A way to find various arrangements of subgroups of a group…

install

To run these scripts you’ll need a working version of Janet and MiniZinc installed.

Once Janet is working, the minizinc-janet interface needs to be installed.

jpm install https://codeberg.org/zzkt/minizinc-janet

schedule

If you have a fixed number of people and group sizes, the group-meeting script will generate the correct number of rounds and group arrangements for everyone to meet each other exactly once. It will also tell you if it is not possible for everyone to meet exactly once.

# 9 people in groups of 3 (outputs 4 rounds)
janet group-meeting.janet 9 3

For more flexibility, the group-meeting-flex script will make arrangements where there are varying groups sizes, and numbers of rounds. It will generate a viable arrangement, and report if there are more people than fit into the groups, or not enough people in each group. It can also provide a summary of who has, or hasn't met each other.

For example, 9 people, arranged in 3 rounds. first round in groups of 3; second round with one group of 4 and one of 5; third round in a group of 9.

janet group-meeting-flex.janet --people 9 --rounds '3,3,3|4,5|9' --svg 'group-diagram.svg'

The output will look something like this…

Group configuration:

People: 9
Rounds: 3
  R1: 3+3+3 = 9
  R2: 4+5 = 9
  R3: 9 = 9
Solver: cp-sat
Model: exact

Solving...
Status: :optimal-solution
Repeats: 25

Meeting Arrangement:

Round 1 (groups: 3, 3, 3):
  Group 1: Aiko, Boris, Ingrid
  Group 2: Deepa, Emeka, Fatima
  Group 3: Chen, Gonzalo, Hiroshi

Round 2 (groups: 4, 5):
  Group 1: Emeka, Fatima, Gonzalo, Hiroshi
  Group 2: Aiko, Boris, Chen, Deepa, Ingrid

Round 3 (groups: 9):
  Group 1: Aiko, Boris, Chen, Deepa, Emeka, Fatima, Gonzalo, Hiroshi, Ingrid

The rounds can be viewed from the perspective of each person…

Compact (name; group per round):
  Aiko; 1, 2, 1
  Boris; 1, 2, 1
  Chen; 3, 2, 1
  Deepa; 2, 2, 1
  Emeka; 2, 1, 1
  Fatima; 2, 1, 1
  Gonzalo; 3, 1, 1
  Hiroshi; 3, 1, 1
  Ingrid; 1, 2, 1

There is also some info about who has met, and how many times…

Pair Coverage:
  Total pairs: 36
  Met: 36 (100%)
  Exactly once: 16
  More than once: 20

Repeated:
  Emeka ↔ Fatima: 3
  Deepa ↔ Emeka: 2
  Aiko ↔ Ingrid: 3
  Deepa ↔ Ingrid: 2
  Chen ↔ Deepa: 2
  Gonzalo ↔ Hiroshi: 3
  Chen ↔ Hiroshi: 2
  Aiko ↔ Boris: 3
  Chen ↔ Ingrid: 2
  Boris ↔ Deepa: 2
  Boris ↔ Chen: 2
  Fatima ↔ Gonzalo: 2
  Emeka ↔ Hiroshi: 2
  Fatima ↔ Hiroshi: 2
  Aiko ↔ Deepa: 2
  Deepa ↔ Fatima: 2
  Emeka ↔ Gonzalo: 2
  Aiko ↔ Chen: 2
  Chen ↔ Gonzalo: 2
  Boris ↔ Ingrid: 3

The script can also be given a list of names, separated by spaces.

janet group-meeting-flex.janet --rounds "4x4x5" --names Fidelia Marcus Donnette Garrett Lida Reagan Myrta Ginny Juliann Maxwell Serena Chantel Wen Malcom Lizbeth Aleida

Group configuration:

People: 16
Rounds: 5
  R1: 4+4+4+4 = 16
  R2: 4+4+4+4 = 16
  R3: 4+4+4+4 = 16
  R4: 4+4+4+4 = 16
  R5: 4+4+4+4 = 16
Solver: cp-sat
Model: exact

Solving...
Status: :optimal-solution
Repeats: 0

Meeting Arrangement:

Round 1 (groups: 4, 4, 4, 4):
  Group 1: Fidelia, Garrett, Reagan, Ginny
  Group 2: Lida, Myrta, Chante, Aleida
  Group 3: Donnette, Juliann, Wen, Lizbeth
  Group 4: Marcus, Maxwell, Serena, Malcom

