In bipartite matching problems, vertices on one side of a bipartite
graph are paired with those on the other. In its online
variant, one side of the graph is available offline, while the
vertices on the other side arrive online. When a vertex arrives,
an irrevocable and immediate decision should be made
by the algorithm; either match it to an available vertex or
drop it. Examples of such problems include matching workers
to firms, advertisers to keywords, organs to patients, and
so on. Much of the literature focuses on maximizing the total
relevance—modeled via total weight—of the matching.
However, in many real-world problems, it is also important
to consider contributions of diversity: hiring a diverse pool of
candidates, displaying a relevant but diverse set of ads, and so
on. In this paper, we propose the Online Submodular Bipartite
Matching (OSBM) problem, where the goal is to maximize
a submodular function f over the set of matched edges.
This objective is general enough to capture the notion of both
diversity (e.g., a weighted coverage function) and relevance
(e.g., the traditional linear function)—as well as many other
natural objective functions occurring in practice (e.g., limited
total budget in advertising settings). We propose novel algorithms
that have provable guarantees and are essentially optimal
when restricted to various special cases. We also run
experiments on real-world and synthetic datasets to validate
our algorithms.
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An Algorithm for Multi-Attribute Diverse Matching
Bipartite b-matching, where agents on one side of a market are matched to one or more agents or items on the other, is a classical model that is used in myriad application areas such as healthcare, advertising, education, and general resource allocation. Traditionally, the primary goal of such models is to maximize a linear function of the constituent matches (e.g., linear social welfare maximization) subject to some constraints. Recent work has studied a new goal of balancing whole-match diversity and economic efficiency, where the objective is instead a monotone submodular function over the matching. Basic versions of this problem are solvable in polynomial time. In this work, we prove that the problem of simultaneously maximizing diversity along several features (e.g., country of citizenship, gender, skills) is NP-hard. To address this problem, we develop the first combinatorial algorithm that constructs provably-optimal diverse b-matchings in pseudo-polynomial time. We also provide a Mixed-Integer Quadratic formulation for the same problem and show that our method guarantees optimal solutions and takes less computation time for a reviewer assignment application. The source code is made available at https://github.com/faezahmed/diverse_matching.
more » « less- NSF-PAR ID:
- 10214101
- Date Published:
- Journal Name:
- International Joint Conference on Artificial Intelligence (IJCAI)
- Page Range / eLocation ID:
- 3 to 9
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.24963/ijcai.2020/1
