Research map / Graph learning / Graph algorithms and clustering
Fair Short Paths in Vertex-Colored Graphs
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Encode color lower and upper bounds as a matroid and use representative families | SPLU · General SPLU, parameterized by path length | running time: 5.181^{\ell} \log (1/\varepsilon) n^{\mathcal{O}(1)} | Helped |
| Track color-count tuples in dynamic programming | SPLU on shortest paths · Shortest-path SPLU (\ell = \dist(s,t)) | running time: \mathcal{O}(n^{c}\cdot m) | Helped |
| Require the path to be shortest rather than allowing any path | Fair path finding · Two-color fairness constraints | computational complexity: NP-hard | Mixed |
| Allow zero-length arcs | BSP · Two colors | computational complexity: NP-hard | Hurt |
| Use general lower-bound constraints that permit detours | SPLU · Unit arc lengths and one color | computational complexity: NP-hard | Hurt |
| Parameterize BSP by the number of colors | BSP · Balance-fair shortest paths | parameterized complexity: \W{1}-hard | Hurt |
| Seek a general fair path with a short path-length bound | SPLU · General SPLU | fixed-parameter tractability: 5.181^{\ell} \log (1/\varepsilon) n^{\mathcal{O}(1)} | Helped |
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