Resource title

Optimal myopic algorithms for random 3-SAT

Resource image

image for OpenScout resource :: Optimal myopic algorithms for random 3-SAT

Resource description

Let F3(n,m) be a random 3-SAT formula formed by selecting uniformly, independently and with replacement, m clauses among all 8(nC3) possible 3-clauses over n variables. It has been conjectured that there exists a constant r3 such that, for any ε>0, F3[n,(r3-ε)n] is almost surely satisfiable, but F3[n,(r3+ε)n] is almost surely unsatisfiable. The best lower bounds for the potential value of r3 have come form analyzing rather simple extensions of unit-clause propagation. It was shown by D. Achlioptas (2000) that all these extensions can be cast in a common framework and analyzed in a uniform manner by employing differential equations. We determine optimal algorithms that are expressible in that framework, establishing r3 >3.26. We extend the analysis via differential equations, and make extensive use of a new optimization problem that we call the “max-density multiple-choice knapsack” problem. The structure of optimal knapsack solutions elegantly characterizes the choices made by an optimal algorithm.

Resource author

Resource publisher

Resource publish date

Resource language

en

Resource content type

Resource resource URL

http://eprints.lse.ac.uk/35848/

Resource license