diff --git a/fcore/bin-vec.sml b/fcore/bin-vec.sml
index 21e4631..87cb46b 100644
--- a/fcore/bin-vec.sml
+++ b/fcore/bin-vec.sml
@@ -213,3 +213,15 @@ structure DistVec =
 
        fun g ({distance = a, ...}: elem, {distance = b, ...}: elem) = a > b
      end)
+
+structure PlatSet =
+  MakeBinVec
+    (struct
+       type elem = {distance: int, id: int}
+
+       fun l ({id = a, ...}: elem, {id = b, ...}: elem) = a < b
+
+       fun eq ({id = a, ...}: elem, {id = b, ...}: elem) = a = b
+
+       fun g ({id = a, ...}: elem, {id = b, ...}: elem) = a > b
+     end)
diff --git a/fcore/graph.sml b/fcore/graph.sml
new file mode 100644
index 0000000..56b8791
--- /dev/null
+++ b/fcore/graph.sml
@@ -0,0 +1,212 @@
+structure Graph =
+struct
+  fun insertIfNew (dist, platSet, foldPlatID) =
+    let
+      val insRecord = {id = foldPlatID, distance = dist}
+      val pos = PlatSet.findInsPos (insRecord, platSet)
+    in
+      if pos <> ~1 andalso pos <> Vector.length platSet then
+        (* platSet may already contain foldPlatID; check *)
+        let
+          val {id = key, ...} = PlatSet.sub (platSet, pos)
+        in
+          if key = foldPlatID then
+            (* alread contains foldPlatID so return *)
+            platSet
+          else
+            (* foldPlatID is new; insert it *)
+            PlatSet.insert (platSet, insRecord, pos)
+        end
+      else
+        (* foldPlatID is new; insert it *)
+        PlatSet.insert (platSet, insRecord, pos)
+    end
+
+  type env =
+    {platforms: GameType.platform vector, currentPlat: GameType.platform}
+
+  structure Vertical =
+    MakeQuadTreeFold
+      (struct
+         type env = env
+
+         type state = PlatSet.elem vector
+
+         fun fold (foldPlatID, env: env, platSet) =
+           let
+             val {platforms, currentPlat} = env
+
+             val {y = foldPlatY, ...} = Platform.find (foldPlatID, platforms)
+             val {y = currentPlatY, ...} = currentPlat
+             val newDist = abs (foldPlatY - currentPlatY)
+           in
+             insertIfNew (newDist, platSet, foldPlatID)
+           end
+       end)
+
+  structure Horizontal =
+    MakeQuadTreeFold
+      (struct
+         type env = env
+
+         type state = PlatSet.elem vector
+
+         fun minWidth (p1: GameType.platform, p2: GameType.platform) =
+           let
+             val {x = p1x, width = p1w, ...} = p1
+             val {x = p2x, width = p2w, ...} = p2
+
+             val p1fx = p1x + p1w
+             val p2fx = p2x + p2w
+
+             val w1 = abs (p1fx - p2fx)
+             val w2 = abs (p1fx - p2x)
+             val w3 = abs (p1x - p2x)
+             val w4 = abs (p1x - p2fx)
+
+             val min = Int.min (w1, w2)
+             val min = Int.min (min, w3)
+           in
+             Int.min (min, w4)
+           end
+
+         fun pythagoras (width, height) =
+           let
+             val wsq = width * width
+             val hsq = height * height
+             val hypotenuseSq = wsq + hsq
+             val hypSq = Real.fromInt hypotenuseSq
+             val hyp = Math.sqrt hypSq
+           in
+             Real.toInt IEEEReal.TO_NEAREST hyp
+           end
+
+         fun fold (foldPlatID, env: env, platSet) =
+           let
+             val {platforms, currentPlat} = env
+
+             val foldPlat = Platform.find (foldPlatID, platforms)
+             val foldPlatY = #y foldPlat
+             val {y = currentPlatY, ...} = currentPlat
+
+             val height = abs (foldPlatY - currentPlatY)
+             val width = minWidth (currentPlat, foldPlat)
+
+             val newDist = pythagoras (width, height)
+           in
+             insertIfNew (newDist, platSet, foldPlatID)
+           end
+       end)
+
+  fun traceRightDescent (x, y, platTree, env, platSet) =
+    if x >= Constants.worldWidth orelse y >= Constants.worldHeight then
+      (* we hit bounds of screen and saw that there was 
+       * no way to jump to next nextPlatID *)
