diff --git a/src/analyses/call_graph.cpp b/src/analyses/call_graph.cpp
index 4413d56c205..a4a1ff65ec1 100644
--- a/src/analyses/call_graph.cpp
+++ b/src/analyses/call_graph.cpp
@@ -6,10 +6,12 @@ Author: Daniel Kroening, kroening@kroening.com
 
 \*******************************************************************/
 
+#include "call_graph.h"
 #include <util/std_expr.h>
 #include <util/xml.h>
+#include <algorithm>
+#include <iterator>
 
-#include "call_graph.h"
 
 /*******************************************************************\
 
@@ -70,11 +72,31 @@ void call_grapht::add(
     {
       const exprt &function_expr=to_code_function_call(i_it->code).function();
       if(function_expr.id()==ID_symbol)
-        add(function, to_symbol_expr(function_expr).get_identifier());
+        add(function, to_symbol_expr(function_expr).get_identifier(), {i_it});
     }
   }
 }
 
+/*******************************************************************\
+
+Function: call_grapht::swap
+
+  Inputs:
+
+ Outputs:
+
+ Purpose:
+
+\*******************************************************************/
+
+void call_grapht::swap(call_grapht &other)
+{
+  std::swap(graph, other.graph);
+  std::swap(map_from_edges_to_call_locations,
+            other.map_from_edges_to_call_locations);
+}
+
+
 /*******************************************************************\
 
 Function: call_grapht::add
@@ -96,7 +118,7 @@ void call_grapht::add(
 
 /*******************************************************************\
 
-Function: call_grapht::output_dot
+Function: call_grapht::add
 
   Inputs:
 
@@ -106,37 +128,60 @@ Function: call_grapht::output_dot
 
 \*******************************************************************/
 
-void call_grapht::output_dot(std::ostream &out) const
+void call_grapht::add(
+  const irep_idt &caller,
+  const irep_idt &callee,
+  const map_from_edges_to_call_locationst::mapped_type &call_sites)
 {
-  out << "digraph call_graph {\n";
-
-  for(const auto &edge : graph)
+  bool exists=false;
+  const call_grapht::call_edges_ranget range=out_edges(caller);
+  for(auto it=range.first; it!=range.second; ++it)
   {
-    out << "  \"" << edge.first << "\" -> "
-        << "\"" << edge.second << "\" "
-        << " [arrowhead=\"vee\"];"
-        << "\n";
+    if(it->second==callee)
+    {
+      exists=true;
+      break;
+    }
   }
-
-  out << "}\n";
+  if(!exists)
+    add(caller, callee);
+  std::copy(
+    call_sites.cbegin(), call_sites.cend(),
+    std::back_inserter(map_from_edges_to_call_locations[{caller, callee}]));
 }
 
 
-void call_grapht::output_dot(
-  const goto_functionst &functions,
-  std::ostream &out) const
+/*******************************************************************\
+
+Function: call_grapht::output_dot
+
+  Inputs:
+
+ Outputs:
+
+ Purpose:
+
+\*******************************************************************/
+
+void call_grapht::output_dot(std::ostream &out) const
 {
-  out << "digraph call_graph {\n";
-  for(const auto &elem : functions.function_map)
-    out << "  \"" << elem.first << "\";\n";
-  for(grapht::const_iterator it=graph.begin();
-      it!=graph.end();
-      it++)
+  out << "digraph call_graph {\n"
+      << "  node [fontsize=12 shape=box];\n";
+  for(const auto &edge : graph)
   {
-    out << "  \"" << it->first << "\" -> "
-        << "\"" << it->second << "\" "
-        << " [arrowhead=\"vee\"];"
-        << "\n";
+    out << "  \"" << edge.first << "\" -> "
+        << "\"" << edge.second << "\" "
+        << " [label=\"{";
+    bool first=true;
+    for(const auto instr_it :
+        get_map_from_edges_to_call_locations().at({edge.first, edge.second}))
+    {
+      if(!first)
+        out << ",";
+      out << instr_it->location_number;
+      first=false;
+    }
+    out << "}\"];\n";
   }
   out << "}\n";
 }
@@ -382,7 +427,10 @@ void compute_inverted_call_graph(
 {
   assert(output_inverted_call_graph.graph.empty());
   for(const auto &elem : original_call_graph.graph)
-    output_inverted_call_graph.add(elem.second, elem.first);
+    output_inverted_call_graph.add(
+      elem.second, elem.first,
+      original_call_graph.get_map_from_edges_to_call_locations().at(
+        {elem.first, elem.second}));
 }
 
