Risk-Averse Matchings over Uncertain Graph Databases

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11052)


In this work we study a problem that naturally arises in the context of several important applications, such as online dating, kidney exchanges, and team formation.

Given an uncertain, weighted (hyper)graph, how can we efficiently find a (hyper)matching with high expected reward, and low risk?

We introduce a novel formulation for finding matchings with maximum expected reward and bounded risk under a general model of uncertain weighted (hyper)graphs. Given that our optimization problem is NP-hard, we turn our attention to designing efficient approximation algorithms. For the case of uncertain weighted graphs, we provide a \(\frac{1}{3}\)-approximation algorithm, and a \(\frac{1}{5}\)-approximation algorithm with near optimal run time. For the case of uncertain weighted hypergraphs, we provide a \(\varOmega (\frac{1}{k})\)-approximation algorithm, where k is the rank of the hypergraph (i.e., any hyperedge includes at most k nodes), that runs in almost (modulo log factors) linear time.

We complement our theoretical results by testing our algorithms on a wide variety of synthetic experiments, where we observe in a controlled setting interesting findings on the trade-off between reward, and risk. We also provide an application of our formulation for providing recommendations of teams that are likely to collaborate, and have high impact. Code related to this paper is available at:


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Boston UniversityBostonUSA
  2. 2.Harvard UniversityCambridgeUSA
  3. 3.Yale UniversityNew HavenUSA

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