II. Notes on Data Structuring * - Cornell University

NOTES ON DATA STRUCTURING 159
The problem now remains of selecting a suitable session at each stage.
In principle, there is no reason to suppose that the "best" choice at each
stage will lead to a "best" or even a "good" timetable in the end. However,
it would seem that in general it will pay to select a combination of remaining
exams that most nearly fills the hall, or most nearly approaches the limit k.
This will probably mean that the majority of students and exams will be
catered for in a reasonably compact set of sessions, even though there may
in the end be a fairly long "tail" of small sessions, involving a minority of
students. Although this will not minimise the number of sessions, it may be
reasonably satisfactory to most students and most examiners.
The alternative to accepting an apparent best choice on each occasion is
to attempt some more global optimisation, which will either involve astrono-
mical numbers of trials, or some sophisticated considerations which are
unlikely to become apparent until after practical experience of a simpler
algorithm. So there is nothing else that can be done at this stage except hope
for the best.
It remains to program the function:
function suitable:session,
which selects a suitable session from the remaining set of exams. A possible
method of doing this is to generate a number of trial session satisfying (4)
(5) and (6), and to select the best one found. The best one will probably be
the one with the largest sessioncount, but since we may wish to adjust the
criterion of selection, it is advisable to define it as a separate subroutine,
updating a variable
bestsofar: session;
in accordance with the current value of a variable:
trial: session;
procedure record
if sessioncount (bestsofar) < sessioncount (trial) then
bestsofar: = trial.
The result of suitable is going to be the final value of bestsofar:
suitable: = bestsofar.
It still remains to write a procedure that will generate and record a sequence
of trial sessions which satisfy (4) (5) and (6). Inspection of these conditions
shows that if a trial fails to satisfy one of them, no larger trial will satisfy it.
In other words, having found an impossible trial, there is no need to generate
any further trials which contain it. This suggests that we organise the
generation process to generate all supersets of each trial that has been found