Message #1814

From: Roice Nelson <roice3@gmail.com>
Subject: Re: [MC4D] Re: God’s Number for n^3 cubes.
Date: Fri, 01 Jul 2011 19:34:04 -0500

Very interesting that the asymptotics change if you use macros or not.

Parallelization may also change the balancing point, since the 4/5 point is
currently contingent on our assumption of 2^k sequences. Presumably, we may
instead have another expression for sequence length as a function of piece
type, and some other piece will then dominate. Can one make an
argument that the final point will live somewhere within this (2/3,4/5)
interval? As long as the difficult of solving pieces increases with k, it
seems safe to claim that will be the case.

Roice

On Fri, Jul 1, 2011 at 6:20 PM, schuma <mananself@gmail.com> wrote:

> Yes the ability of parallelization is hard to specify. It’s also the key
> contribution of Demaine’s paper.
>
> An interesting interpretation of my calculation is as follows. The
> (2/3)n-color pieces are the most, but the number of moves per piece is not
> the greatest. The n-color pieces requires the most number of moves per
> piece, but there’re not too many of them. So there’s a balancing point
> between them, in terms of the total number of moves. That balancing point is
> (4/5)n-color pieces. Those are the hardest part.
>
> If one is using macro to solve it and has recorded a 3-cycle macro for each
> type of pieces, the solving time is proportional to the number of pieces
> rather than the total number of moves. In that case (2/3)n-color pieces are
> the major difficulty.
>
> Nan
>