Online bipartite matching is a fundamental problem in online optimization, extensively studied both in its integral and fractional forms due to its theoretical significance and practical applications, such as online advertising and resource allocation. Motivated by recent progress in learning-augmented algorithms, we study online bipartite fractional matching when the algorithm is given advice in the form of a suggested matching in each iteration. We develop algorithms for both the vertex-weighted and unweighted variants that provably dominate the naive "coin flip" strategy of randomly choosing between the advice-following and advice-free algorithms. Moreover, our algorithm for the vertex-weighted setting extends to the AdWords problem under the small bids assumption, yielding a significant improvement over the seminal work of Mahdian, Nazerzadeh, and Saberi (EC 2007, TALG 2012). Complementing our positive results, we establish a hardness bound on the robustness-consistency tradeoff that is attainable by any algorithm.
Joint work with Davin Choo (Harvard) and Billy Jin (Purdue).

Yongho Shin is a postdoctoral researcher in the Combinatorial Optimization Group at the Institute of Computer Science, University of Wrocław, Poland, mentored by Prof. Jarek Byrka. He received his PhD degree in Computer Science from Yonsei University, advised by Prof. Hyung-Chan An. His research interest is in theoretical computer science, with slight emphasis on approximation/online/learning-augmented algorithms for combinatorial optimization problems.