Over the last three decades, the online bipartite matching (OBM) problem has emerged as a central problem in the area of Online Algorithms. Perhaps even more important is its role in the area of Matching-Based Market Design. The resurgence of this area, with the revolutions of the Internet and mobile computing, has opened up novel, path-breaking applications, and OBM has emerged as its paradigmatic algorithmic problem.
In a 1990 joint paper with Richard Karp and Umesh Vazirani, we gave an optimal algorithm, called RANKING, for OBM, achieving a competitive ratio of (1 – 1/e); however, its analysis was difficult to comprehend. Over the years, several researchers simplified the analysis.
We will start by presenting a “textbook quality” proof of RANKING. Its simplicity raises the possibility of extending RANKING all the way to a generalization of OBM called the adwords problem. This problem is both notoriously difficult and very significant, the latter because of its role in the AdWords marketplace of Google. We will show how far this endeavor has gone and what remains. We will also provide a broad overview of the area of Matching-Based Market Design and pinpoint the role of OBM.
Based on:
https://arxiv.org/pdf/2107.10777.pdf
Bio: Vijay Vazirani got his undergraduate degree from MIT in 1979 and his PhD from the University of California, Berkeley in 1983. He is currently a Distinguished Professor at the University of California, Irvine.
Vazirani has made fundamental contributions to several areas of the theory of algorithms, including algorithmic matching theory, approximation algorithms and algorithmic game theory, as well as to complexity theory, in which he established, with Les Valiant, the hardness of unique solution instances of NP-complete problems. Over the last four years, he has been working on algorithms for matching markets. He is one of the founders of algorithmic game theory.
In 2001 he published Approximation Algorithms, which is widely regarded as the definitive book on the topic. In 2007, he published the co-edited book Algorithmic Game Theory. Another co-edited book, Online and Matching-Based Market Design, will be published by Cambridge University Press in early 2022; see its flyer:
https://www.ics.uci.edu/~vazirani/flyer.pdf
