%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% %W strategies.tex ACE documentation - strategies Alexander Hulpke %W Joachim Neub"user %W Greg Gamble %% %Y Copyright (C) 2000 Centre for Discrete Mathematics and Computing %Y Department of Information Tech. & Electrical Eng. %Y University of Queensland, Australia. %%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \Chapter{Strategy Options for ACE}
It can be difficult to select appropriate options when presented with
a new enumeration. The problem is compounded by the fact that no
generally applicable rules exist to predict, given a presentation,
which option settings are ``good''. To help overcome this problem,
{\ACE} contains various commands which select particular enumeration
strategies. One or other of these strategies may work and, if not, the
results may indicate how the options can be varied to obtain a
successful enumeration.
If no strategy option is passed to {\ACE}, the `default' strategy is
assumed, which starts out presuming that the enumeration will be easy,
and if it turns out not to be so, {\ACE} switches to a strategy
designed for more difficult enumerations. The other straightforward
options for beginning users are `easy' and `hard'. Thus, `easy' will
quickly succeed or fail (in the context of the given resources);
`default' may succeed quickly, or if not will try the `hard' strategy;
and `hard' will run more slowly, from the beginning trying to succeed.
Strategy options are merely options that set a number of the options
seen in Chapter~"Options for ACE", all at once; they are parsed in
*exactly* the same way as other options; order *is* important. It is
usual to specify one strategy option and possibly follow it with a number of options defined in Chapter~"Options for ACE", some of which
may over-ride those options set by the strategy option. Please refer
to the introductory sections of Chapter~"Options for ACE", paying
particular attention to Sections "Warnings regarding Options", "What
happens if no ACE Strategy Option or if no ACE Option is passed",
and~"Interpretation of ACE Options", which give various warnings,
hints and information on the interpretation of options.
There are eight strategy options. Each is passed without a value (see
Section~"Interpretation of ACE Options") except for `sims' which
expects one of the integer values: 1, 3, 5, 7, or 9; and, `felsch' can
accept a value of 0 or 1, where 0 has the same effect as passing
`felsch' with no value. Thus the eight strategy options define
thirteen standard strategies; these are listed in the table below,
along with all but three of the options (of Chapter~"Options for ACE")
that they set. Additionally, each strategy sets `path = 0', `psize =
256', and `dsize = 1000'. Recall `mend', `look' and `com' abbreviate
`mendelsohn' (see~"option mendelsohn"), `lookahead' (see~"option
lookahead") and `compaction' (see~"option compaction"), respectively.
Note that we explicitly (re)set all of the listed enumerator options
in all of the predefined strategies, even though some of them have no
effect. For example, the `fill' value is irrelevant in HLT-type
enumeration (see Section~"Enumeration Style"). The idea behind this is
that, if you later change some options individually, then the
enumeration retains the ``flavour'' of the last selected predefined
strategy.
Note also that other options which may effect an enumeration are left
untouched by setting one of the predefined strategies; for example,
the values of `max' (see~"option max") and `asis' (see~"option asis").
These options have an effect which is independent of the selected
strategy.
Note that, apart from the `felsch := 0' and `sims := 9' strategies,
all of the strategies are distinct, although some are very similar.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \Section{The Strategies in Detail}
\atindex{C style}{@C style}\atindex{Cr style}{@Cr style} \atindex{CR style}{@CR style}\atindex{R style}{@R style} \atindex{R\* style}{@R\* style}\atindex{Rc style}{@Rc style} \atindex{R/C style}{@R/C style} \atindex{Defaulted R/C style}{@Defaulted R/C style} \atindex{R/C (defaulted) style}{@R/C (defaulted) style}
Please note that the strategies are based on various *enumeration
styles*: *C style*, *Cr style*, *CR style*, *R style*, *R\* style*,
*Rc style*, *R/C style* and *defaulted R/C style*, all of which are
described in detail in Section~"Enumeration Style".
\beginitems
\>`default'{option default}@{option `default'}&
Selects the default strategy. (Shortest abbreviation: `def'.)
This strategy is based on the *defaulted R/C style* (see
Section~"Enumeration Style"). The idea here is that we assume that the
enumeration is ``easy'' and start out in *R style*. If it turns out
not to be easy, then we regard it as ``hard'', and switch to *CR
style*, after performing a `lookahead' (see~"option lookahead") on the
entire table.
