{ "cells": [ { "cell_type": "markdown", "id": "e4a9abff", "metadata": {}, "source": [ "# Maximum Weight Stable Set\n", "\n", "## Problem definition\n", "\n", "Given a simple undirected graph $G=(V,E)$ and weights $w \\in \\mathbb{R}^V$, the problem is to find a stable set $S \\subseteq V$ that maximizes $\\sum_{v \\in V} w_v$. We recall that a subset $S \\subseteq V$ is a *stable set* if no two vertices of $S$ are adjacent. This is one of Karp's 21 NP-complete problems.\n", "\n", "## Random instance generator\n", "\n", "The class `MaxWeightStableSetGenerator` can be used to generate random instances of this problem, with user-specified probability distributions. When the constructor parameter `fix_graph=True` is provided, one random Erdős-Rényi graph $G_{n,p}$ is generated during the constructor, where $n$ and $p$ are sampled from user-provided probability distributions `n` and `p`. To generate each instance, the generator independently samples each $w_v$ from the user-provided probability distribution `w`. When `fix_graph=False`, a new random graph is generated for each instance, while the remaining parameters are sampled in the same way.\n", "\n", "## Challenge A\n", "\n", "* Fixed random Erdős-Rényi graph $G_{n,p}$ with $n=200$ and $p=5\\%$\n", "* Random vertex weights $w_v \\sim U(100, 125)$\n", "* 512 training instances, 64 test instances" ] }, { "cell_type": "code", "execution_count": 1, "id": "f99c2c79", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CPU times: user 43.6 s, sys: 1min 42s, total: 2min 25s\n", "Wall time: 1min 56s\n" ] }, { "data": { "image/svg+xml": [ "\n", "\n", "\n" ], "text/plain": [ "

" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%%time\n", "%config InlineBackend.figure_formats = ['svg']\n", "%matplotlib inline\n", "\n", "from miplearn.benchmark import run_benchmarks\n", "from miplearn.problems.stab import MaxWeightStableSetGenerator\n", "from scipy.stats import uniform, randint\n", "\n", "instances = MaxWeightStableSetGenerator(\n", " w=uniform(loc=100.0, scale=25.0),\n", " n=randint(low=150, high=151),\n", " p=uniform(loc=0.05, scale=0.0),\n", " fix_graph=True,\n", ").generate(576)\n", "\n", "run_benchmarks(\n", " train_instances = instances[:512],\n", " test_instances = instances[512:],\n", " n_jobs=16,\n", ");" ] }, { "cell_type": "code", "execution_count": null, "id": "6973a585", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "miplearn", "language": "python", "name": "miplearn" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.10" } }, "nbformat": 4, "nbformat_minor": 5 }