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Optimal myopic algorithms for random 3-SAT Dimitris Achlioptas Gregory B. Sorkin
 

Summary: Optimal myopic algorithms for random 3-SAT
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 3-SATformula formed by
selecting uniformly, independently,and with replacement,
m clauses among all 8(y) possible 3-clauses over n vari-
ables. It has been conjectured that there exists a constant
7-3 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 unit-clausepropagation. 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-

  

Source: Achlioptas, Dimitris - Department of Computer Engineering, University of California at Santa Cruz

 

Collections: Computer Technologies and Information Sciences