Sublinear-time algorithms for monomer-dimer systems on bounded degree graphs

@inproceedings{Lelarge2014SublineartimeAF,
  title={Sublinear-time algorithms for monomer-dimer systems on bounded degree graphs},
  author={Marc Lelarge and Hang Zhou},
  booktitle={Theoretical Computer Science},
  year={2014}
}
  • M. LelargeHang Zhou
  • Published in Theoretical Computer Science 17 August 2012
  • Computer Science, Mathematics

Graph Algorithms: Network Inference and Planar Graph Optimization. (Algorithmes des Graphes: Inférence des Réseaux et Optimisation dans les Graphes Planaires)

For planar graphs, the correlation clustering problem is reduced to two-edge-connected augmentation, and it is shown that both problems, although they are NP-hard, have a polynomial-time approximation scheme.

Bypassing correlation decay for matchings with an application to XORSAT

  • M. Lelarge
  • Mathematics, Computer Science
    2013 IEEE Information Theory Workshop (ITW)
  • 2013
It is shown that monotonicity properties of the maximum matching problem allows us to define solutions for the cavity equations and to identify the `right' solution of these equations and then to compute the asymptotics for the size of a maximum matching.

Topics in random graphs, combinatorial optimization, and statistical inference

The manuscript is made of three chapters presenting three different topics on which I worked with Ph.D. students, and a gentle introduction to the theory of random graphs with an emphasis on contagions on such networks.

Law of large numbers for matchings, extension and applications

The fact that global properties of matchings can be read from local properties of the underlying graph has been rediscovered many times in statistical physics, combinatorics, group theory and

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