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graph/path: Improve performance of YenKShortestPaths #2004

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graph/path: Improve performance of YenKShortestPaths #2004

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7649851
graph/path: add single-pair shortest path variant
BarrensZeppelin Nov 27, 2024
f112007
graph/path: re-use test setup for `DijkstraFromTo` tests
BarrensZeppelin Dec 2, 2024
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graph/path: add single-pair shortest path variant 
This variant can terminate early when the target is reached. This can
make a large difference in running time for Yen's k-shortest paths
algorithm, as it makes many calls to the shortest path subroutine.
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@BarrensZeppelin
BarrensZeppelin committed Nov 27, 2024
commit 764985128fd61e997e2acfd4e4fde72835da1d24
27 changes: 26 additions & 1 deletion graph/path/dijkstra.go
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Original file line number Diff line number Diff line change
Expand Up @@ -20,8 +20,30 @@ import (
//
// The time complexity of DijkstraFrom is O(|E|.log|V|).
func DijkstraFrom(u graph.Node, g traverse.Graph) Shortest {
return dijkstraFrom(u, nil, g)
}

// DijkstraFromTo returns a shortest path from u to v in the graph g. The
// result is equivalent to DijkstraFrom(u, g).To(v), but DijkstraFromTo can be
// more efficient, as it can terminate early if v is reached. If the graph does
// not implement Weighted, UniformCost is used. DijkstraFromTo will panic if g
// has a u-reachable negative edge weight that is discovered before reaching v.
//
// The time complexity of DijkstraFromTo is O(|E|.log|V|).
func DijkstraFromTo(u graph.Node, v graph.Node, g traverse.Graph) (path []graph.Node, weight float64) {
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Suggested change
func DijkstraFromTo(u graph.Node, v graph.Node, g traverse.Graph) (path []graph.Node, weight float64) {
func DijkstraFromTo(u, t graph.Node, g traverse.Graph) (path []graph.Node, weight float64) {

The second param is not a v.

// An implementation of Bidirectional Dijkstra's algorithm could be even
// more efficient, but it requires a transposed (or undirected) graph.
if v == nil {
panic("dijkstra: nil target node")
}
return dijkstraFrom(u, v, g).To(v.ID())
}

// Shared implementation of DijkstraFrom and DijkstraFromTo.
func dijkstraFrom(u, target graph.Node, g traverse.Graph) Shortest {
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Suggested change
// Shared implementation of DijkstraFrom and DijkstraFromTo.
func dijkstraFrom(u, target graph.Node, g traverse.Graph) Shortest {
func dijkstraFrom(u, t graph.Node, g traverse.Graph) Shortest {

var path Shortest
if h, ok := g.(graph.Graph); ok {
// Use the incremental version when a target is provided
if h, ok := g.(graph.Graph); target == nil && ok {
if h.Node(u.ID()) == nil {
return Shortest{from: u}
}
Expand Down Expand Up @@ -58,6 +80,9 @@ func DijkstraFrom(u graph.Node, g traverse.Graph) Shortest {
continue
}
mnid := mid.node.ID()
if target != nil && mnid == target.ID() {
break
}
to := g.From(mnid)
for to.Next() {
v := to.Node()
Expand Down
66 changes: 46 additions & 20 deletions graph/path/dijkstra_test.go
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Expand Up @@ -24,6 +24,29 @@ func TestDijkstraFrom(t *testing.T) {
g.SetWeightedEdge(e)
}

checkPath := func(typ string, p []graph.Node, weight float64) {
if weight != test.Weight {
t.Errorf("%q %s: unexpected weight from To: got:%f want:%f",
test.Name, typ, weight, test.Weight)
}

var got []int64
for _, n := range p {
got = append(got, n.ID())
}
ok := len(got) == 0 && len(test.WantPaths) == 0
for _, sp := range test.WantPaths {
if reflect.DeepEqual(got, sp) {
ok = true
break
}
}
if !ok {
t.Errorf("%q %s: unexpected shortest path:\ngot: %v\nwant from:%v",
test.Name, typ, p, test.WantPaths)
}
}

for _, tg := range []struct {
typ string
g traverse.Graph
Expand Down Expand Up @@ -56,38 +79,41 @@ func TestDijkstraFrom(t *testing.T) {
t.Fatalf("%q %s: unexpected from node ID: got:%d want:%d", test.Name, tg.typ, pt.From().ID(), test.Query.From().ID())
}

p, weight := pt.To(test.Query.To().ID())
if weight != test.Weight {
t.Errorf("%q %s: unexpected weight from To: got:%f want:%f",
test.Name, tg.typ, weight, test.Weight)
}
if weight := pt.WeightTo(test.Query.To().ID()); weight != test.Weight {
t.Errorf("%q %s: unexpected weight from Weight: got:%f want:%f",
test.Name, tg.typ, weight, test.Weight)
}

var got []int64
for _, n := range p {
got = append(got, n.ID())
}
ok := len(got) == 0 && len(test.WantPaths) == 0
for _, sp := range test.WantPaths {
if reflect.DeepEqual(got, sp) {
ok = true
break
}
}
if !ok {
t.Errorf("%q %s: unexpected shortest path:\ngot: %v\nwant from:%v",
test.Name, tg.typ, p, test.WantPaths)
}
p, weight := pt.To(test.Query.To().ID())
checkPath(tg.typ, p, weight)

np, weight := pt.To(test.NoPathFor.To().ID())
if pt.From().ID() == test.NoPathFor.From().ID() && (np != nil || !math.IsInf(weight, 1)) {
t.Errorf("%q %s: unexpected path:\ngot: path=%v weight=%f\nwant:path=<nil> weight=+Inf",
test.Name, tg.typ, np, weight)
}
}

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I think this should be in the loop, with helper sharing.

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Done.

// Test the single-destination variant.
var (
p []graph.Node
weight float64
panicked bool
)
func() {
defer func() {
panicked = recover() != nil
}()
p, weight = DijkstraFromTo(test.Query.From(), test.Query.To(), g.(graph.Graph))
}()
if panicked || test.HasNegativeWeight {
if !test.HasNegativeWeight {
t.Errorf("%q: unexpected panic", test.Name)
}
continue
}

checkPath("from-to", p, weight)
}
}

Expand Down
4 changes: 2 additions & 2 deletions graph/path/yen_ksp.go
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Expand Up @@ -33,7 +33,7 @@ func YenKShortestPaths(g graph.Graph, k int, cost float64, s, t graph.Node) [][]
yk.weight = UniformCost(g)
}

shortest, weight := DijkstraFrom(s, yk).To(t.ID())
shortest, weight := DijkstraFromTo(s, t, yk)
cost += weight // Set cost to absolute cost limit.
switch len(shortest) {
case 0:
Expand Down Expand Up @@ -73,7 +73,7 @@ func YenKShortestPaths(g graph.Graph, k int, cost float64, s, t graph.Node) [][]
yk.removeNode(u.ID())
}

spath, weight := DijkstraFrom(spur, yk).To(t.ID())
spath, weight := DijkstraFromTo(spur, t, yk)
if weight > cost || math.IsInf(weight, 1) {
continue
}
Expand Down