title: Exact solutions for diluted spin glasses and optimization problems.
abstract: We study the low temperature properties of p-spin glass models with finite connectivity and of some optimization problems. Using a one-step functional replica symmetry breaking ansatz we can solve exactly the saddle-point equations for graphs with uniform connectivity. The resulting ground state energy is in perfect agreement with numerical simulations. For fluctuating connectivity graphs, the same ansatz can be used in a variational way: For p-spin models (known as p-XOR-SAT in computer science) it provides the exact configurational entropy together with the dynamical and static critical connectivities (for p = 3, gamma(d) = 0.818, and gamma(s) = 0.918), whereas for hard optimization problems like 3-SAT or Bicoloring it provides new upper bounds for their critical thresholds ( gamma(var)(c) = 4.396 and gamma(var)(c) = 2.149).
authors.affiliation: ICTP, Condensed Matter Group, P.O. Box 586, I-34014 Trieste, Italy.
authors.forename: S
authors.initials: S
authors.lastname: Franz
authors.forename: M
authors.initials: M
authors.lastname: Leone
authors.forename: F
authors.initials: F
authors.lastname: Ricci-Tersenghi
authors.forename: R
authors.initials: R
authors.lastname: Zecchina