Approximating Maximum Satisfaction in Group Formation

1
Approximating Maximum Satisfaction in Group
Formation
Sean Munson, Grant HutchinsOlin College
Exposition21 December 2004
Design Lifelong Learning Communication
Qualitative Analysis
2
goal

• Maximize happiness, or satisfaction
• Input
• Preferences -1, 0, or 1 for each person
• Worked with before
• Work style preferences
• Satisfaction how many preferences you meet

3

• satisfaction
• For each team, the sum of how each person feels
  about the each other person in the group.
• Maximize this for each set of teams

1
-1
1
-1
-1
-2
1
-1
-1
4
possible combinations in our class

• Teams of 4
• Teams of 2

5
approximations
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form teams of three based on preferences
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chain approximation
1
0
1
0
-5
0
-2
-2
3
8
chain approximation
1
0
1
0
-5
0
-2
-2
3
9
chain approximation
1
0
1
0
-5
0
-2
-2
3
10
chain approximation

• Fast, simple
• Variation choose on most popular or pickiness
• Problem only looks at one persons preferences
  at a time

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group approximation, teams of 3
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1
0
1
0
-5
0
-2
-2
3
13
1
0
1
0
-5
0
-2
-2
3
14
1
0
1
0
-2
-2
3
15
1
0
1
0
-2
-2
3
16
1
0
1
0
-2
-2
17
0
1
1
0
-2
-2
18
1
0
1
0
-2
-2
19
0
1
1
0
-2
-2
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group approximation

• Includes everyones preferences
• Still explores very little space

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hill climbing
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hill climbing
10
4
3
23
hill climbing
10
4
3
24
hill climbing
10
4
3
25
hill climbing
10
6
5
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results prediction accurate?
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results
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future work?

• Assess more seed and convergent processes
• Weight edges based on prior experience
• Break ties with work style
• Conduct long-term study to evaluate performance
  of formed teams
• Evaluate effects of number of preferences
  expressed

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questions