Round 2 (groups: 4, 4, 4, 4):
  Group 1: Marcus, Garrett, Myrta, Wen
  Group 2: Fidelia, Juliann, Maxwell, Aleida
  Group 3: Reagan, Serena, Chante, Lizbeth
  Group 4: Donnette, Lida, Ginny, Malcom

Round 3 (groups: 4, 4, 4, 4):
  Group 1: Myrta, Ginny, Juliann, Serena
  Group 2: Garrett, Lida, Maxwell, Lizbeth
  Group 3: Fidelia, Marcus, Donnette, Chante
  Group 4: Reagan, Wen, Malcom, Aleida

Round 4 (groups: 4, 4, 4, 4):
  Group 1: Donnette, Reagan, Myrta, Maxwell
  Group 2: Garrett, Juliann, Chante, Malcom
  Group 3: Fidelia, Lida, Serena, Wen
  Group 4: Marcus, Ginny, Lizbeth, Aleida

Round 5 (groups: 4, 4, 4, 4):
  Group 1: Ginny, Maxwell, Chante, Wen
  Group 2: Donnette, Garrett, Serena, Aleida
  Group 3: Marcus, Lida, Reagan, Juliann
  Group 4: Fidelia, Myrta, Malcom, Lizbeth

Compact (name; group per round):
  Fidelia; 1, 2, 3, 3, 4
  Marcus; 4, 1, 3, 4, 3
  Donnette; 3, 4, 3, 1, 2
  Garrett; 1, 1, 2, 2, 2
  Lida; 2, 4, 2, 3, 3
  Reagan; 1, 3, 4, 1, 3
  Myrta; 2, 1, 1, 1, 4
  Ginny; 1, 4, 1, 4, 1
  Juliann; 3, 2, 1, 2, 3
  Maxwell; 4, 2, 2, 1, 1
  Serena; 4, 3, 1, 3, 2
  Chante; 2, 3, 3, 2, 1
  Wen; 3, 1, 4, 3, 1
  Malcom; 4, 4, 4, 2, 4
  Lizbeth; 3, 3, 2, 4, 4
  Aleida; 2, 2, 4, 4, 2

Pair Coverage:
  Total pairs: 120
  Met: 120 (100%)
  Exactly once: 120
  More than once: 0

Partial arrangements can include people who are not allocated to a group, they are listed as 'Extra' and the groups may need to be adjusted manually. Consider the arragements as a starting point…

% janet group-meeting-flex.janet --people 5 --rounds '3x3x2'

Group configuration:

People: 5
Rounds: 2
  R1: 3+3+3 = 9 [4 extra capacity]
  R2: 3+3+3 = 9 [4 extra capacity]
Solver: cp-sat
Model: extras

Solving...
Status: :optimal-solution
Extras: 0
Repeats: 0

Meeting Arrangement:

Round 1 (groups: 2, 1, 2):
  Group 1: Aiko, Emeka
  Group 3: Chen, Deepa
  Extra:   Boris

Round 2 (groups: 1, 1, 3):
  Group 3: Boris, Deepa, Emeka
  Extra:   Chen, Aiko

Compact (name; group per round):
  Aiko; 1, 2
  Boris; 2, 3
  Chen; 3, 1
  Deepa; 3, 3
  Emeka; 1, 3

Pair Coverage:
  Total pairs: 10
  Met: 5 (50%)
  Exactly once: 5
  More than once: 0

Did not meet:
  Aiko ↔ Boris
  Aiko ↔ Chen
  Aiko ↔ Deepa
  Boris ↔ Chen
  Chen ↔ Emeka

waiting

Some arrangements may not be possible, or take an extremely long time to produce an approximate solution

e.g.

% janet group-meeting-flex.janet --rounds "8x2x2" --names Fidelia Marcus Donnette Garrett Lida Reagan Myrta Ginny Juliann Maxwell Serena Chante Wen Malcom Lizbeth Aleida
Group configuration:

People: 16
Rounds: 2
  R1: 8+8 = 16
  R2: 8+8 = 16
Solver: cp-sat
Model: exact

Solving...
Status: :unknown
No solution found (time limit exceeded or unsolvable)

further

• May I sit here? by Tim Boykett
• Dancing Links, Exact Cover Problem and Algorithm X
• Size of groups, organizations, and communities