diff --git a/compiler/DirectedGraph/DirectedGraphAlgorythm.hh b/compiler/DirectedGraph/DirectedGraphAlgorythm.hh
index 45554c1be7..4f1a76f2bc 100644
--- a/compiler/DirectedGraph/DirectedGraphAlgorythm.hh
+++ b/compiler/DirectedGraph/DirectedGraphAlgorythm.hh
@@ -260,7 +260,7 @@ inline std::vector<std::vector<N>> parallelize(const digraph<N, Comparator>& g)
         }
     };
 
-    std::map<N, int> levelcache;
+    std::map<N, int, Comparator> levelcache;
     // compute the level of each node in the graph
     int l = -1;
     for (const N& n : g.nodes()) {
@@ -582,8 +582,8 @@ inline std::vector<N> leaves(const digraph<N, Comparator>& G)
  * @param G
  * @return std::vector<N>
  */
-template <typename N>
-inline std::vector<N> criticalpath(const digraph<N>& G, const N& n)
+template <typename N, typename Comparator = std::less<N>>
+inline std::vector<N> criticalpath(const digraph<N, Comparator>& G, const N& n)
 {
     std::vector<N> P;
     for (const auto& c : G.destinations(n)) {
@@ -643,8 +643,8 @@ static std::list<N> interleave(std::list<N>& list1, std::list<N>& list2)
  * @param n a node of G
  * @return std::list<N> scheduling with duplicates
  */
-template <typename N>
-inline std::list<N> recschedulenode(const digraph<N>& G, const N& n)
+template <typename N, typename Comparator = std::less<N>>
+inline std::list<N> recschedulenode(const digraph<N, Comparator>& G, const N& n)
 {
     std::list<N> P;
     for (const auto& c : G.destinations(n)) {
@@ -662,8 +662,8 @@ inline std::list<N> recschedulenode(const digraph<N>& G, const N& n)
  * @param G a DAG
  * @return std::list<N> scheduling with duplicates
  */
-template <typename N>
-inline std::list<N> recschedule(const digraph<N>& G)
+template <typename N, typename Comparator = std::less<N>>
+inline std::list<N> recschedule(const digraph<N, Comparator>& G)
 {
     std::list<N> P;
     for (const N& n : roots(G)) {
@@ -673,7 +673,6 @@ inline std::list<N> recschedule(const digraph<N>& G)
     return P;
 }
 
-
 /*******************************************************************************
 ********************************************************************************
 
@@ -848,8 +847,8 @@ inline std::ostream& operator<<(std::ostream& file, const digraph<N, Comparator>
  * @param g graph we want to analyze
  * @return std::vector<int> [n, a, c, l0, l1, ...]
  */
-template <typename N>
-inline std::vector<int> topology(const digraph<N>& g)
+template <typename N, typename Comparator = std::less<N>>
+inline std::vector<int> topology(const digraph<N, Comparator>& g)
 {
     std::vector<int> v;
     int              n = 0;
diff --git a/compiler/DirectedGraph/Schedule.hh b/compiler/DirectedGraph/Schedule.hh
index 8e22d57728..1eeeb2ecd8 100644
--- a/compiler/DirectedGraph/Schedule.hh
+++ b/compiler/DirectedGraph/Schedule.hh
@@ -77,7 +77,7 @@ class schedule {
     // A schedule in reverse order
     schedule reverse() const
     {
-        schedule<N> S;
+        schedule<N, Comparator> S;
         for (auto it = fElements.rbegin(); it != fElements.rend(); ++it) {
             S.append(*it);
         }
@@ -166,11 +166,11 @@ inline schedule<N, Comparator> bfschedule(const digraph<N, Comparator>& G)
  * @param G
  * @return schedule<N>
  */
-template <typename N>
-inline schedule<N> spschedule(const digraph<N>& G)
+template <typename N, typename Comparator = std::less<N>>
+inline schedule<N, Comparator> spschedule(const digraph<N, Comparator>& G)
 {
-    std::set<N> V;  // already scheduled nodes
-    schedule<N> S;  // the final schedule
+    std::set<N>             V;  // already scheduled nodes
+    schedule<N, Comparator> S;  // the final schedule
 
