We study the behavior of a heuristic for solving random satisfiability problems by stochastic local search near the satisfiability threshold. The heuristic for average satisfiability (ASAT), is similar to the Focused Metropolis Search heuristic, and shares the property of being focused, i.e., only variables in unsatisfied clauses are updated in each step. It is significantly simpler than the benchmark WALKSAT heuristic. We show that ASAT solves instances as large as N=10(6) in linear time, on average, up to a ratio of 4.21 clauses per variable in random three-satisfiability. For K higher than 3, ASAT appears to solve instances of K -satisfiability up to the Montanari-Ricci-Tersenghi-Parisi full replica symmetry breaking (FSRB) threshold denoted alpha(s)(K) in linear time.

We study the performance of stochastic local search algorithms for random instances of the K-satisfiability (K-SAT) problem. We present a stochastic local search algorithm, ChainSAT, which moves in the energy landscape of a problem instance by never going upwards in energy. ChainSAT is a focused algorithm in the sense that it focuses on variables occurring in unsatisfied clauses. We show by extensive numerical investigations that ChainSAT and other focused algorithms solve large K-SAT instances almost surely in linear time, up to high clause-to-variable ratios ␣; for example, for K ‫؍‬ 4 we observe linear-time performance well beyond the recently postulated clustering and condensation transitions in the solution space. The performance of ChainSAT is a surprise given that by design the algorithm gets trapped into the first local energy minimum it encounters, yet no such minima are encountered. We also study the geometry of the solution space as accessed by stochastic local search algorithms.geometry of solutions ͉ local search ͉ performance ͉ random K-SAT

Abstract-While real-time service assurance is critical for emerging telecom cloud services, understanding and predicting performance metrics for such services is hard. In this paper, we pursue an approach based upon statistical learning whereby the behavior of the target system is learned from observations. We use methods that learn from device statistics and predict metrics for services running on these devices. Specifically, we collect statistics from a Linux kernel of a server machine and predict client-side metrics for a video-streaming service (VLC). The fact that we collect thousands of kernel variables, while omitting service instrumentation, makes our approach serviceindependent and unique. While our current lab configuration is simple, our results, gained through extensive experimentation, prove the feasibility of accurately predicting client-side metrics, such as video frame rates and RTP packet rates, often within 10-15% error (NMAE), also under high computational load and across traces from different scenarios.