path: root/src/swarm/topology.rs

//! Which members a node syncs with: its neighbours.
//!
//! In a full mesh every change reaches every node from every other node (Automerge
//! decides per pair, so nobody knows that a third peer already passed it on), so the
//! copies of one write grow with N². Above `k` members, each node keeps only a few
//! neighbours, and changes travel over several hops.
//!
//! Every node computes the graph from the member list and which members it can reach,
//! with no coordination:
//! * a ring ordered by key hash: each member's nearest reachable member in both
//!   directions, which keeps the reachable members connected;
//! * plus, for each member, the `k - 2` reachable others with the lowest pair score (a
//!   hash of both keys, so both ends agree on it), which keeps paths short.
//!
//! A link exists if either end chose it, so links are symmetric and a node has at least
//! `k` neighbours. With at most `k + 1` reachable members the graph is the full mesh:
//! small swarms behave exactly as before. A member joining, leaving or going offline
//! changes only links near it.
//!
//! Members on several transports (Mycelium, libp2p) get such a graph per transport,
//! among the members on it (as their addresses in the member list say), and a node's
//! neighbours are the union of its neighbours on each transport it is on
//! (`neighbours_across`). Each of those graphs is connected (its ring), and a member on
//! two transports is in both: as long as members on several transports link the
//! transports, the swarm stays connected, and such a member has about `k` neighbours per
//! transport. With one transport, it is the one graph as before.

use std::collections::{BTreeMap, BTreeSet};

use sha2::{Digest, Sha256};
use tracing::info;

use crate::locks::RwLockExt;
use crate::state::AppState;
use crate::swarm::members;

/// This node's current neighbours, and the member list they were computed from.
#[derive(Debug, Default)]
pub(crate) struct NeighbourView {
    members: Vec<String>,
    k: usize,
    unreachable: BTreeSet<String>,
    stable: BTreeSet<String>,
    /// The transports (address schemes) of each member, and ours.
    transports: BTreeMap<String, BTreeSet<String>>,
    local_transports: BTreeSet<String>,
    neighbours: BTreeSet<String>,
    /// Every reachable member is a neighbour.
    full_mesh: bool,
}

/// Whether the neighbours are computed from the member list yet (before, everyone
/// counts as a neighbour).
pub(crate) fn view_known(state: &AppState) -> bool {
    state.neighbours.read_or_recover().is_some()
}

/// Whether every reachable member is our neighbour (also while the view is unknown).
pub(crate) fn is_full_mesh(state: &AppState) -> bool {
    state
        .neighbours
        .read_or_recover()
        .as_ref()
        .is_none_or(|view| view.full_mesh)
}

/// The current view in numbers, once known.
#[derive(Debug, Clone, Copy)]
pub(crate) struct Summary {
    /// Registered members, us included.
    pub(crate) members: usize,
    /// Members other than us not currently judged unreachable.
    pub(crate) reachable: usize,
    pub(crate) stable: usize,
    pub(crate) neighbours: usize,
    pub(crate) stable_neighbours: usize,
    pub(crate) full_mesh: bool,
}

pub(crate) fn summary(state: &AppState) -> Option<Summary> {
    let local = state.local_id();
    state
        .neighbours
        .read_or_recover()
        .as_ref()
        .map(|view| Summary {
            members: view.members.len(),
            reachable: view
                .members
                .iter()
                .filter(|m| m.as_str() != local && !view.unreachable.contains(*m))
                .count(),
            stable: view.stable.len(),
            neighbours: view.neighbours.len(),
            stable_neighbours: view
                .neighbours
                .iter()
                .filter(|m| view.stable.contains(*m))
                .count(),
            full_mesh: view.full_mesh,
        })
}

/// Whether we initiate contact with `peer`: HELLOs, keepalives, dormancy checks, sync
/// openings. Everyone is a neighbour until the view is known (while joining, or before
/// any member registered), so joining works as in a full mesh. We always *answer*
/// anyone who contacts us.
pub(crate) fn is_neighbour(state: &AppState, peer: &str) -> bool {
    match &*state.neighbours.read_or_recover() {
        Some(view) => view.neighbours.contains(peer),
        None => true,
    }
}

