2026-07-23T06:06:12Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:9083 2024-03-06T10:43:19Z ddc:004 open_access

Online Vertex-Weighted Bipartite Matching: Beating 1-1/e with Random Arrivals Huang, Zhiyi Tang, Zhihao Gavin Wu, Xiaowei Zhang, Yuhao Vertex Weighted Online Bipartite Matching Randomized Primal-Dual 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 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Zhiyi Huang and Zhihao Gavin Tang and Xiaowei Wu and Yuhao Zhang 2018 Is Part Of LIPIcs, Volume 107, 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ICALP.2018.79 urn:nbn:de:0030-drops-90830 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2018.79 eng https://creativecommons.org/licenses/by/3.0/legalcode