Rust HashMap find and remove minimum value

I have a HashMap<(usize,usize),Point3d> and I want to remove the minimum element according to some metric.

        let closest_edge = {
            let edges = exterior.keys();
            edges.reduce(|k1:&(usize,usize),k2:&(usize,usize)|-> &(usize,usize) {
                // return minimal value
            }).unwrap()
        };

        exterior.remove(closest_edge);

However, I cannot remove the minimal edge because of a borrow as immutable in getting the keys from exterior. Specifically this is my error:

cannot borrow `exterior` as mutable because it is also borrowed as immutable

Is there an idiomatic way to write a queue that reshuffles?

Queue doesn't work because I want the minimal element, not the oldest element.

retain also doesn't work because I would need to know what the minimal distance is before hand, and I want to only remove one element.

PriorityQueue is also not quite right, since the priority may change from round to round. (Each round I want to find an edge that is closest to the point I'm looking at, so the distance function changes each time)

Since your key is Copy, you can copy it by dereferencing so it isn't borrowing from the map.

let closest_edge = {
    let edges = exterior.keys();
    // Dereference *
    *edges.reduce(|k1:&(usize,usize),k2:&(usize,usize)|-> &(usize,usize) {
        // return minimal value
    }).unwrap()
};

// Make temporary reference &
exterior.remove(&closest_edge);