/// How the neighbours changed.
pub(crate) struct NeighbourChange {
    pub(crate) added: Vec<String>,
    pub(crate) removed: Vec<String>,
}

/// Recomputes the neighbours whenever something they depend on may have changed
/// (`AppState::topology_changed`): the member list (`swarm::sync::run_change_publisher`),
/// a peer becoming unreachable or reachable again (`swarm::peer`), and every 5 s as a
/// fallback. A burst of notifications coalesces into one recomputation.
pub(crate) async fn run_worker(state: AppState) {
    loop {
        state.topology_changed.notified().await;
        if let Some(change) = refresh(&state).await {
            crate::swarm::peer::apply_neighbour_change(&state, change).await;
        }
    }
}

/// Whether a change at `path` may change the neighbours: one in the member list, or the
/// root (the whole document replaced, as after an epoch switch).
pub(crate) fn affects_neighbours(path: &[String]) -> bool {
    path.is_empty() || path.starts_with(&members::members_dir())
}

/// Recomputes the neighbours once ready, if the member list, the reachable members or
/// `k` changed.
pub(crate) async fn refresh(state: &AppState) -> Option<NeighbourChange> {
    if !state.is_ready().await {
        return None;
    }
    let (current, stable, transports) = {
        let replica = state.doc.read().await;
        members::learn_addresses(state, &replica.doc);
        let current = members::members(&replica.doc);
        let stable: BTreeSet<String> = current
            .iter()
            .filter(|m| members::tier(&replica.doc, m) == members::Tier::Stable)
            .cloned()
            .collect();
        let transports: BTreeMap<String, BTreeSet<String>> = current
            .iter()
            .map(|m| (m.clone(), schemes(&members::addresses(&replica.doc, m))))
            .collect();
        (current, stable, transports)
    };
    let local_transports: BTreeSet<String> = state.transport.transports().into_iter().collect();
    let k = state.neighbours_k;
    // Those that don't answer, and those on none of our transports.
    let mut unreachable = BTreeSet::new();
    for member in &current {
        if member == state.local_id() {
            continue;
        }
        if !state.transport.can_reach(member) {
            unreachable.insert(member.clone());
        } else if let Some(peer_state) = state.get_peer_state(member).await
            && peer_state.lock().await.is_unreachable()
        {
            unreachable.insert(member.clone());
        }
    }
    let previous = {
        let view = state.neighbours.read_or_recover();
        if view.as_ref().is_some_and(|view| {
            view.members == current
                && view.k == k
                && view.unreachable == unreachable
                && view.stable == stable
                && view.transports == transports
                && view.local_transports == local_transports
        }) {
            return None;
        }
        view.as_ref().map(|view| view.neighbours.clone())
    };

    // Before the first view everyone known counted as a neighbour.
    let previous = match previous {
        Some(previous) => previous,
        None => state.peer_states.read().await.keys().cloned().collect(),
    };
    let computed = neighbours_across(
        &transports,
        state.local_id(),
        &local_transports,
        k,
        &|m| unreachable.contains(m),
        &|m| stable.contains(m),
    );
    let change = NeighbourChange {
        added: computed
            .iter()
            .filter(|m| !previous.contains(*m))
            .cloned()
            .collect(),
        removed: previous
            .iter()
            .filter(|m| !computed.contains(*m))
            .cloned()
            .collect(),
    };
    info!(
        members = current.len(),
        unreachable = unreachable.len(),
        stable = stable.len(),
        k,
        neighbours = computed.len(),
        added = change.added.len(),
        removed = change.removed.len(),
        "Neighbours computed from the member list"
    );
    let reachable_others = current
        .iter()
        .filter(|m| m.as_str() != state.local_id() && !unreachable.contains(*m))
        .count();
    *state.neighbours.write_or_recover() = Some(NeighbourView {
        full_mesh: computed.len() >= reachable_others,
        members: current,
        k,
        unreachable,
        stable,
        transports,
        local_transports,
        neighbours: computed,
    });
    Some(change)
}

const RING_LABEL: &[u8] = b"continuum/topology-ring/1";
const PAIR_LABEL: &[u8] = b"continuum/topology-pair/2";

