[Aspuru-Guzik group list] arXiv eprint of note on random constraint satisfaction problems

Dear everybody, The paper I mentioned today about spin glass people trying to calculate energy landscapes of random instances of NP-complete optimization problems and trying to find average-case classical polynomial time algorithms for certain classes thereof is the following. I think it's especially valuable as a guide to the literature (though note it's more on the question of "when is annealing efficient" than message-passing / belief-propagation). A Landscape Analysis of Constraint Satisfaction Problems http://arxiv.org/abs/cond-mat/0702546 Authors: <http://arxiv.org/find/cond-mat/1/au:+Krzakala_F/0/1/0/all/0/1>Florent Krzakala, <http://arxiv.org/find/cond-mat/1/au:+Kurchan_J/0/1/0/all/0/1>Jorge Kurchan Comments: 16 pages, 60 citations, 12 figures Subj-class: Statistical Mechanics; Disordered Systems and Neural Networks; Computational Complexity We discuss an analysis of Constraint Satisfaction problems, such as Sphere Packing, K-SAT and Graph Coloring, in terms of an effective energy landscape. Several intriguing geometrical properties of the solution space become in this light familiar in terms of the well-studied ones of rugged (glassy) energy landscapes. A `benchmark' algorithm naturally suggested by this construction finds solutions in polynomial time up to a point beyond the `clustering' and in some cases even the `thermodynamic' transitions. This point has a simple geometric meaning and can be in principle determined with standard Statistical Mechanical methods, thus pushing the analytic bound up to which problems are guaranteed to be easy. We illustrate this for the graph three and four-coloring problem. For Packing problems the present discussion allows to better characterize the `J-point', proposed as a systematic definition of Random Close Packing, and to place it in the context of other theories of glasses. [NB: The tantalizing "to be published" reference in the above paper claiming that "quantum annealing" can't efficiently generate the ground states of a famous type of mean field spin glass is [25] L.F. Cugliandolo, D. Grempel, G. Lozano, and H. Lozza... these 4 people are physicists who've done seminal work in the thermal dynamics of classical and quantum spin glasses.] Regards, Bill