Slithering-tortoise algorithm

Regarding the critical slowing-down of the slithering tortoise algorithm, we can argue heuristically that... 

We remark that deletion from a linear-probing hash table requires some care if done naively, entries can get lost (Ref. 198, pp. 526-7). However, these subtleties are irrelevant if deletions always occur in a last-in-first-out manner (as in the slithering-tortoise algorithm), or occur only when cleaning up the table at the end (as in the pivot and cut-and-paste algorithms). In the latter case it suffices to keep a linear hst of the memory locations in which elements have been inserted these locations can then be cleared at the end. 

What is the precise dynamic critical exponent of the slithering-tortoise algorithm Is it strictly between 2 and 1 -h 7 (Section 2.6.6.1)... 

An alternative way of making the reptation algorithm ergodic is to switch to the variable-A ensemble and introduce A A = 1 moves (L and M in Fig. 2.9), as proposed by Kron et al But once one does this, there is no great reason to retain the slithering-snake moves one can just as well use only the AA= 1 moves. This leads to the slithering-tortoise (Berretti-Sokal) algorithm (see Section 2.6.6.1). 

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