In this talk, I will discuss the efficiency of Incomplete-Enumeration(IE) Monte-Carlo algorithm for linear and branched polymers.  IE is a genetic type MC algorithm which randomly generates a small number of configurations in each run.  We find that there is a qualitative difference in the efficiency of the algorithm for the two kinds of polymers.  For linear polymers the time to generate an independent sample of n monomers for large n increases as a polynomial in n but for branched polymers it increases as a stretched exponential(exp(cn^a), 0<a<1).