\>`easy'{option easy}@{option `easy'}&
Selects an ``easy'' R style strategy.
If this strategy is selected, we follow a HLT-type enumeration style,
i.e. *R style* (see Section~"Enumeration Style"), but turn `lookahead'
(see~"option lookahead") and `compaction' (see~"option compaction")
off. For small and/or easy enumerations, this strategy is likely to be
the fastest.
\>`felsch'{option felsch}@{option `felsch'} \>`felsch:=<val>'{option felsch}@{option `felsch'}&
Selects a Felsch strategy; <val> should be 0 or 1.
(Shortest abbreviation: `fel'.)
Here a *C style* (see Section~"Enumeration Style") enumeration is
selected. Assigning `felsch' 0 or no value selects a pure Felsch
strategy, and a value of 1 selects a Felsch strategy with all relators
in the subgroup, i.e.~`no'${}=-1$ (see~"option no"), and turns
gap-`fill'ing (see "option fill") on.
\>`hard'{option hard}@{option `hard'}&
Selects a mixed *R style* and *C style* strategy.
In many ``hard'' enumerations, a mixture of *R style* and *C style*
(see Section~"Enumeration Style") definitions, all tested in all
essentially different positions, is appropriate. This option selects
such a mixed strategy. The idea here is that most of the work is done
C style (with the relators in the subgroup, i.e.~`no'${}=-1$
(see~"option no"), and with gap-`fill'ing (see "option fill") on), but
that every $1000$ C style definitions a further coset number is
applied to all relators.
*Guru Notes:*
The $1000/1$ mix is not necessarily optimal, and some experimentation
may be needed to find an acceptable balance (see, for example, \cite{HR01}). Note also that, the longer the total length of the
presentation, the more work needs to be done for each coset number
application to the relators; one coset number application can result
in more than $1000$ definitions, reversing the balance between R style
and C style definitions.
\>`hlt'{option hlt}@{option `hlt'}&
Selects {\ACE}'s standard HLT strategy.
Unlike Sims' \cite{Sim94} default HLT strategy, `hlt' sets the
`lookahead' option (see~"option lookahead"). However, the option
sequence ```hlt, lookahead := 0''' easily achieves Sims' default HLT
strategy (recall, the ordering of options is respected; see
Section~"Honouring of the order in which ACE Options are passed").
This is an *R style* (see Section~"Enumeration Style") strategy.
\>`purec'{option purec}@{option `purec'}&
Sets the strategy to basic *C style* (see Section~"Enumeration Style").
In this strategy there is no `compaction' (see~"option compaction"),
no gap-`fill'ing (see "option fill") and no relators in subgroup,
i.e.~`no'${}=0$ (see~"option no").
\>`purer'{option purer}@{option `purer'}&
Sets the strategy to basic *R style* (see Section~"Enumeration Style").
In this strategy there is no `mendelsohn' (see "option mendelsohn"),
no `compaction' (see~"option compaction"), no `lookahead' (see~"option
lookahead") and no `row'-filling (see "option row").
\>`sims:=<val>'{option sims}@{option `sims'}&
Sets a Sims strategy; <val> should be one of 1, 3, 5, 7 or 9.
In his book~\cite{Sim94}, Sims discusses (and lists in Table 5.5.1)
ten standard enumeration strategies. The Sims' strategies are
effectively `hlt' (see~"option hlt") without `lookahead' (see~"option
lookahead"), with or without `mendelsohn' (see~"option mendelsohn")
set, in R (`rt' positive, `ct := 0') or R\* style (`rt' negative, `ct
:= 0'); and `felsch' (see~"option felsch"); all either with or without
(`lenlex') table standardisation (see Section~"Coset Table
Standardisation Schemes" and~"ACEStandardCosetNumbering" or~"option
standard") as the enumeration proceeds. {\ACE} does not implement
table standardisation during an enumeration, and so only provides the
odd-numbered strategies of Sims ({\ACE}'s numbering coincides with
that of Sims).
With care, it is often possible to duplicate the statistics given
in~\cite{Sim94} for his odd-numbered strategies and it is also
possible (using the interactive facilities) to approximate his
even-numbered strategies. Examples and a more detailed exposition of
the Sims strategies are given in Section~"Emulating Sims".
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