23 Test remove node - shortest path problem - algorithm 11.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "ae288796",
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "# This file tests Algorithm 11.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "c01655ee",
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "exec(open(\"./funcs/tool_funcs.py\").read())\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "2846295f",
   "metadata": {},
   "outputs": [],
   "source": [
    " \n",
    "\n",
    "def dijkstra_one_to_all(distance_matrix, src, need_up_i, remove_node):\n",
    "    \n",
    "    N = len(distance_matrix)\n",
    "    dist = [np.inf] * N\n",
    "    dist[src] = 0\n",
    "    visited = [False] * N\n",
    "\n",
    "    # Priority queue: (distance, node)\n",
    "    pq = [(0, src)]\n",
    "    \n",
    "    kk = len(need_up_i)\n",
    "    counter = 0\n",
    "    visited[remove_node] = True\n",
    "\n",
    "    while pq:\n",
    "        current_dist, u = heapq.heappop(pq)\n",
    "\n",
    "        if visited[u]:\n",
    "            continue\n",
    "        visited[u] = True\n",
    "        \n",
    "        if u in need_up_i:\n",
    "            counter += 1\n",
    "            if counter == kk:\n",
    "                return np.array(dist)\n",
    " \n",
    "\n",
    "        # Update distances for neighbors\n",
    "        for v in range(N):\n",
    "            if not visited[v] and distance_matrix[u][v] > 0:\n",
    "                new_dist = current_dist + distance_matrix[u][v]\n",
    "                if new_dist < dist[v]:\n",
    "                    dist[v] = new_dist\n",
    "                    heapq.heappush(pq, (new_dist, v))\n",
    "\n",
    "    return np.array(dist)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "567ce66a",
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "\n",
    "def generate_new_distance_matrix(X_distance_matrix, remove_node):\n",
    "    X_distance_matrix_new = X_distance_matrix.copy()\n",
    " \n",
    "    N = len(X_distance_matrix)\n",
    "    for i in range(N):\n",
    "        for j in range(N):\n",
    "            if i == remove_node or j == remove_node:\n",
    "                X_distance_matrix_new[i,j] = np.inf\n",
    "\n",
    "    X_distance_matrix_new[remove_node,remove_node] = 0  \n",
    "    \n",
    "    return X_distance_matrix_new\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "ad74e5d8",
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "def cal_new_APSP_matrix_warm(X_distance_matrix, X_APSP_matrix, remove_node):\n",
    "    N = len(X_distance_matrix)\n",
    "    X_APSP_matrix_new = X_APSP_matrix.copy()\n",
    "    remaining_list = [i for i in np.arange(N) if i != remove_node]\n",
    "\n",
    "    need_update_list, how_many = cal_need_update_list_algo_11(remove_node, X_APSP_matrix, X_distance_matrix)\n",
    "    \n",
    "    Cost = np.round(how_many/(N - 1), 3)\n",
    "    \n",
    "    print(f\"The cost for re-caculating the APSP matrix is: {Cost}.\")\n",
    "\n",
    "    X_distance_matrix_new = generate_new_distance_matrix(X_distance_matrix, remove_node)\n",
    " \n",
    "    total = 0\n",
    "    num_equal = 0\n",
    " \n",
    "    for i in remaining_list:  \n",
    "        if len(need_update_list[i]) > 0:\n",
    "            temp = dijkstra_one_to_all(X_distance_matrix_new, i, need_update_list[i], remove_node)\n",
    "            for j in need_update_list[i]:\n",
    "                X_APSP_matrix_new[i,j] = temp[j]\n",
    "                total += 1\n",
    "                if X_APSP_matrix[i,j] == X_APSP_matrix_new[i,j]:\n",
    "                    num_equal += 1\n",
    " \n",
    "    for i in range(N):\n",
    "        for j in range(N):\n",
    "            if i == remove_node or j == remove_node:\n",
    "                X_APSP_matrix_new[i,j] = np.inf\n",
    "\n",
    "    X_APSP_matrix_new[remove_node,remove_node] = 0\n",
    "    \n",
    "\n",
    "    print(f\"Total number of recalculation: \", total)\n",
    "    print(f\"Number of equal to previous value: \", num_equal)\n",
    "    \n",
    "    return X_APSP_matrix_new \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "6a936eee",
   "metadata": {},
   "outputs": [],
   "source": [
    "def cal_need_update_list_algo_11(remove_node, X_APSP_matrix, X_distance_matrix):\n",
    "    N = len(X_APSP_matrix)\n",
