@article{
    SeAO05b,
    author = "Seitz, Sakari and Alava, Mikko and Orponen, Pekka",
    note = "",
    title = "Focused local search for random 3-satisfiability",
    url = "http://dx.doi.org/10.1088/1742-5468/2005/06/P06006",
    journal = "Journal of Statistical Mechanics: Theory and Experiment",
    number = "",
    abstract = "A local search algorithm solving an NP-complete optimisation problem can be viewed as a stochastic process moving in an 'energy landscape' towards eventually finding an optimal solution. For the random 3-satisfiability problem, the heuristic of {\em focusing} the local moves on the presently unsatisfied clauses is known to be very effective: the time to solution has been observed to grow only linearly in the number of variables, for a given clauses-to-variables ratio $\alpha$ sufficiently far below the critical satisfiability threshold $\alpha_c \approx 4.27$. We present numerical results on the behaviour of three focused local search algorithms for this problem, considering in particular the characteristics of a focused variant of simple Metropolis dynamics. We estimate the optimal value for the ``temperature'' parameter $\eta$ for this algorithm, such that its linear-time regime extends as close to $\alpha_c$ as possible. Similar parameter optimisation is performed also for the well-known WalkSAT algorithm and for the less studied, but very well performing Focused Record-to-Record Travel method. We observe that with an appropriate choice of parameters, the linear time regime for each of these algorithms seems to extend well into ratios $\alpha > 4.2$ --- much further than has so far been generally assumed. We discuss the statistics of solution times for the algorithms, relate their performance to the process of ``whitening'', and present some conjectures on the shape of their computational phase diagrams.",
    month = "June",
    volume = "P06006",
    flags = "public",
    year = "2005",
    keywords = "satisfiability, local search, phase transition, WalkSAT, Metropolis algorithm, Record to Record Travel",
    pages = "1--27"
}