Subquadratic Algorithms for Succinct Stable Matching

  • Daniel Moeller
  • Ramamohan Paturi
  • Stefan Schneider
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9691)

Abstract

We consider the stable matching problem when the preference lists are not given explicitly but are represented in a succinct way and ask whether the problem becomes computationally easier. We give subquadratic algorithms for finding a stable matching in special cases of two very natural succinct representations of the problem, the d-attribute and d-list models. We also give algorithms for verifying a stable matching in the same models. We further show that for \(d = \omega (\log n)\) both finding and verifying a stable matching in the d-attribute model requires quadratic time assuming the Strong Exponential Time Hypothesis. The d-attribute model is therefore as hard as the general case for large enough values of d.

Keywords

Stable matching Attribute model Subquadratic algorithms Conditional lower bounds SETH 

Notes

Acknowledgment

We would like to thank Russell Impagliazzo, Vijay Vazirani, and the anonymous reviewers for helpful discussions and comments.

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Daniel Moeller
    • 1
  • Ramamohan Paturi
    • 1
  • Stefan Schneider
    • 1
  1. 1.University of CaliforniaSan Diego, La JollaUSA

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