II. Notes on Data Structuring * - Cornell University

The condition may be formalised:
NOTES ON DATA STRUCTURING 157
s in timetable ~ sessioncount (s) ~< hallsize.
(6) No student takes more than one exam in a session. To formalise this
we introduce the concept of incompatibility of exams: two exams are in-
compatible if some student is taking both of them. For each exam el there is
a set incompat (el) of exams which are incompatible with it:
incompat (el) = {e2:exam I e2 -¢- el & 3 st:student (el in load (st)
& e2 in load (st))}
Now we can define that every pair of exams in a session must be compatible:
s in timetable & el, e2 in s D -l el in incompat (e2).
These six conditions, defined in terms of load, hallsize, and k, must be
possessed by any successful timetable in the real world, and by any successful
computer representation of the timetable. They serve to define the objectives
and criterion of correctness of our timetabling program.
11.1 THE ABSTRACT PROGRAM
Inspection of the conditions reveals that construction of the timetable does
not require full knowledge of the load of each student. All that is needed is
the examcount of each exam, and for each exam the set of other exams
which are incompatible with it:
examcount: array exam of integer;
incompat: array exam of powerset exam.
These two arrays embody an abstraction from the real life data, which
concentrate attention on exactly those features which are for the present
purpose relevant, and permitting us to ignore for the time being the other
features of the situation. It is plain that these two arrays can be readily
constructed from a single scan of the student load data:
examcount: = all (0);
incompat:= all ( { } );
for st: student do
for e in load (st) do
begin examcount (e)" + 1;
end;
incompat (e): v (load (st) - {e})
One of the simplifying factors in the search for a solution to the given
problem is that the conditions fall readily into two classes: (1) (2) and (3)
relate to the timetable as a whole, whereas (4) (5) and (6) relate only to