{ "cells": [ { "cell_type": "markdown", "id": "11f59bc8", "metadata": {}, "source": [ "# Estimate Step Complexity" ] }, { "cell_type": "markdown", "id": "2dcbf04a", "metadata": {}, "source": [ "The simulator allows to compare Kleinberg's original bounds with simulation and to conjecture tighter bounds." ] }, { "cell_type": "code", "execution_count": 1, "id": "6e246b32", "metadata": {}, "outputs": [], "source": [ "from kleinberg_grid_simulator import estimate_alpha, parallelize\n", "from matplotlib import pyplot as plt" ] }, { "cell_type": "code", "execution_count": 2, "id": "913cc4a6", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "100%|███████████████████████████████████████████████████████████████████████████████████| 41/41 [00:00<00:00, 95.43it/s]\n" ] } ], "source": [ "rr = [r/10 for r in range(0, 41)]\n", "res = parallelize([{'r': r, 'budget': 10000 if r!=2 else 1000} for r in rr], function=estimate_alpha)" ] }, { "cell_type": "code", "execution_count": 3, "id": "f9bc6e01", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(rr, [re[0] for re in res], marker='o', markersize=2, label='Simulation')\n", "plt.plot(rr, [(2-r)/(3-r) if r<2 else ( r-2 if r<3 else 1 ) for r in rr], '--', label=\"Conjectured bounds\")\n", "plt.plot(rr, [(2-r)/3 if r<2 else (r-2)/(r-1) for r in rr], '-.', label=\"Kleinberg's original bounds\")\n", "plt.legend()\n", "plt.xlim([0, 4])\n", "plt.xlabel('$r$')\n", "plt.ylabel('$\\\\alpha$')\n", "plt.ylim([0, 1.1])\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "911ac943", "metadata": {}, "source": [ "Look how far we went to compute the values:" ] }, { "cell_type": "code", "execution_count": 4, "id": "87198a13", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.semilogy(rr, [re[1] for re in res])\n", "plt.xlim([0, 4])\n", "plt.xlabel('$r$')\n", "plt.ylabel('Max value of $n$ considered')\n", "plt.show()" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.10.9" } }, "nbformat": 4, "nbformat_minor": 5 }