/// How many members may prefer the same stable member, as a multiple of `k`. Without a
/// bound, 20 stable members among 2000 get about 500 neighbours each: every
/// announcement in the swarm lands on them, and the backbone saturates first. Members
/// that find a stable member full prefer the next one, then go by pair score, so the
/// graph stays connected and symmetric.
const STABLE_FANIN_FACTOR: usize = 4;

/// The transports `addresses` are on: their schemes (`mycelium` of `mycelium:<key>`);
/// the empty one for an address without (a transport whose identities are addresses).
pub(crate) fn schemes(addresses: &[String]) -> BTreeSet<String> {
    addresses
        .iter()
        .map(|address| {
            address
                .split_once(':')
                .map_or("", |(scheme, _)| scheme)
                .to_owned()
        })
        .collect()
}

/// The neighbours of `local` among `members` (by the transports each is on), on each of
/// `local_transports`: on each, its neighbours among the members on it
/// (`neighbours`), all together.
pub(crate) fn neighbours_across(
    members: &BTreeMap<String, BTreeSet<String>>,
    local: &str,
    local_transports: &BTreeSet<String>,
    k: usize,
    unreachable: &dyn Fn(&str) -> bool,
    stable: &dyn Fn(&str) -> bool,
) -> BTreeSet<String> {
    let mut all = BTreeSet::new();
    for transport in local_transports {
        let on_it: Vec<String> = members
            .iter()
            .filter(|(member, transports)| *member != local && transports.contains(transport))
            .map(|(member, _)| member.clone())
            .collect();
        all.extend(neighbours(&on_it, local, k, unreachable, stable));
    }
    all
}

/// The neighbours of `local` among `members` (which may or may not contain `local`),
/// skipping members for which `unreachable` holds.
pub(crate) fn neighbours(
    members: &[String],
    local: &str,
    k: usize,
    unreachable: &dyn Fn(&str) -> bool,
    stable: &dyn Fn(&str) -> bool,
) -> BTreeSet<String> {
    let mut all: Vec<String> = members.to_vec();
    all.push(local.to_owned());
    graph(&all, k, &|m: &str| m != local && unreachable(m), stable)
        .remove(local)
        .unwrap_or_default()
}

/// Every reachable member's neighbours. Hashes each member once and scores pairs by
/// mixing the two hashes (`pair_score`), so the N² scores are a few nanoseconds each:
/// tens of milliseconds for thousands of members. `stable` members (`swarm::stability`)
/// are preferred for half of each member's scored slots, each by at most
/// `STABLE_FANIN_FACTOR * k` members.
///
/// Each reachable member walks the ring (by key hash) both ways to the first reachable
/// member, which gives a ring over the reachable members, and adds the `k - 2`
/// reachable members with the lowest pair score. A link exists if either end chose it.
/// With at most `k + 1` reachable members, the reachable members form a full mesh.
///
/// Each node judges reachability by itself, so nodes may briefly disagree; that only
/// adds links (whoever chose a link initiates, the other answers), it never cuts one.
/// The preference budget is spent in key order, which every node shares, so nodes that
/// agree on reachability compute the same links.
pub(crate) fn graph(
    members: &[String],
    k: usize,
    unreachable: &dyn Fn(&str) -> bool,
    stable: &dyn Fn(&str) -> bool,
) -> BTreeMap<String, BTreeSet<String>> {
    let k = k.max(2);
    let all: BTreeSet<&str> = members.iter().map(String::as_str).collect();
    let live: BTreeSet<&str> = all.iter().copied().filter(|m| !unreachable(m)).collect();
    let mut links: BTreeMap<String, BTreeSet<String>> = live
        .iter()
        .map(|m| ((*m).to_owned(), BTreeSet::new()))
        .collect();

    let mut link = |a: &str, b: &str| {
        if a != b {
            links.get_mut(a).expect("live member").insert(b.to_owned());
            links.get_mut(b).expect("live member").insert(a.to_owned());
        }
    };

    if live.len() <= k + 1 {
        for a in &live {
            for b in &live {
                link(a, b);
            }
        }
        return links;
    }

