I want to schedule a meeting between (P) number of parties, having (T) number of timeslots such that multiple meetings are arranged in one timeslot and of course, no party has more than one meeting in a single timeslot. This however, is not a classical round-robin problem because I have a peculiar requirement: The timeslots T and locations L will ALWAYS be less than the number required to accommodate all meetings for all P parties. So the most lucrative meetings will be pre-determined and they have to placed in a schedule. The pre-determination is not-calculable, it will be made at the last moment by a third-party without any way for me to compute it.
Let me clarify this by an example scenario that I face: 12 delegations (P) are coming for a training event. My organizations wishes the delegations to meet amongst themselves in a formal method using a round-robin method. If we want to cover all meetings we will need (12 x 11) / 2 = 66 meetings with 11 timeslots (T), with 6 meetings conducted in each timeslot. However, we have only 6 timeslots = 36 meetings. So the 'expert' will decide the 36 most-promising meetings, such that each party has only 6 instead of 11 meetings; this at the last moment and give me the 36 meetings to schedule. How can I generate a schedule for a list of pre-determined meetings such that no party has overlapping meetings in a slot? The number of parties (P) and the number of timeslots (T) changes every-time. (I tried doing this manually, it was a nightmare!)
Question rephrased for more clarification: If I have to layout 66 meetings for 12 parties in 11 timeslots, I know how to do that. However, if random meetings are knocked out, how do I reschedule? We cannot have empty timeslots, so I have to 'fit' 36 meetings in 6 timeslots only. (The expert does not give me a schedule with meetings crossed out, rather a linear list of meetings: X meets Y, C meets F, A meets K etc.) Is there an algo to layout a linear list of ramdom meetings into a schedule?