Elimination Of Infrequent Variables Improves Average Case Performance Of Satisfiability Algorithms
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. We consider pre-processing a random instance I of CNF Satisfiability in order to remove infrequent variables (those which appear once or twice in an instance) from I. The model used to generate random instances is the popular random-clause-size model with parametersn, the number of clauses, r, the number of Boolean variables from which clauses are composed, and p, the probability that a variable appears in a clause as a positive (or negative) literal. It is shown that exhaustive search over such pre-processed instances runs in polynomial average time over a significantly larger parameter space than has been shown for any other algorithm under the random-clause-size model when n = r ffl , ffl ! 1, and pr ! p fflr ln(r). Specifically, the results are that random instances of Satisfiability are "easy" in the average case if n = r ffl , 2=3 ? ffl ? 0, and pr ! (ln(n)=4) 1=3 r 2=3\Gammaffl ; or n = r ffl , 1 ? ffl 2=3, pr ! (1 \Gamma ffl \Gamma ffi) ln(n)=ffl for any ffi ? 0...