+      platSet
+    else
+      let
+        val width = Constants.moveEnemyBy
+        val height = Constants.worldHeight - y
+        val platSet = Horizontal.foldRegion
+          (x, y, width, height, env, platSet, platTree)
+
+        val nextX = x + Constants.moveEnemyBy
+        val nextY = y + Constants.moveEnemyBy
+      in
+        traceRightDescent (nextX, nextY, platTree, env, platSet)
+      end
+
+  fun traceRightJumpAscent (x, y, remainingJump, platTree, env, platSet) =
+    if remainingJump >= Constants.jumpLimit - Constants.enemySize then
+      traceRightDescent (x, y, platTree, env, platSet)
+    else
+      let
+        val width = Constants.moveEnemyBy
+        val height = Constants.worldHeight - y
+
+        val platSet = Horizontal.foldRegion
+          (x, y, width, height, env, platSet, platTree)
+
+        val nextX = x + Constants.moveEnemyBy
+        val nextY = y - Constants.moveEnemyBy
+        val nextJump = remainingJump + Constants.moveEnemyBy
+      in
+        traceRightJumpAscent (nextX, nextY, nextJump, platTree, env, platSet)
+      end
+
+  fun traceRightJump (currentPlat: GameType.platform, env, platSet, platTree) =
+    let
+      val {x, y, width, ...} = currentPlat
+      val x = x - Constants.enemySize + width
+    in
+      traceRightJumpAscent (x, y, 0, platTree, env, platSet)
+    end
+
+  fun traceLeftDescent (x, y, platTree, env, platSet) =
+    if x <= 0 orelse y >= Constants.worldHeight then
+      platSet
+    else
+      let
+        val width = Constants.moveEnemyBy
+        val height = Constants.worldHeight - y
+        val platSet = Horizontal.foldRegion
+          (x, y, width, height, env, platSet, platTree)
+
+        val nextX = x - Constants.moveEnemyBy
+        val nextY = y + Constants.moveEnemyBy
+      in
+        traceLeftDescent (nextX, nextY, platTree, env, platSet)
+      end
+
+  fun traceLeftJumpAscent (x, y, remainingJump, platTree, env, platSet) =
+    if remainingJump >= Constants.jumpLimit - Constants.enemySize then
+      traceLeftDescent (x, y, platTree, env, platSet)
+    else
+      let
+        val width = Constants.moveEnemyBy
+        val height = Constants.worldHeight - y
+
+        val platSet = Horizontal.foldRegion
+          (x, y, width, height, env, platSet, platTree)
+
+        val nextX = x - Constants.moveEnemyBy
+        val nextY = y - Constants.moveEnemyBy
+        val nextJump = remainingJump + Constants.moveEnemyBy
+      in
+        traceLeftJumpAscent (nextX, nextY, nextJump, platTree, env, platSet)
+      end
+
+  fun traceLeftJump (currentPlat: GameType.platform, env, platSet, platTree) =
+    let
+      val {x, y, ...} = currentPlat
+      val x = x + Constants.enemySize
+    in
+      traceLeftJumpAscent (x, y, 0, platTree, env, platSet)
+    end
+
+  fun start (currentPlat: GameType.platform, env: env, platSet, platformTree) =
+    let
+      val {x, y, width, ...} = currentPlat
+
+      (* calculate area to search in y axis *)
+      val searchY = y - Constants.jumpLimit
+      val height = Constants.worldHeight - searchY
+
+      val platSet = Vertical.foldRegion
+        (x, searchY, width, height, env, platSet, platformTree)
+
+      val platSet = traceRightJump (currentPlat, env, platSet, platformTree)
+    in
+      traceLeftJump (currentPlat, env, platSet, platformTree)
+    end
+
+  fun build (currentPlat, platforms, platformTree) =
+    let
+      val env = {currentPlat = currentPlat, platforms = platforms}
+    in
+      start (currentPlat, env, PlatSet.empty, platformTree)
+    end
+
+  fun fromPlatforms (platforms: GameType.platform vector, platformTree) =
+    Vector.map (fn plat => build (plat, platforms, platformTree)) platforms
+end
diff --git a/oms.mlb b/oms.mlb
index 91105b2..97f1f2b 100644
--- a/oms.mlb
+++ b/oms.mlb
@@ -27,6 +27,7 @@ fcore/enemy-patch.sml
 fcore/physics.sml
 
 fcore/build-graph.sml
+fcore/graph.sml
 fcore/path-finding.sml
 
 fcore/trace-jump.sml