# splitting of people betwen groups with group prioritiy list per person

Computer Science Asked by Gomunkul on December 15, 2020

Looking for an algorithm for splitting a list of people (S) into groups (G), |S| <= |G|, more than one person wants to be in a certain group.
Every person has a monotone ranking from highest (most desired) to lowest of all the groups.
Using this list I want to find the "best matching".
"best matching" is when you maximize the "score of the matching".
"score of the matching" is the sum of the group rankings of the people that got matched with the group, i.e. summing the ranking that the people gave to the group which was chosen for them.

I’m also interested in ideas for other "fairness" values for maximization.

If you want to maximize the sum of the scores for each participant, this is an instance of the assignment problem; use the Hungarian algorithm, or any other algorithm for computing a maximum matching.

You might also be interested in stable marriage algorithms, which have a different notion of fairness.

Answered by D.W. on December 15, 2020

## Related Questions

### How to generate graphs with a Hamiltonian path?

3  Asked on February 21, 2021 by always-newbie

### Wifi throughput calculation

1  Asked on February 20, 2021 by copsa

### Searching for points near given point in a multidimensional space

1  Asked on February 20, 2021 by saku

### Group adjacent sections to create groups with biggest value, value is changing in groups

1  Asked on February 20, 2021 by rossko_dca

### Thirty-one game. Prediction of the winner

1  Asked on February 17, 2021 by donvitomarco

### Explanation of conventional solutions to the Firing Squad Synchronization problem

0  Asked on February 16, 2021 by von-spotz

### If $B$ is worse than $A$ on some inputs, how do their worst-case time complexities compare?

1  Asked on February 13, 2021 by aviv-barel

### How to edge-color a directed acyclic graph so that every path visits none or all edges of each color?

5  Asked on February 10, 2021 by gizmo

### Complexity of a cutting operation on a list of binary trees

0  Asked on February 10, 2021 by arthur-b

### speed of preorder traversal

1  Asked on February 8, 2021 by keith-paton

### Mergesort and some claims on comparison

1  Asked on February 7, 2021 by user3661613

### Proving the language of non-primes is in NP

1  Asked on February 6, 2021 by builderthebob00

### Does writing more data to disk consume more energy than writing less?

0  Asked on February 5, 2021 by pookie

### In Strassen’s algorithm, why does padding the matrices with zeros not affect the asymptopic complexity?

1  Asked on February 4, 2021 by retsek680

### How to find the language of a CFG from Production rules

1  Asked on February 3, 2021 by stark2022

### Machine Learning algorithm for predicting a user’s rating on an item?

0  Asked on February 1, 2021 by david-grnberger

### Finding the Hamiltonian cycle that uses the least amount of straight lines

0  Asked on January 30, 2021 by tzlil

### Can I have 2 free adjacent nodes in the fit algorithm for data management

0  Asked on January 29, 2021 by angelic-demonic

### Longest path on a full tree

1  Asked on January 27, 2021 by bm1125