 /*******************************************************************\
@@ -443,3 +491,91 @@ void find_leaves_below_function(
   std::unordered_set<irep_idt, dstring_hash> to_avoid;
   find_leaves_below_function(call_graph, function, to_avoid, output);
 }
+
+/*******************************************************************\
+
+Function: find_direct_or_indirect_callees_of_function
+
+  Inputs:
+
+ Outputs:
+
+ Purpose:
+
+\*******************************************************************/
+
+void find_direct_or_indirect_callees_of_function(
+  const call_grapht &call_graph,
+  const irep_idt &function,
+  std::unordered_set<irep_idt, dstring_hash> &output)
+{
+  std::unordered_set<irep_idt, dstring_hash> leaves;
+  find_leaves_below_function(call_graph, function, output, leaves);
+  output.insert(leaves.cbegin(), leaves.cend());
+}
+
+/*******************************************************************\
+
+Function: find_nearest_common_callees
+
+  Inputs:
+
+ Outputs:
+
+ Purpose:
+
+\*******************************************************************/
+
+void find_nearest_common_callees(
+  const call_grapht &call_graph,
+  const std::set<irep_idt> &functions,
+  std::set<irep_idt> &output)
+{
+  if(functions.empty())
+    return;
+  if(functions.size()==1UL)
+  {
+    output.insert(*functions.cbegin());
+    return;
+  }
+
+  std::map<irep_idt, std::size_t> counting;
+  for(const auto &elem : call_graph.graph)
+  {
+    counting[elem.first]=0U;
+    counting[elem.second]=0U;
+  }
+  for(const auto &fn : functions)
+  {
+    std::unordered_set<irep_idt, dstring_hash> callees;
+    find_direct_or_indirect_callees_of_function(call_graph, fn, callees);
+    assert(callees.count(fn)==1U);
+    for(const auto &callee : callees)
+      ++counting[callee];
+  }
+
+  std::set<irep_idt> leaves;
+  for(const auto &elem : counting)
+    if(elem.second!=0U)
+    {
+      const call_grapht::call_edges_ranget range=
+        call_graph.out_edges(elem.first);
+      if(range.first==range.second)
+        leaves.insert(elem.first);
+    }
+
+  for(auto &elem : counting)
+    if(leaves.count(elem.first)!=0UL)
+      output.insert(elem.first);
+    else if(elem.second!=0U && elem.second<functions.size())
+    {
+      const call_grapht::call_edges_ranget range=
+        call_graph.out_edges(elem.first);
+      for(auto it=range.first; it!=range.second; ++it)
+      {
+        auto cit=counting.find(it->second);
+        if(cit->second==functions.size())
+          output.insert(cit->first);
+      }
+    }
+}
diff --git a/src/analyses/call_graph.h b/src/analyses/call_graph.h
index f852272b20e..5f43aa680e0 100644
--- a/src/analyses/call_graph.h
+++ b/src/analyses/call_graph.h
@@ -23,23 +23,31 @@ class call_grapht
   explicit call_grapht(const goto_functionst &);
 
   void output_dot(std::ostream &out) const;
-
-  /**
-   * It writes this into the passed stream in the Graphviz's DOT format.
-   * The method accepts also functions, because the callgraph does not
-   * store funtions (nodes). It only stores edges (from caller to callee).
-   * So, the resulting graph would not show not-called functions.
-   */
-  void output_dot(const goto_functionst &functions, std::ostream &out) const;
-
   void output(std::ostream &out) const;
   void output_xml(std::ostream &out) const;
 
   typedef std::multimap<irep_idt, irep_idt> grapht;
   grapht graph;
 
+  void swap(call_grapht &other);
+
   void add(const irep_idt &caller, const irep_idt &callee);
 
+  /**
+   * The type provides a mapping from edges of the call-graph to particular
+   * instructions in the caller GOTO programs, where the calls are performed.
+   */
+  typedef std::map<
+            std::pair<irep_idt, irep_idt>,
+            std::vector<goto_programt::instructionst::const_iterator> >
+          map_from_edges_to_call_locationst;
+
+  const map_from_edges_to_call_locationst &
+  get_map_from_edges_to_call_locations() const
+  { return map_from_edges_to_call_locations; }
+
+  void add(const irep_idt &caller, const irep_idt &callee,
+           const map_from_edges_to_call_locationst::mapped_type &call_sites);
 protected:
   void add(const irep_idt &function,
            const goto_programt &body);
@@ -74,6 +82,9 @@ class call_grapht
    *    std::cout << it->second << ", ";
    */
   call_edges_ranget out_edges(const irep_idt &caller) const;
+
+private:
+  map_from_edges_to_call_locationst map_from_edges_to_call_locations;
 };
 
 /*******************************************************************\
@@ -160,4 +171,26 @@ void find_leaves_below_function(
   const irep_idt &function,
   std::unordered_set<irep_idt, dstring_hash> &output);
 
+void find_direct_or_indirect_callees_of_function(
+  const call_grapht &call_graph,
+  const irep_idt &function,
+  std::unordered_set<irep_idt, dstring_hash> &output);
+
+void find_nearest_common_callees(
+  const call_grapht &call_graph,
+  const std::set<irep_idt> &functions,
+  std::set<irep_idt> &output);
+
+/**
+ * The "callee" must be a DIRECT callee of the "caller" in the "call_graph".
+ */
+inline const std::vector<goto_programt::instructionst::const_iterator> &
+get_call_sites(
+  const call_grapht &call_graph,
+  const irep_idt &caller,
+  const irep_idt &callee)
+{
+  return call_graph.get_map_from_edges_to_call_locations().at({caller, callee});
+}
+
 #endif // CPROVER_ANALYSES_CALL_GRAPH_H