//! Bi-directional Dijkstra distance labeling.
use std::hash::Hash;
use timely::order::Product;
use timely::dataflow::*;
use crate::{Collection, ExchangeData};
use crate::operators::*;
use crate::lattice::Lattice;
use crate::operators::iterate::Variable;
/// Returns the subset of `goals` that can reach each other in `edges`, with distance.
///
/// This method performs bidirectional search, from both ends of each goal in forward
/// and reverse direction, for the sources and targets respectively. Each search can
/// examine a fraction of the graph before meeting, and multiple searches can be managed
/// concurrently.
///
/// Goals that cannot reach from the source to the target are relatively expensive, as
/// the entire graph must be explored to confirm this. A graph connectivity pre-filter
/// could be good insurance here.
pub fn bidijkstra<G, N>(edges: &Collection<G, (N,N)>, goals: &Collection<G, (N,N)>) -> Collection<G, ((N,N), u32)>
where
G: Scope,
G::Timestamp: Lattice+Ord,
N: ExchangeData+Hash,
{
use crate::operators::arrange::arrangement::ArrangeByKey;
let forward = edges.arrange_by_key();
let reverse = edges.map(|(x,y)| (y,x)).arrange_by_key();
bidijkstra_arranged(&forward, &reverse, goals)
}
use crate::trace::TraceReader;
use crate::operators::arrange::Arranged;
/// Bi-directional Dijkstra search using arranged forward and reverse edge collections.
pub fn bidijkstra_arranged<G, N, Tr>(
forward: &Arranged<G, Tr>,
reverse: &Arranged<G, Tr>,
goals: &Collection<G, (N,N)>
) -> Collection<G, ((N,N), u32)>
where
G: Scope<Timestamp=Tr::Time>,
N: ExchangeData+Hash,
Tr: for<'a> TraceReader<Key<'a>=&'a N, Val<'a>=&'a N, Diff=isize>+Clone+'static,
{
forward
.stream
.scope().iterative::<u64,_,_>(|inner| {
let forward_edges = forward.enter(inner);
let reverse_edges = reverse.enter(inner);
// Our plan is to start evolving distances from both sources and destinations.
// The evolution from a source or destination should continue as long as there
// is a corresponding destination or source that has not yet been reached.
// forward and reverse (node, (root, dist))
let forward = Variable::new_from(goals.map(|(x,_)| (x.clone(),(x.clone(),0))).enter(inner), Product::new(Default::default(), 1));
let reverse = Variable::new_from(goals.map(|(_,y)| (y.clone(),(y.clone(),0))).enter(inner), Product::new(Default::default(), 1));
forward.map(|_| ()).consolidate().inspect(|x| println!("forward: {:?}", x));
reverse.map(|_| ()).consolidate().inspect(|x| println!("reverse: {:?}", x));
let goals = goals.enter(inner);
// let edges = edges.enter(inner);
// Let's determine which (src, dst) pairs are ready to return.
//
// done(src, dst) := forward(src, med), reverse(dst, med), goal(src, dst).
//
// This is a cyclic join, which should scare us a bunch.
let reached =
forward
.join_map(&reverse, |_, (src,d1), (dst,d2)| ((src.clone(), dst.clone()), *d1 + *d2))
.reduce(|_key, s, t| t.push((*s[0].0, 1)))
.semijoin(&goals);
let active =
reached
.negate()
.map(|(srcdst,_)| srcdst)
.concat(&goals)
.consolidate();
// Let's expand out forward queries that are active.
let forward_active = active.map(|(x,_y)| x).distinct();
let forward_next =
forward
.map(|(med, (src, dist))| (src, (med, dist)))
.semijoin(&forward_active)
.map(|(src, (med, dist))| (med, (src, dist)))
.join_core(&forward_edges, |_med, (src, dist), next| Some((next.clone(), (src.clone(), *dist+1))))
.concat(&forward)
.map(|(next, (src, dist))| ((next, src), dist))
.reduce(|_key, s, t| t.push((*s[0].0, 1)))
.map(|((next, src), dist)| (next, (src, dist)));
forward_next.map(|_| ()).consolidate().inspect(|x| println!("forward_next: {:?}", x));
forward.set(&forward_next);
// Let's expand out reverse queries that are active.
let reverse_active = active.map(|(_x,y)| y).distinct();
let reverse_next =
reverse
.map(|(med, (rev, dist))| (rev, (med, dist)))
.semijoin(&reverse_active)
.map(|(rev, (med, dist))| (med, (rev, dist)))
.join_core(&reverse_edges, |_med, (rev, dist), next| Some((next.clone(), (rev.clone(), *dist+1))))
.concat(&reverse)
.map(|(next, (rev, dist))| ((next, rev), dist))
.reduce(|_key, s, t| t.push((*s[0].0, 1)))
.map(|((next,rev), dist)| (next, (rev, dist)));
reverse_next.map(|_| ()).consolidate().inspect(|x| println!("reverse_next: {:?}", x));
reverse.set(&reverse_next);
reached.leave()
})
}