From ed2075e3847552bf825dde988a0140a5efc0a2ab Mon Sep 17 00:00:00 2001
From: Mitchell Hashimoto <mitchell.hashimoto@gmail.com>
Date: Fri, 27 Feb 2015 19:12:19 -0800
Subject: [PATCH] dag: TransitiveReduction

---
 dag/dag.go      | 74 +++++++++++++++++++++++++++++++++++++++++++++++++
 dag/dag_test.go | 57 +++++++++++++++++++++++++++++++++++++
 dag/set.go      | 14 ++++++++++
 3 files changed, 145 insertions(+)

diff --git a/dag/dag.go b/dag/dag.go
index 9490cf98a..d319e84c5 100644
--- a/dag/dag.go
+++ b/dag/dag.go
@@ -40,6 +40,46 @@ func (g *AcyclicGraph) Root() (Vertex, error) {
 	return roots[0], nil
 }
 
+// TransitiveReduction performs the transitive reduction of graph g in place.
+// The transitive reduction of a graph is a graph with as few edges as
+// possible with the same reachability as the original graph. This means
+// that if there are three nodes A => B => C, and A connects to both
+// B and C, and B connects to C, then the transitive reduction is the
+// same graph with only a single edge between A and B, and a single edge
+// between B and C.
+//
+// The graph must be valid for this operation to behave properly. If
+// Validate() returns an error, the behavior is undefined and the results
+// will likely be unexpected.
+//
+// Complexity: O(V(V+E)), or asymptotically O(VE)
+func (g *AcyclicGraph) TransitiveReduction() {
+	// Find the root-like objects to start a depthFirstWalk from.
+	frontier := make([]Vertex, 0, 5)
+	for _, v := range g.Vertices() {
+		if g.UpEdges(v).Len() == 0 {
+			frontier = append(frontier, v)
+		}
+	}
+
+	// Do a DFS
+	g.depthFirstWalk(frontier, func(v Vertex) error {
+		parents := g.UpEdges(v).List()
+		targets := g.DownEdges(v)
+
+		for _, rawParent := range parents {
+			parent := rawParent.(Vertex)
+			shared := g.DownEdges(parent).Intersection(targets)
+			for _, rawTarget := range shared.List() {
+				target := rawTarget.(Vertex)
+				g.RemoveEdge(BasicEdge(parent, target))
+			}
+		}
+
+		return nil
+	})
+}
+
 // Validate validates the DAG. A DAG is valid if it has a single root
 // with no cycles.
 func (g *AcyclicGraph) Validate() error {
@@ -161,3 +201,37 @@ func (g *AcyclicGraph) Walk(cb WalkFunc) error {
 	<-doneCh
 	return errs
 }
+
+// depthFirstWalk does a depth-first walk of the graph starting from
+// the vertices in start. This is not exported now but it would make sense
+// to export this publicly at some point.
+func (g *AcyclicGraph) depthFirstWalk(start []Vertex, cb WalkFunc) error {
+	seen := make(map[Vertex]struct{})
+	frontier := make([]Vertex, len(start))
+	copy(frontier, start)
+	for len(frontier) > 0 {
+		// Pop the current vertex
+		n := len(frontier)
+		current := frontier[n-1]
+		frontier = frontier[:n-1]
+
+		// Check if we've seen this already and return...
+		if _, ok := seen[current]; ok {
+			continue
+		}
+		seen[current] = struct{}{}
+
+		// Visit the current node
+		if err := cb(current); err != nil {
+			return err
+		}
+
+		// Visit targets of this in reverse order.
+		targets := g.DownEdges(current).List()
+		for i := len(targets) - 1; i >= 0; i-- {
+			frontier = append(frontier, targets[i].(Vertex))
+		}
+	}
+
+	return nil
+}
diff --git a/dag/dag_test.go b/dag/dag_test.go
index cc9442be5..feead7968 100644
--- a/dag/dag_test.go
+++ b/dag/dag_test.go
@@ -3,6 +3,7 @@ package dag
 import (
 	"fmt"
 	"reflect"
+	"strings"
 	"sync"
 	"testing"
 )
@@ -48,6 +49,44 @@ func TestAcyclicGraphRoot_multiple(t *testing.T) {
 	}
 }
 
+func TestAyclicGraphTransReduction(t *testing.T) {
+	var g AcyclicGraph
+	g.Add(1)
+	g.Add(2)
+	g.Add(3)
+	g.Connect(BasicEdge(1, 2))
+	g.Connect(BasicEdge(1, 3))
+	g.Connect(BasicEdge(2, 3))
+	g.TransitiveReduction()
+
+	actual := strings.TrimSpace(g.String())
+	expected := strings.TrimSpace(testGraphTransReductionStr)
+	if actual != expected {
+		t.Fatalf("bad: %s", actual)
+	}
+}
+
+func TestAyclicGraphTransReduction_more(t *testing.T) {
+	var g AcyclicGraph
+	g.Add(1)
+	g.Add(2)
+	g.Add(3)
+	g.Add(4)
+	g.Connect(BasicEdge(1, 2))
+	g.Connect(BasicEdge(1, 3))
+	g.Connect(BasicEdge(1, 4))
+	g.Connect(BasicEdge(2, 3))
+	g.Connect(BasicEdge(2, 4))
+	g.Connect(BasicEdge(3, 4))
+	g.TransitiveReduction()
+
+	actual := strings.TrimSpace(g.String())
+	expected := strings.TrimSpace(testGraphTransReductionMoreStr)
+	if actual != expected {
+		t.Fatalf("bad: %s", actual)
+	}
+}
+
 func TestAcyclicGraphValidate(t *testing.T) {
 	var g AcyclicGraph
 	g.Add(1)
@@ -156,3 +195,21 @@ func TestAcyclicGraphWalk_error(t *testing.T) {
 
 	t.Fatalf("bad: %#v", visits)
 }
+
+const testGraphTransReductionStr = `
+1
+  2
+2
+  3
+3
+`
+
+const testGraphTransReductionMoreStr = `
+1
+  2
+2
+  3
+3
+  4
+4
+`
diff --git a/dag/set.go b/dag/set.go
index 2b1d7f21b..9cc0d98e2 100644
--- a/dag/set.go
+++ b/dag/set.go
@@ -36,6 +36,20 @@ func (s *Set) Include(v interface{}) bool {
 	return ok
 }
 
+// Intersection computes the set intersection with other.
+func (s *Set) Intersection(other *Set) *Set {
+	result := new(Set)
+	if other != nil {
+		for _, v := range s.m {
+			if other.Include(v) {
+				result.Add(v)
+			}
+		}
+	}
+
+	return result
+}
+
 // Len is the number of items in the set.
 func (s *Set) Len() int {
 	if s == nil {