Research map / Graph learning / Graph algorithms and clustering
A Little Charity Guarantees Fair Connected Graph Partitioning
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Allow up to n − 1 node exclusions | Connected graph partitioning among n agents · General connected graphs | balancedness: 2 | Helped |
| Allow up to n − 1 node exclusions | Connected graph partitioning among n agents · General connected graphs | proportionality: 2 − 1/n | Helped |
| Use Algorithm 1 for two agents with at most one excluded node | Connected graph partitioning · n = 2 | balancedness: 2 | Helped |
| Use Algorithm 1 for two agents with at most one excluded node | Connected graph partitioning · n = 2 | proportionality: 1.5 | Helped |
| Use a polynomial-time construction with at most two exclusions | Connected graph partitioning · n = 3 | balancedness: 2 | Helped |
| Use a polynomial-time construction with at most two exclusions | Connected graph partitioning · n = 3 | proportionality: 5/3 | Helped |
| Use Algorithm 2 to recursively split the largest current part | Connected graph partitioning · n ≥ 2, m ≥ n · (n − 1) | proportionality: 3-proportionality | Helped |
| Use Algorithm 3 with target sizes adjusted to prior part sizes | Connected graph partitioning · n ≥ 2, m ≥ 2n − 1 | proportionality: 2-proportionality | Helped |
| Convert a connected balanced tree edge-partition into a node partition | Connected graph partitioning · n ≥ 2, m ≥ 4n2 | balancedness: (2+8n2/m) | Helped |
| Allow one node exclusion | Connected graph partitioning · n ≥ 2 | proportionality: O(n) | Helped |
| Require fewer than n − 1 exclusions | Connected graph partitioning · n ≥ 2 | balancedness: 3 − ϵ | Hurt |
Closest papers by meaning
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