X-Git-Url: http://www.chiark.greenend.org.uk/ucgi/~ian/git?p=topbloke-formulae.git;a=blobdiff_plain;f=strategy.tex;h=d9a2545f1db52b98ed9d8330cd1dfd55e91c561f;hp=7b977e5870ea2a34256850fee8ab34eee2c2f54e;hb=f0f7eceb4c3b65e4728d0b04b23e28906d5038fb;hpb=cc6f8a852918817eecd961f9d2ce85b7ba13eb6f diff --git a/strategy.tex b/strategy.tex index 7b977e5..d9a2545 100644 --- a/strategy.tex +++ b/strategy.tex @@ -86,26 +86,97 @@ dependencies to use. This allows the specification of any desired \section{Ranking phase} -{\bf Ranking} is: +We run the following algorithm: \begin{enumerate} \item Set $\allpatches = \{ \}$. \item Repeatedly: \begin{enumerate} -\item Clear out the graph $\hasdirdep$ so it has neither nodes nor edges. -\item Execute {\bf Rank-Recurse}($\pc_0$) . +\item Clear out the graph $\hasdirdep$ so it has no edges. +\item Execute {\bf Rank-Recurse}($\pc_0$) \item Until $\allpatches$ remains unchanged. \end{enumerate} \end{enumerate} {\bf Rank-Recurse}($\pc$) is: \begin{enumerate} + +\item If we have already done {\bf Rank-Recurse}($\pc$) in this +ranking iteration, do nothing. Otherwise: + \item Add $\pc$ to $\allpatches$ if it is not there already. -\item Let $\set S_{\pcn} = h(\pcn) - \cup \{ \baseof{E} \; | \; \pendsof{ \left[ - \bigcup_{\p \in \allpatches} h(\pn) \cup h(\py) - \right] - }{ \pcy } \} $ + +\item Let +$$ + \set S = h(\pcn) + \cup + \bigcup_{\p \in \allpatches} + \bigcup_{H \in h(\pn) \lor H \in h(\py)} + \{ \baseof{E} \; | \; E \in \pendsof{H}{\pcy} \} +$$ + +and $W = w(h(\pcn))$ + +\item While $\exists_{S \in \set S} S \ge W$, +update $W \assign S$ and $\set S \assign \set S \, \backslash \{ S \}$ + +(This will often remove $W$ from $\set S$. Afterwards, $\set S$ +is a collection of heads to be merged into $W$.) + +\item Choose an order of $\set S$, $S_i$ for $i=1 \ldots n$. + +\item For each $S_i$ in turn, choose a corresponding $M_i$ +such that $$ + M_i \le S_i \land \left[ + M_i \le W \lor \bigexists_{S_i, j