plot_theoretical_complexities.ipynb

{
  "cells": [
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "id": "hNCwRjijgHM8"
      },
      "outputs": [],
      "source": [
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "import operator as op\n",
        "from functools import reduce"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {
        "id": "cu990X0LumT-"
      },
      "outputs": [],
      "source": [
        "def ncr(n, r):\n",
        "    r = min(r, n-r)\n",
        "    numer = reduce(op.mul, range(n, n-r, -1), 1)\n",
        "    denom = reduce(op.mul, range(1, r+1), 1)\n",
        "    return numer // denom"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ZZEWgosegHDb",
        "outputId": "b0acf7d8-2e74-4525-c922-d79fe64dba0d"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([ 1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17,\n",
              "       18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34,\n",
              "       35, 36, 37, 38, 39, 40])"
            ]
          },
          "execution_count": 3,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "n_max = 41\n",
        "n=np.arange(1,n_max).astype(np.int64)\n",
        "n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "P45rs4HioS24"
      },
      "source": [
        "----------------------------------------------------------------------------------------------------------------------------------------------------------------\n",
        "##C-LINK: \n",
        "$$\\mathcal{O}(n^3)$$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "WL-s7mRAXLoF",
        "outputId": "2a6db59c-1dc7-4b48-82b0-a6007194b6f8"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([ 0.        ,  3.        ,  4.7548875 ,  6.        ,  6.96578428,\n",
              "        7.7548875 ,  8.42206477,  9.        ,  9.509775  ,  9.96578428,\n",
              "       10.37829486, 10.7548875 , 11.10131915, 11.42206477, 11.72067179,\n",
              "       12.        , 12.26238852, 12.509775  , 12.74378254, 12.96578428,\n",
              "       13.17695227, 13.37829486, 13.57068587, 13.7548875 , 13.93156857,\n",
              "       14.10131915, 14.26466251, 14.42206477, 14.57394299, 14.72067179,\n",
              "       14.86258893, 15.        , 15.13318236, 15.26238852, 15.38784905,\n",
              "       15.509775  , 15.6283601 , 15.74378254, 15.85620666, 15.96578428])"
            ]
          },
          "execution_count": 4,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "clink = 3*np.log2(n)\n",
        "clink"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3e3jHHY1omTK"
      },
      "source": [
        "##BOSS/ IDP:  \n",
        "$$\\sum_{s=1}^n \\binom{n}{s} 2^{s-1} \\rightarrow \\mathcal{O}(3^n)$$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "E1eD0yXKoCRT",
        "outputId": "7a147540-3a83-460b-9140-dc3fc468b053"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([ 1.5849625 ,  3.169925  ,  4.7548875 ,  6.33985   ,  7.9248125 ,\n",
              "        9.509775  , 11.09473751, 12.67970001, 14.26466251, 15.84962501,\n",
              "       17.43458751, 19.01955001, 20.60451251, 22.18947501, 23.77443751,\n",
              "       25.35940001, 26.94436251, 28.52932501, 30.11428751, 31.69925001,\n",
              "       33.28421252, 34.86917502, 36.45413752, 38.03910002, 39.62406252,\n",
              "       41.20902502, 42.79398752, 44.37895002, 45.96391252, 47.54887502,\n",
              "       49.13383752, 50.71880002, 52.30376252, 53.88872502, 55.47368753,\n",
              "       57.05865003, 58.64361253, 60.22857503, 61.81353753, 63.39850003])"
            ]
          },
          "execution_count": 5,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "boss_idp = n*np.log2(3)\n",
        "boss_idp"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "x2mfjuXKovKt"
      },
      "source": [
        "##CFSS/ IP:  \n",
        "$$\\mathcal{O}(n^n)$$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ios8M-LwoG6J",
