Improved Analysis of RANKING for Online Vertex-Weighted Bipartite Matching

This repository contains the code for the paper "Improved Analysis of RANKING for Online Vertex-Weighted Bipartite Matching". (https://arxiv.org/abs/2007.12823)

Usage

Warning: With the values of the parameters below, the code may take a long time to run. You can replace them with smaller numbers to experiment.

1. Run the code in lp.ipynb to generate the file g_values_50.txt, which contains the values of g on a 50x50 discretized grid.
2. Run the command python fill_g_table_parallel.py 16834 to compute a 16384x16384 table g_table_16384.txt with the values of g on the finer discretized grid.
3. Run the command python fill_ss_table_parallel.py 16834 1024 to compute a 1024x1024x1024 table ss_table_1024.npy with the values of the inner minimum.
4. Run the command python evaluate_cr.py 16384 1024 16384 to evaluate the bound in Theorem 1, using the above precomputed tables.

Upper bound

The file LP Upper Bound.ipynb contains the code to create and solve the LP described in Section 7 of the paper, which provides an upper bound on the best competitive ratio obtainable using our methods.