    // The ring over all members, so its order doesn't change when one goes offline.
    let mut ring: Vec<([u8; 32], &str)> =
        all.iter().map(|m| (hash(RING_LABEL, &[*m]), *m)).collect();
    ring.sort_unstable();
    let n = ring.len();
    let position: BTreeMap<&str, usize> =
        ring.iter().enumerate().map(|(i, (_, m))| (*m, i)).collect();
    let first_live = |from: usize, step: usize| {
        (1..n)
            .map(|d| ring[(from + d * step) % n].1)
            .find(|m| live.contains(m))
            .expect("more than k + 1 live members")
    };

    // Live members in key order, with their pair keys; and those of them that are stable.
    let keyed: Vec<(&str, u64)> = live.iter().map(|m| (*m, pair_key(m))).collect();
    let stable_keyed: Vec<(&str, u64)> = keyed.iter().copied().filter(|(m, _)| stable(m)).collect();

    // How many members have preferred each stable member so far (`keyed` is in key
    // order, the same on every node).
    let budget = STABLE_FANIN_FACTOR * k;
    let mut preferred_by: BTreeMap<&str, usize> = BTreeMap::new();
    // Half the slots (rounded up) prefer stable members, so long-running nodes form a
    // backbone; the rest go by pair score alone, keeping paths short. A stable member
    // enough others prefer already is skipped, so no hub grows with the swarm.
    let stable_slots = (k - 2).div_ceil(2);

    for &(member, key) in &keyed {
        let at = position[member];
        let next = first_live(at, 1);
        let prev = first_live(at, n - 1);
        link(member, next);
        link(member, prev);
        let skip = [member, next, prev];
        // The stable candidates in score order (there are few).
        let mut stable_candidates = scored(&stable_keyed, key, skip);
        stable_candidates.sort_unstable();
        let preferred: Vec<&str> = stable_candidates
            .iter()
            .map(|(_, other)| *other)
            .filter(|other| preferred_by.get(other).copied().unwrap_or(0) < budget)
            .take(stable_slots)
            .collect();
        for other in preferred.iter().copied() {
            *preferred_by.entry(other).or_default() += 1;
        }
        // The rest: the lowest scores among the others that aren't preferred, which are
        // among the `need + preferred` lowest overall. Selecting those is linear; only
        // they are sorted.
        let need = k - 2 - preferred.len();
        let mut candidates = scored(&keyed, key, skip);
        let lowest = (need + preferred.len()).min(candidates.len());
        if lowest < candidates.len() {
            candidates.select_nth_unstable(lowest);
            candidates.truncate(lowest);
        }
        candidates.sort_unstable();
        let rest = candidates
            .iter()
            .map(|(_, other)| *other)
            .filter(|other| !preferred.contains(other))
            .take(need);
        for partner in preferred.iter().copied().chain(rest) {
            link(member, partner);
        }
    }
    links
}

/// `others` but those in `skip`, scored as pairs with the member whose key is `key`.
fn scored<'a>(others: &[(&'a str, u64)], key: u64, skip: [&str; 3]) -> Vec<(u64, &'a str)> {
    others
        .iter()
        .filter(|(other, _)| !skip.contains(other))
        .map(|&(other, other_key)| (mix_pair(key, other_key), other))
        .collect()
}

/// Symmetric: the same for (a, b) and (b, a).
pub(crate) fn pair_score(a: &str, b: &str) -> u64 {
    mix_pair(pair_key(a), pair_key(b))
}

/// What a member contributes to its pair scores: computed once per member.
fn pair_key(member: &str) -> u64 {
    let digest = hash(PAIR_LABEL, &[member]);
    u64::from_be_bytes(digest[..8].try_into().expect("8 bytes"))
}