        "outputId": "29166bd9-9d33-4d77-ba1e-1be2cf26cc80"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([  0.        ,   2.        ,   4.7548875 ,   8.        ,\n",
              "        11.60964047,  15.509775  ,  19.65148445,  24.        ,\n",
              "        28.52932501,  33.21928095,  38.05374781,  43.01955001,\n",
              "        48.10571634,  53.30296891,  58.60335893,  64.        ,\n",
              "        69.4868683 ,  75.05865003,  80.71062276,  86.4385619 ,\n",
              "        92.23866588,  98.10749561, 104.04192499, 110.03910002,\n",
              "       116.09640474, 122.21143267, 128.38196256, 134.60593782,\n",
              "       140.88144886, 147.20671787, 153.58008562, 160.        ,\n",
              "       166.46500594, 172.9737366 , 179.52490559, 186.11730005,\n",
              "       192.74977453, 199.42124551, 206.13068654, 212.8771238 ])"
            ]
          },
          "execution_count": 6,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "ip_cfss = n*np.log2(n)\n",
        "ip_cfss"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "75JYv-Sbo7CI"
      },
      "source": [
        "##BILP-Q: \n",
        "$$\\mathcal{O}((2^n-1)+p*(3*(2^n-1)+2*(2^n)-1))$$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "metadata": {
        "id": "Zros0Jo9n55K"
      },
      "outputs": [],
      "source": [
        "p_min = 1"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "6vz84-ehnFt9",
        "outputId": "db894bb0-3add-40b0-97a8-86a3b9d8f90d"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([ 2.5849625 ,  4.169925  ,  5.39231742,  6.4918531 ,  7.53915881,\n",
              "        8.56224242,  9.57364719, 10.57931594, 11.58214198, 12.58355293,\n",
              "       13.58425789, 14.58461024, 15.58478638, 16.58487444, 17.58491847,\n",
              "       18.58494049, 19.58495149, 20.584957  , 21.58495975, 22.58496112,\n",
              "       23.58496181, 24.58496216, 25.58496233, 26.58496241, 27.58496246,\n",
              "       28.58496248, 29.58496249, 30.5849625 , 31.5849625 , 32.5849625 ,\n",
              "       33.5849625 , 34.5849625 , 35.5849625 , 36.5849625 , 37.5849625 ,\n",
              "       38.5849625 , 39.5849625 , 40.5849625 , 41.5849625 , 42.5849625 ])"
            ]
          },
          "execution_count": 8,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "bilpq = np.log2((2**(n) - 1) + p_min * (3 * (2**n - 1) + 2*(2**(n) - 1)))\n",
        "bilpq"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6j0Th9NJp0ux"
      },
      "source": [
        "##CSG over graphs (by Voice et. al):  \n",
        "$$\\mathcal{O}((n^2)*\\binom{(n^2)}{n}$$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 9,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "LzTwhZuqdKmk",
        "outputId": "f867e29d-35ce-413b-91b4-8b0145937d09"
      },
      "outputs": [
        {
          "name": "stderr",
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:4: RuntimeWarning: overflow encountered in long_scalars\n",
            "  after removing the cwd from sys.path.\n",
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:4: RuntimeWarning: invalid value encountered in log2\n",
            "  after removing the cwd from sys.path.\n"
          ]
        }
      ],
      "source": [
        "csg_over_graphs_voice = []\n",
        "for n_i in n:\n",
        "  try:\n",
        "    csg_over_graphs_voice.append(np.log2((n_i**2)*(ncr(n_i**2,n_i))))\n",
        "  except:\n",
        "    csg_over_graphs_voice.append(np.nan)\n",
        "    continue\n",
        "csg_over_graphs_voice = np.array(csg_over_graphs_voice)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 10,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "dl49uOExfRme",
        "outputId": "6771c6e7-27eb-4963-9afd-f2a1eb11b870"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([ 0.        ,  4.5849625 ,  9.56224242, 14.82972274, 20.34109528,\n",
              "       26.06333319, 31.97087445, 38.04341021, 44.26448872, 50.62055294,\n",
              "       57.10026068,         nan, 60.1486507 ,         nan,         nan,\n",
