 
Summary: Optimal myopic algorithms for random 3SAT
Dimitris Achlioptas Gregory B. Sorkin
Microsoft Research
One Microsoft Way
Department of Mathematical Sciences
IBM T.J. Watson Research Center
Redmond WA 98052
Abstract
Let F3(n,m) be a random 3SATformula formed by
selecting uniformly, independently,and with replacement,
m clauses among all 8(y) possible 3clauses over n vari
ables. It has been conjectured that there exists a constant
73 such that for any E > 0, F3(n,(r3  e)n) is almost
surely satisfiable, but F3 (n,( 7 3 +E).) is almost surely un
satisjiable. The best lower boundsfor the potential value
of r3 have comefrom analyzing rather simple extensions
of unitclausepropagation. Recently, it was shown [2] that
all these extensions can be cast in a common framework
and analyzed in a uniformmannerby employingdifferential
equations. Here, we determineoptimal algorithms express