    "    removal = remove_node\n",
    "    remaining_list = [i for i in np.arange(N) if i != removal]\n",
    "    need_update_list = [[] for i in range(N)]\n",
    "    how_many_counter = np.zeros(N)\n",
    "    for i in remaining_list:\n",
    "        for j in remaining_list:\n",
    "            if i != j:\n",
    "                if X_APSP_matrix[i,j] >= X_APSP_matrix[i,removal] + X_APSP_matrix[removal,j]:\n",
    "                    key_node_list = cal_key_node_list_one(i, j, X_distance_matrix, X_APSP_matrix)\n",
    "                    if remove_node in key_node_list:   \n",
    "                        need_update_list[i].append(j)\n",
    "                        how_many_counter[i] += 1\n",
    "    \n",
    "    how_many = np.sum(how_many_counter > 0)\n",
    "    \n",
    "    return need_update_list, how_many"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "8dcd5715",
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "def cal_all_paths_warm_start(i, j, X_APSP_matrix, X_distance_matrix):\n",
    "    candidate_node_list = cal_candidate_node_list(i, j, X_APSP_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",
    "\n",
    "    temp_list = [q for q in range(K) if q not in path]\n",
    "\n",
    "    if len(temp_list) > 0:\n",
    "        previous_nodes = dijkstra_cal_previous_nodes(small_matrix, 0)\n",
    "    \n",
    "    # previous_nodes = dijkstra_cal_previous_nodes(small_matrix, 0)\n",
    "\n",
    "    for m in temp_list:\n",
    "        \n",
    "        temp_path1 = dijkstra_show_path_from_previous_nodes(previous_nodes, 0, m)\n",
    " \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\n",
    "\n",
    "def dijkstra_cal_previous_nodes(adj_matrix, start):\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)]  \n",
    "\n",
    "    while priority_queue:\n",
    "        current_distance, current_node = heapq.heappop(priority_queue)\n",
    "\n",
    "        if current_distance > distances[current_node]:\n",
    "            continue\n",
    " \n",
    "        for neighbor, weight in enumerate(adj_matrix[current_node]):\n",
    "            if weight > 0:  \n",
    "                distance = current_distance + weight\n",
    " \n",
    "                if distance < distances[neighbor]:\n",
    "                    distances[neighbor] = distance\n",
    "                    previous_nodes[neighbor] = current_node\n",
    "                    heapq.heappush(priority_queue, (distance, neighbor))\n",
    " \n",
    "    return previous_nodes\n",
    "\n",
    "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)]  \n",
    "\n",
    "    while priority_queue:\n",
    "        current_distance, current_node = heapq.heappop(priority_queue)\n",
    "\n",
    "        if current_node == end:\n",
    "            break\n",
    "\n",
    "        if current_distance > distances[current_node]:\n",
    "            continue\n",
    "\n",
    "        for neighbor, weight in enumerate(adj_matrix[current_node]):\n",
    "            if weight > 0:  \n",
    "                distance = current_distance + weight\n",
    "\n",
    "                \n",
    "                if distance < distances[neighbor]:\n",
    "                    distances[neighbor] = distance\n",
    "                    previous_nodes[neighbor] = current_node\n",
    "                    heapq.heappush(priority_queue, (distance, neighbor))\n",
    "  \n",
    "    path = []\n",
    "    current = end\n",
    "    while current != -1:\n",
    "        path.append(current)\n",
    "        current = previous_nodes[current]\n",
    "    path.reverse()\n",
    "\n",
    "    return path if path[0] == start else []\n",
    "\n",
    "\n",
    "def cal_candidate_node_list(i, j, X_APSP_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 X_APSP_matrix[i,j] < X_APSP_matrix[i,t] + X_APSP_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",
    "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",
    "\n",
    "\n",
    "def dijkstra_show_path_from_previous_nodes(previous_nodes, start, end): \n",
    "    path = []\n",
    "    current = end\n",
    "    while current != -1:\n",
    "        path.append(current)\n",
    "        current = previous_nodes[current]\n",
    "    path.reverse()\n",
    "    return path if path[0] == start else []\n",
    "\n",
    "\n",
    "def translate_path(path, candidate_node_list):\n",