/// The score of a pair from its members' keys, symmetric: SplitMix64's finalizer over
/// the lower key and the mixed higher one. Keys are uniform (SHA-256), so for each member
/// the others' scores are in an order unrelated to anyone else's.
fn mix_pair(a: u64, b: u64) -> u64 {
    let (low, high) = if a <= b { (a, b) } else { (b, a) };
    mix(low ^ mix(high))
}

fn mix(mut z: u64) -> u64 {
    z = z.wrapping_add(0x9e37_79b9_7f4a_7c15);
    z = (z ^ (z >> 30)).wrapping_mul(0xbf58_476d_1ce4_e5b9);
    z = (z ^ (z >> 27)).wrapping_mul(0x94d0_49bb_1331_11eb);
    z ^ (z >> 31)
}

fn hash(label: &[u8], fields: &[&str]) -> [u8; 32] {
    let mut hasher = Sha256::new();
    for field in [label]
        .into_iter()
        .chain(fields.iter().map(|f| f.as_bytes()))
    {
        hasher.update((field.len() as u32).to_be_bytes());
        hasher.update(field);
    }
    hasher.finalize().into()
}

#[cfg(test)]
mod tests {
    use super::*;
    use std::collections::VecDeque;

    fn members(n: usize) -> Vec<String> {
        (0..n).map(|i| format!("{:064x}", i * 7919 + 13)).collect()
    }

    fn all_reachable(_: &str) -> bool {
        false
    }

    fn none_stable(_: &str) -> bool {
        false
    }

    fn graph(members: &[String], k: usize) -> BTreeMap<String, BTreeSet<String>> {
        super::graph(members, k, &all_reachable, &none_stable)
    }

    fn connected(g: &BTreeMap<String, BTreeSet<String>>) -> bool {
        let Some(start) = g.keys().next() else {
            return true;
        };
        let mut seen = BTreeSet::from([start.clone()]);
        let mut queue = VecDeque::from([start.clone()]);
        while let Some(m) = queue.pop_front() {
            for next in &g[&m] {
                if seen.insert(next.clone()) {
                    queue.push_back(next.clone());
                }
            }
        }
        seen.len() == g.len()
    }

    fn edges(graph: &BTreeMap<String, BTreeSet<String>>) -> BTreeSet<(String, String)> {
        graph
            .iter()
            .flat_map(|(a, ns)| {
                ns.iter().map(move |b| {
                    if a < b {
                        (a.clone(), b.clone())
                    } else {
                        (b.clone(), a.clone())
                    }
                })
            })
            .collect()
    }

    fn hex(bytes: [u8; 32]) -> String {
        bytes.iter().map(|byte| format!("{byte:02x}")).collect()
    }

    /// Over random swarms (size, `k`, who is reachable, who is stable): links only
    /// between reachable members, never to oneself, symmetric; a full mesh while small,
    /// otherwise at least `k` links each and connected; independent of the order members
    /// are listed in; and each member's own view (`neighbours`) agrees with the graph.
    #[test]
    fn random_swarms() {
        crate::testrand::for_seeds(300, |rng| {
            let n = rng.between(1, 60);
            let k = rng.between(2, 14);
            let mut all: Vec<String> = (0..n).map(|_| hex(rng.bytes32())).collect();
            let unreachable: BTreeSet<String> =
                all.iter().filter(|_| rng.chance(0.3)).cloned().collect();
            let stable: BTreeSet<String> =
                all.iter().filter(|_| rng.chance(0.3)).cloned().collect();
            let is_unreachable = |m: &str| unreachable.contains(m);
            let is_stable = |m: &str| stable.contains(m);

            let g = super::graph(&all, k, &is_unreachable, &is_stable);
            // Owned: `all` is shuffled below.
            let live: BTreeSet<String> = all
                .iter()
                .filter(|m| !unreachable.contains(*m))
                .cloned()
                .collect();
            assert_eq!(g.keys().cloned().collect::<BTreeSet<_>>(), live);
            for (a, ns) in &g {
                assert!(!ns.contains(a), "{a} links to itself");
                for b in ns {
                    assert!(live.contains(b), "{a} links to unreachable {b}");
                    assert!(g[b].contains(a), "{a} -> {b} but not back");
                }
            }
            if live.len() <= k + 1 {
                assert!(
                    g.values().all(|ns| ns.len() + 1 == live.len()),
                    "not a full mesh"
                );
            } else {
                assert!(
                    g.values().all(|ns| ns.len() >= k),
                    "a member with fewer than k links"
                );
                assert!(connected(&g), "not connected");
            }

            rng.shuffle(&mut all);
            assert_eq!(super::graph(&all, k, &is_unreachable, &is_stable), g);

            if let Some(local) = live.iter().nth(rng.below(live.len())) {
                let others: Vec<String> = all.iter().filter(|m| *m != local).cloned().collect();
                assert_eq!(
                    neighbours(&others, local, k, &is_unreachable, &is_stable),
                    g[local]
                );
            }
        });
    }

