15  Warm-start calculation of all shortest paths.ipynb

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  {
   "cell_type": "code",
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   "source": [
    "exec(open(\"./funcs/tool_funcs.py\").read())\n",
    "\n"
   ]
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  {
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   "source": [
    "def dijkstra_show_path(adj_matrix, start, end):\n",
    " \n",
    "    n = len(adj_matrix)\n",
    "    distances = [float('inf')] * n\n",
    "    previous_nodes = [-1] * n\n",
    "    distances[start] = 0\n",
    "    priority_queue = [(0, start)]  # (distance, node)\n",
    "\n",
    "    while priority_queue:\n",
    "        current_distance, current_node = heapq.heappop(priority_queue)\n",
    "\n",
    "        # Stop if we reached the destination node\n",
    "        if current_node == end:\n",
    "            break\n",
    "\n",
    "        # If the distance is no longer optimal, skip\n",
    "        if current_distance > distances[current_node]:\n",
    "            continue\n",
    "\n",
    "        # Explore neighbors\n",
    "        for neighbor, weight in enumerate(adj_matrix[current_node]):\n",
    "            if weight > 0:  # Only consider edges with weight > 0\n",
    "                distance = current_distance + weight\n",
    "\n",
    "                # Update distance if it's better\n",
    "                if distance < distances[neighbor]:\n",
    "                    distances[neighbor] = distance\n",
    "                    previous_nodes[neighbor] = current_node\n",
    "                    heapq.heappush(priority_queue, (distance, neighbor))\n",
    "\n",
    "    # Reconstruct the path from end to start\n",
    "    path = []\n",
    "    current = end\n",
    "    while current != -1:\n",
    "        path.append(current)\n",
    "        current = previous_nodes[current]\n",
    "    path.reverse()\n",
    "\n",
    "    # If the start node isn't reachable, return an empty path\n",
    "    return path if path[0] == start else []"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8c3c2a38",
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  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "a96d92af",
   "metadata": {},
   "outputs": [],
   "source": [
    "def translate_path(path, candidate_node_list):\n",
    "    new_path = [candidate_node_list[i] for i in path]\n",
    "    return new_path\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ad6bbacb",
   "metadata": {},
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  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "ff1876be",
   "metadata": {},
   "outputs": [],
   "source": [
    "def output_small_matrix(X_distance_matrix, candidate_node_list):\n",
    "    small_matrix = np.zeros((len(candidate_node_list), len(candidate_node_list)))\n",
    "    for i, ii in enumerate(candidate_node_list):\n",
    "        for j, jj in enumerate(candidate_node_list):\n",
    "            small_matrix[i,j] = X_distance_matrix[ii, jj]\n",
    "    return small_matrix\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "9c210f08",
   "metadata": {},
   "outputs": [],
   "source": [
    "def cal_candidate_node_list(i, j, shortest_path_matrix, X_distance_matrix):\n",
    "    \n",
    "    N = len(X_distance_matrix)\n",
    "    \n",
    "    remaining_list = [k for k in np.arange(N) if k != i and k != j]\n",
    "    candidate_node_list = []\n",
    "    candidate_node_list.append(i)\n",
    "    for t in remaining_list:\n",
    "        if shortest_path_matrix[i,j] < shortest_path_matrix[i,t] + shortest_path_matrix[t,j]:\n",
    "            pass\n",
    "        else:\n",
    "            candidate_node_list.append(t)\n",
    "    candidate_node_list.append(j)\n",
    " \n",
    "    return candidate_node_list\n",
    "        \n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "ae965627",
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "def cal_path_warm_start(i, j, shortest_path_matrix, X_distance_matrix):\n",
    "    candidate_node_list = cal_candidate_node_list(i, j, shortest_path_matrix, X_distance_matrix)\n",
    "    print(\"candidate_node_list:\")\n",
    "    print(candidate_node_list)\n",
    "   \n",
    "    small_matrix = output_small_matrix(X_distance_matrix, candidate_node_list)\n",
    "    path = dijkstra_show_path(small_matrix, 0, len(candidate_node_list) - 1)\n",
    "    path = translate_path(path, candidate_node_list)\n",
    "    \n",
    "    return path\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "4100db2f",
   "metadata": {},
   "outputs": [],
   "source": [
