Online Vertex-Weighted Bipartite Matching: Beating 1-1/e with Random Arrivals

Zhiyi Huang, Zhihao Gavin Tang, Xiaowei Wu, Yuhao Zhang, Michael Wagner
2018 International Colloquium on Automata, Languages and Programming  
We introduce a weighted version of the ranking algorithm by Karp et al. (STOC 1990), and prove a competitive ratio of 0.6534 for the vertex-weighted online bipartite matching problem when online vertices arrive in random order. Our result shows that random arrivals help beating the 1-1/e barrier even in the vertex-weighted case. We build on the randomized primal-dual framework by Devanur et al. (SODA 2013) and design a two dimensional gain sharing function, which depends not only on the rank of
more » ... the offline vertex, but also on the arrival time of the online vertex. To our knowledge, this is the first competitive ratio strictly larger than 1-1/e for an online bipartite matching problem achieved under the randomized primal-dual framework. Our algorithm has a natural interpretation that offline vertices offer a larger portion of their weights to the online vertices as time goes by, and each online vertex matches the neighbor with the highest offer at its arrival.
doi:10.4230/lipics.icalp.2018.79 dblp:conf/icalp/0002TWZ18 fatcat:jh5owerumzhg3lkmt672c65mtm