diff --git a/be-graphes-model/src/main/java/org/insa/graphs/model/Path.java b/be-graphes-model/src/main/java/org/insa/graphs/model/Path.java
index 6ebdb73..6fd9edd 100644
--- a/be-graphes-model/src/main/java/org/insa/graphs/model/Path.java
+++ b/be-graphes-model/src/main/java/org/insa/graphs/model/Path.java
@@ -29,13 +29,47 @@ public class Path {
      * 
      * @throws IllegalArgumentException If the list of nodes is not valid, i.e. two
      *         consecutive nodes in the list are not connected in the graph.
-     * 
-     * @deprecated Need to be implemented.
      */
     public static Path createFastestPathFromNodes(Graph graph, List<Node> nodes)
             throws IllegalArgumentException {
-        List<Arc> arcs = new ArrayList<Arc>();
-        // TODO:
+    	
+        Arc currentArc = null;
+        
+        for(int i=0; i<nodes.size()-1;i++) {
+	    	for(Arc a : nodes.get(i).getSuccessors()) {
+	    		if(a.getDestination().equals(nodes.get(i+1))  ) {
+	    			currentArc = a;	
+	    		}
+	    	}
+	    	if(currentArc == null) {
+	    		throw new IllegalArgumentException();
+	    	}	
+	    	currentArc = null;
+        }
+    	
+        
+    	List<Arc> arcs = new ArrayList<Arc>();
+        double travelTime = 9999;
+        
+        if(nodes.size() == 0) {
+        	return new Path(graph);
+        }
+        if(nodes.size() == 1) {
+        	return new Path(graph, nodes.get(0) );
+        }
+        
+    	for(int i=0; i<nodes.size()-1;i++) {
+	    	for(Arc a : nodes.get(i).getSuccessors()) {
+	    		if(a.getMinimumTravelTime() < travelTime 
+	    				&& a.getDestination().equals(nodes.get(i+1))  ) {
+	    			currentArc = a;
+	    			travelTime = a.getMinimumTravelTime();
+	    		}
+	    	}
+	    	arcs.add(currentArc);
+	    	travelTime = 9999;
+    	}
+          
         return new Path(graph, arcs);
     }
 
@@ -50,13 +84,46 @@ public class Path {
      * 
      * @throws IllegalArgumentException If the list of nodes is not valid, i.e. two
      *         consecutive nodes in the list are not connected in the graph.
-     * 
-     * @deprecated Need to be implemented.
      */
     public static Path createShortestPathFromNodes(Graph graph, List<Node> nodes)
             throws IllegalArgumentException {
+    	
+        Arc currentArc = null;
+        
+        for(int i=0; i<nodes.size()-1;i++) {
+	    	for(Arc a : nodes.get(i).getSuccessors()) {
+	    		if(a.getDestination().equals(nodes.get(i+1))  ) {
+	    			currentArc = a;	
+	    		}
+	    		
+	    	}
+	    	if(currentArc == null) {
+	    		throw new IllegalArgumentException();
+	    	}	
+	    	currentArc = null;
+        }
+        
+        
         List<Arc> arcs = new ArrayList<Arc>();
-        // TODO:
+        float distanceMin = 9999;
+        
+        if(nodes.size() == 0) {
+        	return new Path(graph);
+        }
+        if(nodes.size() == 1) {
+        	return new Path(graph, nodes.get(0) );
+        }
+    	for(int i=0; i<nodes.size()-1;i++) {
+	    	for(Arc a : nodes.get(i).getSuccessors()) {
+	    		if(a.getLength() < distanceMin 
+	    				&& a.getDestination().equals(nodes.get(i+1))  ) {
+	    			currentArc = a;
+	    			distanceMin = a.getLength();
+	    		}
+	    	}
+	    	arcs.add(currentArc);
+	    	distanceMin = 9999;
+    	}
         return new Path(graph, arcs);
     }
 
@@ -197,24 +264,42 @@ public class Path {
      * </ul>
      * 
      * @return true if the path is valid, false otherwise.
-     * 
-     * @deprecated Need to be implemented.
      */
     public boolean isValid() {
-        // TODO:
-        return false;
+        if(this.isEmpty()) {
+        	return true;
+        }
+        if(this.origin != null && this.arcs.isEmpty()) {
+        	return true;
+        }
+        
+        if(!this.arcs.get(0).getOrigin().equals(this.getOrigin()) ) {
+        	return false;
+        }
+        if(!this.arcs.get(this.arcs.size() -1 ).getDestination().equals(this.getDestination()) ) {
+        	return false;
+        }
+        
+        for(int i=0;i<this.arcs.size()-1; i++) {
+        	if(!this.arcs.get(i).getDestination().equals(this.arcs.get(i+1).getOrigin()) )  {
+        		return false;
+        	}
+        }
+        
+        return true;
     }
 
     /**
      * Compute the length of this path (in meters).
      * 
      * @return Total length of the path (in meters).
-     * 
-     * @deprecated Need to be implemented.
      */
     public float getLength() {
-        // TODO:
-        return 0;
+        float res = 0.0f;
+        for(Arc a : this.arcs) {
+        	res+= a.getLength();
+        }
+        return res;
     }
 
     /**
@@ -224,12 +309,9 @@ public class Path {
      * 
      * @return Time (in seconds) required to travel this path at the given speed (in
      *         kilometers-per-hour).
-     * 
-     * @deprecated Need to be implemented.
      */
     public double getTravelTime(double speed) {
-        // TODO:
-        return 0;
+        return this.getLength()/(speed/3.6f);
     }
 
     /**
@@ -237,12 +319,13 @@ public class Path {
      * on every arc.
      * 
      * @return Minimum travel time to travel this path (in seconds).
-     * 
-     * @deprecated Need to be implemented.
      */
     public double getMinimumTravelTime() {
-        // TODO:
-        return 0;
+    	double res = 0.0f;
+        for(Arc a : this.arcs) {
+        	res+= a.getMinimumTravelTime();
+        }
+        return res;
     }
 
 }