Logic (DRC) vs. RA

1. Logic (DRC) vs. RA

2. Scenario Rnum Slot Enum A2 A1 Room Event Assigned • We have several rooms, each one available at different time slot. • Several events, each defined by a unique identifier. • Each event is assigned to a specific room at a specific time slot.

3. Available Slots • We want to know which slots are available • (doesn’t matter which room) • In logic: • In RA: room Room slot AS

4. Maximally Available Rooms • A room is maximally available if it is available in every existing time slot. • A is available at all possibleslots (1, 2 & 3) therefore A ismaximally available

5. Maximally Available Rooms • A room is maximally available if it is available in every existing time slot. • A has the maximal numberof available slots but it is notmaximally available (notavailable at slot 4)

6. Maximally Available Rooms • Formulas: • In Logic: • In RA:

7. Maximally Assigned Rooms • A room is maximally assigned if every slot in which the room is available is assigned to an event. • All of As slots are assignedto events therefore A ismaximally assigned.

8. Maximally Assigned Rooms • A room is maximally assigned if every slot in which the room is available is assigned to an event. • B has a slot (4) which is notassigned to an event thereforeB is not maximally assigned.

9. Maximally Assigned Rooms • Assigned rooms and slots: • In logic: • In RA: • Can also be written as

10. Maximally Assigned Rooms • A logic formula for maximally assigned rooms:

11. Maximally Assigned Rooms • Translation to RA: • Rooms and slots assigned to events.

12. Maximally Assigned Rooms • Rooms and slots not assigned to events • Rooms with event-free slots • Rooms without event-free slots = maximally assigned rooms!