diff --git a/01-knapsack/ks_dp-ng.c b/01-knapsack/ks_dp-ng.c
index 7830651..ddb0d04 100644
--- a/01-knapsack/ks_dp-ng.c
+++ b/01-knapsack/ks_dp-ng.c
@@ -7,12 +7,14 @@
 
 #define NONE -1
 
+enum { RELAX = 0, NO_RELAX };
 enum { SORT_DESC = 0, SORT_ASC };
 enum { UNSORTED = 0, SORT_WR, SORT_VR, SORT_RW, SORT_RV};
 
 static int debug;
 static int sort;
 static int sort_order;
+static int relax;
 
 typedef struct _InputItem
 {
@@ -25,6 +27,7 @@ typedef struct _SolverItem {
      int i;             /* index of the selected item */
      int v;             /* cumulated value */
      int w;             /* cumulated weight */
+     float r;           /* linear relaxation best value */
 } SolverItem;
 
 typedef struct _Solver
@@ -87,11 +90,39 @@ item_cmp(const void *p1, const void *p2)
    return 0;
 }
 
+static inline float relax_item(Solver* solver, SolverItem* data, int start)
+{
+   int w;
+   int i;
+   float relax;
+   const InputItem *item;
+
+   w = data->w;
+   relax= data->v;
+   item = &solver->items[start];
+   for (i = start; i < solver->n; i++, item++)
+     {
+        if ((w + item->w) <= solver->k)
+          {
+             w += item->w;
+             relax += item->v;
+          }
+        else
+          {
+             relax += (item->v * ((solver->k - w) / (float)item->w));
+             break;
+          }
+     }
+
+   return relax;
+}
+
 static void solve(Solver* solver)
 {
    int n, k;
    int v, w;
    int i, j;
+   float r;
    int min_c, lower_bound;
    const InputItem *item;
    SolverItem *data;
@@ -105,7 +136,16 @@ static void solve(Solver* solver)
 
    if (debug > 2)
      {
-        printf("\nformat V(i,W)\n");
+        printf("\nformat V(i,W,r)\n");
+     }
+
+   /* RELAXATION */
+   if (relax == RELAX)
+     {
+        data = solver->column;
+        r = relax_item(solver, data, 0);
+        for (j = 0; j <= k; j++, data++)
+          data->r = r;
      }
 
    /* SOLVE */
@@ -134,6 +174,12 @@ static void solve(Solver* solver)
                   data->v = v + up_left->v;
                   data->w = w + up_left->w;
                }
+
+             /* RELAXTION must be cached */
+             if (relax == RELAX)
+               {
+                  data->r = relax_item(solver, data, (i + 1));
+               }
           }
 
         if (debug > 2)
@@ -141,8 +187,8 @@ static void solve(Solver* solver)
              printf("i=%d; j=k; j<=%d:\n", i, lower_bound);
              data = solver->column;
              for (j = 0; j <= k; j++, data++)
-               printf("  %d : % 4d(% 2d % 2d)\n",
-                      j, data->v, data->i, data->w);
+               printf("  %d : % 4d(% 2d % 2d %.1f)\n",
+                      j, data->v, data->i, data->w, data->r);
              printf("\n");
           }
      }
@@ -152,8 +198,8 @@ static void solve(Solver* solver)
         printf("i=%d:\n", solver->n - 1);
         data = solver->column;
         for (j = 0; j <= k; j++, data++)
-          printf("  % 4d(% 2d % 2d)\n",
-                 data->v, data->i, data->w);
+          printf("  % 4d(% 2d % 2d %.1f)\n",
+                 data->v, data->i, data->w, data->r);
      }
 
    if (debug > 0)
@@ -194,10 +240,11 @@ int main(int argc, char** argv, char** env)
    InputItem *item;
 
    debug = 0;
+   relax = NO_RELAX;
    sort = UNSORTED;
    sort_order = SORT_DESC;
    excpected_value = NONE;
-   while ((opt = getopt(argc, argv, "d:e:s:S")) != -1) {
+   while ((opt = getopt(argc, argv, "d:e:s:SR")) != -1) {
         switch (opt) {
            case 'd':
               debug = atoi(optarg);
@@ -211,6 +258,9 @@ int main(int argc, char** argv, char** env)
            case 'S':
               sort_order = SORT_ASC;
               break;
+           case 'R':
+              relax = RELAX;
+              break;
            default: /* '?' */
               fprintf(stderr, "Usage: %s [falgs] input\n",
                       argv[0]);