecDeque};

// function that returns the cycle length of the passed route
fn measure_route(route: &VecDeque<usize>, ddv: &[Vec<u32>]) -> u32 {
    let mut len = 0;
    for i in 1..route.len() {
        len += ddv[route[i - 1]][route[i]];
    }
    len + ddv[route[0]][route[route.len() - 1]]
}

// Travelling salesman solver - the strategy is:
// 1) create a minimal spanning tree
// 2) reduce all nodes to two or fewer connections by deleting the most expensive connections
// 3) connect all nodes with 0 or 1 connections to each other via the least expensive connections
fn tsp(g: &UnGraph<String, u32>) -> u32 {
    // translation collections: NodeIndex <-> usize
    let n_to_ni: Vec<NodeIndex> = g.node_indices().collect();
    let mut ni_to_n: HashMap<NodeIndex, usize> = HashMap::new();
    for (n, ni) in g.node_indices().enumerate() {
        ni_to_n.insert(ni, n);
    }

    // the original distance data in a vector
    let mut ddv: Vec<Vec<u32>> = vec![vec![u32::MAX; g.node_count()]; g.node_count()];
    for x in 0..g.node_count() {
        ddv[x][x] = 0;
        for y in x + 1..g.node_count() {
            let mut edges = g.edges_connecting(n_to_ni[x], n_to_ni[y]);
            let mut shortest_edge = u32::MAX;
            while let Some(edge) = edges.next() {
                if *edge.weight() < shortest_edge {
                    shortest_edge = *edge.weight();
                }
            }
            ddv[x][y] = shortest_edge;
            ddv[y][x] = shortest_edge;
        }
    }

    // create a graph with only the needed edges to form a minimum spanning tree
    let mut mst = UnGraph::<_, _>::from_elements(min_spanning_tree(&g));

    // delete most expensive connections to reduce connections to 2 or fewer for each node
    'rem_loop: loop {
        for ni1 in mst.node_indices() {
            let mut ev: Vec<(u32, EdgeIndex)> = vec![];
            for ni2 in mst.node_indices() {
                if let Some(ei) = mst.find_edge(ni1, ni2) {
                    ev.push((*mst.edge_weight(ei).unwrap(), ei));
                }
            }
            if ev.len() > 2 {
                ev.sort();
                mst.remove_edge(ev[2].1);
                // since we modified mst, need to start over as one other EdgeIndex will be invalid
                continue 'rem_loop;
            }
        }
        break;
    }

    // build a vector of routes from the nodes
    let mut routes: Vec<VecDeque<usize>> = vec![];
    let mut no_edges: Vec<usize> = vec![];
    let mut visited: HashSet<usize> = HashSet::new();
    let mut stack: VecDeque<usize> = VecDeque::default();
    for n in 0..mst.node_count() {
        if !visited.contains(&n) {
            stack.push_back(n);
        }

        while !stack.is_empty() {
            let n2 = stack.pop_front().unwrap();
            let mut eflag = false;
            visited.insert(n2);

            for n3 in 0..mst.node_count() {
                if mst.find_edge(n_to_ni[n2], n_to_ni[n3]).is_some() {
                    eflag = true;
                    if !visited.contains(&n3) {
                        stack.push_back(n3);
                        let mut fflag = false;
                        for r in routes.iter_mut() {
                            if r[0] == n2 {
                                r.push_front(n3);
                                fflag = true;
                            } else if r[r.len() - 1] == n2 {
                                r.push_back(n3);
                                fflag = true;
                            } else if r[0] == n3 {
                                r.push_front(n2);
                                fflag = true;
                            } else if r[r.len() - 1] == n3 {
                                r.push_back(n2);
                                fflag = true;
                            }
                        }
                        if !fflag {
                            // not found, create a new VecDeque
                            let mut vd = VecDeque::default();
                            vd.push_back(n2);
                            vd.push_back(n3);
                            routes.push(vd);
                        }
                    }
                }
            }
            if !eflag {
                no_edges.push(n2);
            }
        }
    }

    // put each node with no edges on the end of a route based on cost
    for n in &no_edges {
        let mut route_num = usize::MAX;
        let mut insert_loc = 0;
        let mut shortest = u32::MAX;
        for ridx in 0..routes.len() {
            if ddv[*n][routes[ridx][0]] < shortest {
                shortest = ddv[*n][routes[ridx][0]];
                route_num = ridx;
                insert_loc = 0;
            }
            if ddv[routes[ridx][routes[ridx].len() - 1]][*n] < shortest {
                shortest = ddv[routes[ridx][routes[ridx].len() - 1]][*n];
                route_num = ridx;
                insert_loc = routes[ridx].len() - 1;
            }
        }
        if route_num == usize::MAX || shortest == u32::MAX {
            panic!("unable to deal with singleton node {}", *n);
        } else if insert_loc != 0 {
            routes[route_num].push_back(*n);
        } else {
            routes[route_num].push_front(*n);
        }
    }

    // merge routes into a single route based on cost - this could be improved by doing comparisons
    // between routes[n] and routes[m] where m != 0 and n != 0
    let mut tour = routes[0].clone();
    for ridx in 1..routes.len() {
        let mut v: Vec<(u32, bool, bool)> = vec![];
        v.push((ddv[routes[ridx][routes[ridx].len() - 1]][tour[0]], true, false));
        v.push((ddv[routes[ridx][routes[ridx].len() - 1]][tour[tour.len() - 1]], true, true));
        v.push((ddv[routes[ridx][0]][tour[0]], false, false));
        v.push((ddv[routes[ridx][0]][tour[tour.len() - 1]], false, true));
        v.sort_unstable();
        match v[0] {
            (_, true, false) => {
                // end to beginning of tour
                for (insert_loc, n) in routes[ridx].iter().enumerate() {
                    tour.insert(insert_loc, *n);
                }
            }

            (_, true, true) => {
                // end to end of tour
                let insert_loc = tour.len();
                for n in &routes[ridx] {
                    tour.insert(insert_loc, *n);
                }
            }

            (_, false, false) => {
                // beginning to beginning of tour
                for n in &routes[ridx] {
                    tour.push_front(*n);
                }
            }

            (_, false, true) => {
                // beginning to end of tour
                for n in &routes[ridx] {
                    tour.push_back(*n);
                }
            }
        }
    }

    // print out the tour and return its length
    dbg!(tour.clone());
    measure_route(&tour, &ddv)
}