Incomplete enumeration Redner Reynolds algorithm

Incomplete enumeration is a quasi-static algorithm that generates a batch of SAWs from the variable-iV, variable-x ensemble (eq. (2.18)) with p = 0. The idea is to take a standard algorithm for systematically enumerating all self-avoiding walks up to some length Nmix, and modify it so that it pursues each branch of the SAW tree only with some probability / 1  

To perform an incomplete enumeration of the SAW tree beginning at the root , one simply invokes incenum( 0, /J,JVma ), where 0 is the zero-step walk at the origin. Typically one chooses j3 fie = /IJ-, in this case it is safe to set Nmax = oo. (If one sets N vc = oo when fic, then with nonzero probability the algorithm will run forever ) 

A non-recursive implementation of incomplete enumeration can be found in Ref. 11, Section 9. 3. 

The CPU time for one invocation of incomplete enumeration is obviously proportional to the total number of walks encountered during the enumeration. On the average this is 

On the other hand, it is reasonable to guess that, as in enrichment, 

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