    "    new_path = [candidate_node_list[i] for i in path]\n",
    "    return new_path\n",
    "\n",
    "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_key_node_list_one(i, j, X_distance_matrix, X_APSP_matrix):\n",
    "    if i == j:\n",
    "        key_node_list = []\n",
    "    else:\n",
    "        all_paths_list = cal_all_paths_warm_start(i, j, X_APSP_matrix, X_distance_matrix)\n",
    "        key_node_list = set(all_paths_list[0])\n",
    "        for m, path_m in enumerate(all_paths_list):\n",
    "            if m > 0:\n",
    "                aaa = set(path_m)\n",
    "                key_node_list = key_node_list.intersection(aaa)\n",
    "        key_node_list = list(key_node_list)\n",
    "        key_node_list.remove(i)\n",
    "        key_node_list.remove(j)\n",
    "\n",
    "    return key_node_list"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "baf2a684",
   "metadata": {},
   "outputs": [],
   "source": [
    "# N = 100\n",
    "\n",
    "# X_distance_matrix = create_distance_matrix(N)\n",
    "\n",
    "X_distance_matrix = np.loadtxt(\"./data/X_100_distance_matrix.csv\", delimiter=\",\")\n",
    " \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "4dd5a366",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  0., 952., 405., ..., 208., 152., 808.],\n",
       "       [505.,   0., 557., ..., 912., 737.,  17.],\n",
       "       [809., 582.,   0., ..., 932., 459., 276.],\n",
       "       ...,\n",
       "       [821., 183., 596., ...,   0., 984., 276.],\n",
       "       [176., 112., 381., ..., 410.,   0., 241.],\n",
       "       [314., 171., 225., ...,  99., 796.,   0.]])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_distance_matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "bd1a3bf8",
   "metadata": {},
   "outputs": [],
   "source": [
    "remove_node = 3 \n",
    "\n",
    "\n",
    "\n",
    "X_APSP_matrix = floyd_warshall(X_distance_matrix)\n",
    "\n",
    "X_distance_matrix_new = generate_new_distance_matrix(X_distance_matrix, remove_node)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "07ac519c",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "3cb01799",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The cost for re-caculating the APSP matrix is: 0.434.\n",
      "Total number of recalculation:  269\n",
      "Number of equal to previous value:  0\n"
     ]
    }
   ],
   "source": [
    "start = time.time()\n",
    "X_APSP_matrix_new_warm = cal_new_APSP_matrix_warm(X_distance_matrix, X_APSP_matrix, remove_node)\n",
    "end = time.time()\n",
    "\n",
    "\n",
    "time_used1_warm = end - start\n",
    "time_used1_warm = np.round(time_used1_warm, 3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "d7b48ac1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Time used: 0.202s\n"
     ]
    }
   ],
   "source": [
    "print(f\"Time used: {time_used1_warm}s\" )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "bb74a346",
   "metadata": {},
   "outputs": [],
   "source": [
    "start = time.time()\n",
    "X_APSP_matrix_new_floyd_warshall = floyd_warshall(X_distance_matrix_new)\n",
    "end = time.time()\n",
    "\n",
    "\n",
    "time_used2_floyd = end - start\n",
    "time_used2_floyd = np.round(time_used2_floyd, 3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "49f88b7f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Time used: 1.051s\n"
     ]
    }
   ],
   "source": [
    "print(f\"Time used: {time_used2_floyd}s\" )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "f0b7e12b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Ratio: 0.19\n"
     ]
    }
   ],
   "source": [
    " \n",
    "print(f\"Ratio: {np.round(time_used1_warm/time_used2_floyd, 2)}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "b67f94ea",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n"
     ]
    }
   ],
   "source": [
    "print(np.allclose(X_APSP_matrix_new_warm, X_APSP_matrix_new_floyd_warshall))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ce867f1a",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "a8f33b58",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0. 56. 56. inf 77. 45. 69. 49. 47. 49.]\n",
      "(100, 100)\n"
     ]
    }
   ],
   "source": [
    "print(X_APSP_matrix_new_warm[0,:10])\n",
    "\n",
    "print(X_APSP_matrix_new_warm.shape)"
   ]
  }
 ],
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