    #[test]
    fn small_swarms_are_a_full_mesh() {
        let ms = members(13);
        for m in &ms {
            assert_eq!(
                neighbours(&ms, m, 12, &all_reachable, &none_stable).len(),
                12
            );
        }
    }

    #[test]
    fn links_are_symmetric_and_degree_at_least_k() {
        let ms = members(250);
        let g = graph(&ms, 8);
        for (a, ns) in &g {
            assert!(ns.len() >= 8, "{a} has {} neighbours", ns.len());
            assert!(!ns.contains(a));
            for b in ns {
                assert!(g[b].contains(a), "{a} -> {b} not symmetric");
            }
        }
    }

    #[test]
    fn graph_is_connected() {
        for (n, k) in [(250, 8), (250, 2), (60, 3)] {
            assert!(connected(&graph(&members(n), k)), "n={n} k={k}");
        }
    }

    #[test]
    fn one_member_joining_changes_few_links() {
        let ms = members(200);
        let before = edges(&graph(&ms, 8));
        let mut more = ms.clone();
        more.push(format!("{:064x}", 999_999));
        let after = edges(&graph(&more, 8));
        let changed = before.symmetric_difference(&after).count();
        assert!(changed <= 4 * 8, "{changed} links changed");
    }

    #[test]
    fn reachable_members_stay_connected_when_most_are_offline() {
        let ms = members(100);
        // Every tenth member is online.
        let online: BTreeSet<String> = ms.iter().step_by(10).cloned().collect();
        let offline = |m: &str| !online.contains(m);
        let g = super::graph(&ms, 12, &offline, &none_stable);
        assert_eq!(g.len(), 10);
        // Ten reachable members and k = 12: a full mesh among them.
        assert!(g.values().all(|ns| ns.len() == 9));

        let online: BTreeSet<String> = ms.iter().step_by(4).cloned().collect();
        let offline = |m: &str| !online.contains(m);
        let g = super::graph(&ms, 8, &offline, &none_stable);
        assert_eq!(g.len(), 25);
        assert!(connected(&g));
        assert!(
            g.values()
                .all(|ns| ns.len() >= 8 && ns.iter().all(|n| online.contains(n)))
        );
    }

    #[test]
    fn stable_members_become_hubs_with_bounded_degree() {
        let ms = members(250);
        let stable: BTreeSet<String> = ms.iter().step_by(12).take(20).cloned().collect();
        let is_stable = |m: &str| stable.contains(m);
        let g = super::graph(&ms, 12, &all_reachable, &is_stable);
        assert!(connected(&g));

        let degree = |pred: &dyn Fn(&String) -> bool| -> (usize, f64) {
            let degrees: Vec<usize> = g
                .iter()
                .filter(|(m, _)| pred(m))
                .map(|(_, ns)| ns.len())
                .collect();
            let max = *degrees.iter().max().unwrap();
            (
                max,
                degrees.iter().sum::<usize>() as f64 / degrees.len() as f64,
            )
        };
        let (stable_max, stable_mean) = degree(&|m| stable.contains(m));
        let (_, transient_mean) = degree(&|m| !stable.contains(m));
        // 230 transient members put about 5 of their 10 scored slots on 20 stable ones.
        assert!(
            stable_mean > 3.0 * transient_mean,
            "{stable_mean} vs {transient_mean}"
        );
        assert!(
            stable_max <= 100,
            "a stable member has {stable_max} neighbours"
        );
    }