     std::list<N> L = recschedule(G);  // schedule list with duplicated
     for (auto it = L.rbegin(); it != L.rend(); ++it) {
@@ -253,11 +253,11 @@ inline schedule<N, Comparator> bfcyclesschedule(const digraph<N, Comparator>& G)
  * @param G
  * @return schedule<N>
  */
-template <typename N>
-inline schedule<N> rbschedule(const digraph<N>& G)
+template <typename N, typename Comparator = std::less<N>>
+inline schedule<N, Comparator> rbschedule(const digraph<N, Comparator>& G)
 {
     std::vector<std::vector<N>> P = parallelize(reverse(G));
-    schedule<N>                 S;
+    schedule<N, Comparator>     S;
 
     for (uint64_t i = 0; i < P.size(); i++) {
         for (const N& n : P[i]) {
diff --git a/compiler/generator/compile_scal.cpp b/compiler/generator/compile_scal.cpp
index d6f39492c9..51a997ca6a 100644
--- a/compiler/generator/compile_scal.cpp
+++ b/compiler/generator/compile_scal.cpp
@@ -535,7 +535,7 @@ void ScalarCompiler::compileMultiSignal(Tree L)
         std::cerr << "Print siglist inst graph topology : " << topology(G) << '\n';
     }
     // Force a specific scheduling (i.e. compilation order)
-    schedule<Tree> S;
+    schedule<Tree, CTreeComparator> S;
     switch (gGlobal->gSchedulingStrategy) {
         case 0:
             S = dfschedule(G);
diff --git a/compiler/transform/sigDependenciesGraph.cpp b/compiler/transform/sigDependenciesGraph.cpp
index 67f91963de..fff632ddde 100644
--- a/compiler/transform/sigDependenciesGraph.cpp
+++ b/compiler/transform/sigDependenciesGraph.cpp
@@ -13,7 +13,7 @@ class SigDependenciesGraph : public SignalVisitor {
    protected:
     digraph<Tree, CTreeComparator> fGraph;
     bool                           fFullGraph;
-    bool          fLimitOndemand = false;  // don't go beyond tempvar signals
+    bool                           fLimitOndemand = false;  // don't go beyond tempvar signals
 
    public:
     SigDependenciesGraph(bool full, bool limit)
@@ -299,22 +299,6 @@ digraph<Tree, CTreeComparator> immediateGraph(Tree L)
     return g.getGraph();
 }
 
-/**
- * @brief Compute the immediate Graph (containing only immediate dependencies)
- * of a list of signals and not going beyond tempvar signals
- *
- * @param L list of signals
- * @return digraph<Tree>
- */
-digraph<Tree> ondemandGraph(const tvec& signals)
-{
-    SigDependenciesGraph g(false, true);
-    for (Tree s : signals) {
-        g.self(s);
-    }
-    return g.getGraph();
-}
-
 /**
  * @brief Compute the immediate Graph (containing only immediate dependencies)
  * of a list of signals and not going beyond tempvar signals
@@ -364,6 +348,6 @@ std::vector<Tree> compilationOrder(Tree L)
  */
 std::vector<Tree> ondemandCompilationOrder(const tvec& signals)
 {
-    digraph<Tree> G = ondemandGraph(signals);
+    digraph<Tree, CTreeComparator> G = ondemandGraph(signals);
     return serialize(G);
 }
diff --git a/compiler/transform/sigDependenciesGraph.hh b/compiler/transform/sigDependenciesGraph.hh
index 3525e02993..4414775dba 100644
--- a/compiler/transform/sigDependenciesGraph.hh
+++ b/compiler/transform/sigDependenciesGraph.hh
@@ -18,7 +18,7 @@ digraph<Tree, CTreeComparator> immediateGraph(Tree L);
  * @param L list of signals
  * @return digraph<Tree>
  */
-digraph<Tree> ondemandGraph(const tvec& V);
+digraph<Tree, CTreeComparator> ondemandGraph(const tvec& V);
 
 /**
  * @brief Compute the full Graph of a list of signals including immediate and time dependencies