Online Bipartite Matching with Reusable Resources

34 Pages Posted: 31 Oct 2022

See all articles by Steven Delong

Steven Delong

Google Inc.

Alireza Farhadi

Carnegie Mellon University - School of Computer Science

Rad Niazadeh

University of Chicago - Booth School of Business

Balasubramanian Sivan

Google Inc., New York

Rajan Udwani

UC Berkeley

Date Written: October 23, 2022

Abstract

We study the classic online bipartite matching problem with a twist: offline vertices, called resources, are reusable. In particular, when a resource is matched to an online vertex it is unavailable for a deterministic time duration d after which it becomes available again for a re-match. Thus, a resource can be matched to many different online vertices over a period of time. While recent work on the problem have resolved the asymptotic case where we have large starting inventory (i.e., many copies) of every resource, we consider the (more general) case of unit inventory} and give the first algorithms that are provably better than the naive greedy approach which has a competitive ratio of (exactly) 0.5. Our first algorithm, which achieves a competitive ratio of 0.589, generalizes the classic RANKING algorithm for online bipartite matching of non-reusable resources (Karp et al., 1990), by "reranking" resources independently over time. While reranking resources frequently has the same worst case performance as greedy, we show that reranking intermittently on a periodic schedule succeeds in addressing reusability of resources and performs significantly better than greedy in the worst case. Our second algorithm, which achieves a competitive ratio of 0.505, is a primal-dual randomized algorithm that works by suggesting up to two resources as candidate matches for every online vertex, and then breaking the tie to make the final matching selection in a randomized correlated fashion over time. As a key component of our algorithm, we suitably adapt and extend the powerful technique of online correlated selection (Fahrbach et al., 2020) to reusable resources, in order to induce negative correlation in our tie breaking step and to beat the competitive ratio of 0.5. Both of our results also extend to the case where offline vertices have weights.

Keywords: Online resource allocation, matching, reusable resources, revenue management

Suggested Citation

Delong, Steven and Farhadi, Alireza and Niazadeh, Rad and Sivan, Balasubramanian and Udwani, Rajan, Online Bipartite Matching with Reusable Resources (October 23, 2022). Available at SSRN: https://ssrn.com/abstract=4256240 or http://dx.doi.org/10.2139/ssrn.4256240

Steven Delong

Google Inc.

Alireza Farhadi

Carnegie Mellon University - School of Computer Science

Rad Niazadeh (Contact Author)

University of Chicago - Booth School of Business ( email )

5807 S Woodlawn Ave
Chicago, IL 60637

HOME PAGE: http://radniazadeh.github.io/

Balasubramanian Sivan

Google Inc., New York ( email )

111 8th Ave
New York, NY 10011
United States

Rajan Udwani

UC Berkeley ( email )

Etcheverry Hall
Berkeley, CA Almeda 94720
United States

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Downloads
21
Abstract Views
138
PlumX Metrics