    "# APPD stands for all points path distance (APPD).\n",
    "\n",
    "def check_shortest_path(i,j, X_distance_matrix, APPD_matrix, path):\n",
    "    temp1= path[:-1]\n",
    "    temp2= path[1:]\n",
    "    llll = [X_distance_matrix[temp1[i],temp2[i]] for i in range(len(temp1))]\n",
    "    ooo = np.sum(llll)\n",
    "    return ooo == APPD_matrix[i,j]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "75b32da0",
   "metadata": {},
   "outputs": [],
   "source": [
    "def check_if_temp_path_already_in(all_paths_list, temp_path):\n",
    "    aa = set(temp_path)\n",
    "    for bb in all_paths_list:\n",
    "        bb = set(bb)\n",
    "        if aa == bb:\n",
    "            return True\n",
    "    return False\n",
    "\n",
    "def cal_all_paths_warm_start(i, j, shortest_path_matrix, X_distance_matrix):\n",
    "    candidate_node_list = cal_candidate_node_list(i, j, shortest_path_matrix, X_distance_matrix)\n",
    " \n",
    "    small_matrix = output_small_matrix(X_distance_matrix, candidate_node_list)\n",
    "    path = dijkstra_show_path(small_matrix, 0, len(candidate_node_list) - 1)\n",
    "\n",
    "    all_paths_list = []\n",
    "    all_paths_list.append(path)\n",
    "\n",
    "    K = len(candidate_node_list)\n",
    "    # temp_list = [q for q in range(K) if q not in path]\n",
    "    \n",
    "    temp_list = [q for q in range(1, K - 1)]\n",
    "\n",
    "    for m in temp_list:\n",
    "        temp_path1 = dijkstra_show_path(small_matrix, 0, m)\n",
    "        temp_path2 = dijkstra_show_path(small_matrix, m, K - 1)\n",
    "        temp_path =  temp_path1[:-1] + temp_path2\n",
    "        if not check_if_temp_path_already_in(all_paths_list, temp_path):\n",
    "            all_paths_list.append(temp_path)\n",
    "\n",
    "    all_paths_list = [translate_path(ppp, candidate_node_list) for ppp in all_paths_list]    \n",
    "\n",
    "    return all_paths_list"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "025ebebe",
   "metadata": {},
   "outputs": [],
   "source": [
    "# N = 1000\n",
    "\n",
    "# X_distance_matrix = create_distance_matrix(N)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "8e87922b",
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "\n",
    "X_distance_matrix = np.loadtxt(\"./data/X_100_distance_matrix.csv\", delimiter=\",\")\n",
    "\n",
    "shortest_path_matrix = floyd_warshall(X_distance_matrix)\n",
    " "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "fb4b6901",
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "N = len(X_distance_matrix)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "f63bdabe",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "candidate_node_list:\n",
      "[71, 3, 7, 13, 15, 17, 20, 34, 61, 73, 85, 95, 93]\n",
      "[71, 20, 13, 95, 17, 7, 61, 93]\n",
      "[71, 20, 13, 95, 17, 7, 61, 93]\n"
     ]
    }
   ],
   "source": [
    "i = 71\n",
    "j = 93\n",
    " \n",
    "path1 = dijkstra_show_path(X_distance_matrix, i, j)\n",
    "    \n",
    "path2 = cal_path_warm_start(i, j, shortest_path_matrix, X_distance_matrix)   \n",
    "print(path1)\n",
    "print(path2)\n",
    "\n",
    "\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "87b16507",
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "check_shortest_path(i,j, X_distance_matrix, shortest_path_matrix, path2)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "60bbd478",
   "metadata": {},
   "outputs": [],
   "source": [
    "all_paths_list = cal_all_paths_warm_start(i, j, shortest_path_matrix, X_distance_matrix)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "f0142716",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[71, 20, 13, 95, 17, 7, 61, 93] True\n",
      "[71, 3, 85, 15, 34, 73, 7, 61, 93] True\n"
     ]
    }
   ],
   "source": [
    "for path_i in all_paths_list:\n",
    "    aaa = check_shortest_path(i,j, X_distance_matrix, shortest_path_matrix, path_i)\n",
    "    print(path_i, aaa)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "975615ae",
   "metadata": {},
   "outputs": [],
   "source": [
    "# We can maintain a key_node_list for each pair of nodes, \n",
    "# e.g., for the shortest path from node 71 to 93, nodes 7 and 61 are essential, \n",
    "# so the key_node_list is [7, 61]. \n",
    "# When needing to remove a node, we can just check each pair of nodes' key_node_list \n",
    "# to decide if the shortest path is affected.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e77f6ff3",
   "metadata": {},
   "outputs": [],
   "source": []
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   "cell_type": "code",
   "execution_count": null,
   "id": "3e0e54ed",
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