              "               nan,         nan,         nan,         nan,         nan,\n",
              "               nan,         nan,         nan,         nan,         nan,\n",
              "               nan,         nan,         nan,         nan,         nan,\n",
              "               nan,         nan,         nan,         nan,         nan,\n",
              "               nan,         nan,         nan,         nan,         nan])"
            ]
          },
          "execution_count": 10,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "csg_over_graphs_voice"
      ]
    },
    {
      "attachments": {},
      "cell_type": "markdown",
      "metadata": {
        "id": "Vm5ibNmPrZGD"
      },
      "source": [
        "##GCS-Q: \n",
        "$$\\mathcal{O}(n^2)$$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 11,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ZtPeZPPkoAzU",
        "outputId": "a3344245-912e-4037-cffe-5aa4bcfde37f"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([ 0.        ,  2.        ,  3.169925  ,  4.        ,  4.64385619,\n",
              "        5.169925  ,  5.61470984,  6.        ,  6.33985   ,  6.64385619,\n",
              "        6.91886324,  7.169925  ,  7.40087944,  7.61470984,  7.81378119,\n",
              "        8.        ,  8.17492568,  8.33985   ,  8.49585503,  8.64385619,\n",
              "        8.78463485,  8.91886324,  9.04712391,  9.169925  ,  9.28771238,\n",
              "        9.40087944,  9.509775  ,  9.61470984,  9.71596199,  9.81378119,\n",
              "        9.90839262, 10.        , 10.08878824, 10.17492568, 10.25856603,\n",
              "       10.33985   , 10.41890673, 10.49585503, 10.57080444, 10.64385619])"
            ]
          },
          "execution_count": 11,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "gcs_q = 2*np.log2(n)\n",
        "gcs_q"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6Fa8SHVduHKW"
      },
      "source": [
        "##Plot the complexities"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 23,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 420
        },
        "id": "DfAfKtYbpElE",
        "outputId": "4ecd6ad3-a2e4-4aa0-a4f7-296a750aa786"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 720x432 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "#plt.tight_layout()\n",
        "font=24\n",
        "plt.figure(figsize=(10,6))\n",
        "\n",
        "plt.plot(n, ip_cfss, label = 'CFSS/KGC', color='red', linestyle = 'None', marker = 'x')\n",
        "plt.plot(n, boss_idp, label = 'IDP/BOSS/DyCE', color='magenta', linestyle = 'None', marker = '+')\n",
        "plt.plot(n, bilpq, label = 'BILP-Q (QAOA for $p=1$)', color='cyan', linestyle = 'dashdot', marker = 'None')\n",
        "plt.plot(n, clink, label = 'C-Link', color='brown', linestyle = 'dotted', marker = 'None')\n",
        "plt.plot(n, gcs_q, label = 'GCS-Q', color='green', linestyle = 'None', marker = '*')\n",
        "\n",
        "\n",
        "plt.xlabel(r'No. of Agents $(n)$' ,fontdict={'fontsize':font})\n",
        "plt.ylabel(r'(log scale) Time Complexity', fontdict={'fontsize':font})\n",
        "plt.ylim(-5, 50)\n",
        "plt.grid(alpha=0.3)\n",
        "plt.ticklabel_format(style='sci', axis='y', scilimits=(0,0))\n",
        "\n",
        "\n",
        "plt.legend(fontsize=font, bbox_to_anchor=(1.01,.8), ncol =1)\n",
        "plt.xticks(np.arange(0, n_max, 5), fontsize=font)\n",
        "plt.yticks([0, 10, 20, 30, 40, 50, 60],fontsize =font)\n",
        "plt.tick_params(labelsize=12)\n",
        "plt.savefig('theoretical_complexities.png', bbox_inches='tight', dpi =400)\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 13,
      "metadata": {
        "id": "OdOgamsMvNKP"
      },
      "outputs": [],
      "source": []
    }
  ],
  "metadata": {
    "colab": {
      "collapsed_sections": [],
      "provenance": []
    },
    "kernelspec": {
      "display_name": "Python 3",
      "name": "python3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}