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Home / Proceedings / Proceedings of the AAAI Conference on Artificial Intelligence, 36 / No. 9: AAAI-22 Technical Tracks 9

Generalized Stochastic Matching

February 1, 2023

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Authors

Alireza Farhadi

University of Maryland


Jacob Gilbert

University of Maryland


MohammadTaghi Hajiaghayi

University of Maryland


DOI:

10.1609/aaai.v36i9.21239


Abstract:

In this paper, we generalize the recently studied stochastic matching problem to more accurately model a significant medical process, kidney exchange, and several other applications. Up until now the stochastic matching problem that has been studied was as follows: given a graph G= (V,E), each edge is included in the realized sub-graph of G independently with probability pe, and the goal is to find a degree-bounded sub-graph Q of G that has an expected maximum matching that approximates the expected maximum matching of G. This model does not account for possibilities of vertex dropouts, which can be found in several applications, e.g. in kidney exchange when donors or patients opt out of the exchange process as well as in online freelancing and online dating when online profiles are found to be faked. Thus, we will study a more generalized model of stochastic matching in which vertices and edges are both realized independently with some probabilities pv, pe, respectively, which more accurately fits important applications than the previously studied model. We will discuss the first algorithms and analysis for this generalization of the stochastic matching model and prove that they achieve good approximation ratios. In particular, we show that the approximation factor of a natural algorithm for this problem is at least 0.6568 in unweighted graphs, and 1/2+ε in weighted graphs for some constant ε >0. We further improve our result for unweighted graphs to 2/3 using edge degree constrained sub-graphs (EDCS).

Topics: AAAI

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HOW TO CITE:

Alireza Farhadi||Jacob Gilbert||MohammadTaghi Hajiaghayi Generalized Stochastic Matching Proceedings of the AAAI Conference on Artificial Intelligence (2022) 10008-10015.

Alireza Farhadi||Jacob Gilbert||MohammadTaghi Hajiaghayi Generalized Stochastic Matching AAAI 2022, 10008-10015.

Alireza Farhadi||Jacob Gilbert||MohammadTaghi Hajiaghayi (2022). Generalized Stochastic Matching. Proceedings of the AAAI Conference on Artificial Intelligence, 10008-10015.

Alireza Farhadi||Jacob Gilbert||MohammadTaghi Hajiaghayi. Generalized Stochastic Matching. Proceedings of the AAAI Conference on Artificial Intelligence 2022 p.10008-10015.

Alireza Farhadi||Jacob Gilbert||MohammadTaghi Hajiaghayi. 2022. Generalized Stochastic Matching. "Proceedings of the AAAI Conference on Artificial Intelligence". 10008-10015.

Alireza Farhadi||Jacob Gilbert||MohammadTaghi Hajiaghayi. (2022) "Generalized Stochastic Matching", Proceedings of the AAAI Conference on Artificial Intelligence, p.10008-10015

Alireza Farhadi||Jacob Gilbert||MohammadTaghi Hajiaghayi, "Generalized Stochastic Matching", AAAI, p.10008-10015, 2022.

Alireza Farhadi||Jacob Gilbert||MohammadTaghi Hajiaghayi. "Generalized Stochastic Matching". Proceedings of the AAAI Conference on Artificial Intelligence, 2022, p.10008-10015.

Alireza Farhadi||Jacob Gilbert||MohammadTaghi Hajiaghayi. "Generalized Stochastic Matching". Proceedings of the AAAI Conference on Artificial Intelligence, (2022): 10008-10015.

Alireza Farhadi||Jacob Gilbert||MohammadTaghi Hajiaghayi. Generalized Stochastic Matching. AAAI[Internet]. 2022[cited 2023]; 10008-10015.


ISSN: 2374-3468


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Copyright 2022, Association for the Advancement of
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