    /// A hub's degree in a swarm of `n` with `stable_count` stable members stays within
    /// the bound.
    fn hub_degree_is_bounded(n: usize, stable_count: usize) {
        // Few stable members among many: without the fan-in budget each would be chosen
        // by most of the swarm (about 130 neighbours with 10 of 250). With it, a hub has
        // at most the budget plus the links others choose by pair score and the ring.
        let k = 12;
        let ms = members(n);
        let stable: BTreeSet<String> = ms.iter().step_by(n / stable_count).cloned().collect();
        let is_stable = |m: &str| stable.contains(m);
        let g = super::graph(&ms, k, &all_reachable, &is_stable);
        assert!(connected(&g), "n={n} stable={stable_count}");
        let hub_max = g
            .iter()
            .filter(|(m, _)| stable.contains(*m))
            .map(|(_, ns)| ns.len())
            .max()
            .unwrap();
        assert!(
            hub_max <= 8 * k,
            "n={n} stable={stable_count}: a stable member has {hub_max} neighbours"
        );
    }

    /// Two transports with members on one or the other, and two members on both: every
    /// link is over a shared transport, and the two members on both connect the rest.
    #[test]
    fn members_on_two_transports_bridge_the_others() {
        let k = 8;
        let ms = members(201);
        let on = |names: &[&str]| -> BTreeSet<String> {
            names.iter().map(|name| (*name).to_owned()).collect()
        };
        let transports: BTreeMap<String, BTreeSet<String>> = ms
            .iter()
            .enumerate()
            .map(|(i, m)| {
                let transports = match i {
                    0 | 1 => on(&["a", "b"]),
                    i if i % 2 == 0 => on(&["a"]),
                    _ => on(&["b"]),
                };
                (m.clone(), transports)
            })
            .collect();
        let no_stable = |_: &str| false;
        let mut graph: BTreeMap<String, BTreeSet<String>> = BTreeMap::new();
        for (m, own) in &transports {
            for n in neighbours_across(&transports, m, own, k, &all_reachable, &no_stable) {
                assert!(
                    !transports[&n].is_disjoint(own),
                    "{m} and {n} share no transport"
                );
                graph.entry(m.clone()).or_default().insert(n.clone());
                graph.entry(n).or_default().insert(m.clone());
            }
        }
        assert_eq!(graph.len(), ms.len());
        assert!(connected(&graph));
        let bridge = &ms[0];
        assert!(graph[bridge].iter().any(|n| !transports[n].contains("b")));
        assert!(graph[bridge].iter().any(|n| !transports[n].contains("a")));

        // One transport: the one graph, as without transports.
        let one: BTreeMap<String, BTreeSet<String>> =
            ms.iter().map(|m| (m.clone(), on(&[""]))).collect();
        for m in &ms[..5] {
            assert_eq!(
                neighbours_across(&one, m, &on(&[""]), k, &all_reachable, &no_stable),
                neighbours(&ms, m, k, &all_reachable, &no_stable)
            );
        }
    }

    #[test]
    fn schemes_of_addresses() {
        let addresses =
            |all: &[&str]| -> Vec<String> { all.iter().map(|a| (*a).to_owned()).collect() };
        assert_eq!(
            schemes(&addresses(&[
                "mycelium:ab",
                "libp2p:/ip4/1.2.3.4/tcp/1",
                "libp2p:/ip6/::1/tcp/1"
            ])),
            BTreeSet::from(["libp2p".to_owned(), "mycelium".to_owned()])
        );
        assert_eq!(schemes(&addresses(&["a"])), BTreeSet::from([String::new()]));
        assert!(schemes(&[]).is_empty());
    }

    #[test]
    fn hub_degree_is_bounded_however_few_stable_members() {
        for (n, stable_count) in [(250, 10), (400, 5)] {
            hub_degree_is_bounded(n, stable_count);
        }
    }

    /// The same at the sizes the bound was designed for; slow in debug builds, so run
    /// on request (`cargo test --release -- --ignored`).
    #[test]
    #[ignore]
    fn hub_degree_is_bounded_in_large_swarms() {
        for (n, stable_count) in [(1000, 10), (1000, 20), (2000, 20)] {
            hub_degree_is_bounded(n, stable_count);
        }
    }
}