Research map / Graph learning / Graph algorithms and clustering
A graph-theoretic approach to multitasking
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Require every matching of size k to contain a large induced matching | Bipartite network multitasking measure · Bipartite graphs | multitasking capacity | Mixed |
| Increase regular graph degree d | d-regular bipartite networks · Matching size n | multitasking capacity α(n): O(1/√d) | Hurt |
| Increase network depth from 2 to r | d-regular layered networks · Matching size n | multitasking capacity: O(r/d^{1-1/r}) | Hurt |
| Use an irregular graph rather than a regular graph | Bipartite networks · Matching size n | multitasking capacity: 1/20; average degree at least 1/8 log log n | Helped |
| Use an irregular graph construction with layered vertex classes | Bipartite networks · All matching sizes | multitasking capacity: (1/3-ε); (1-o(1)) log log n/(4 log(10/ε)) | Helped |
| Use a spectral-expander architecture | d-regular bipartite networks · All matching sizes | multitasking capacity: Ω(log d/d) | Helped |
| Use high-girth d-regular graphs | Bipartite networks · Matching sizes k ≤ Ω(log_d n) | multitasking capacity: 1/2 | Helped |
| Use locally sparse graphs for bounded-size task sets | Bipartite networks with average degree d · Matching sizes k ≤ Ω(n/d^{1+4α}) | multitasking capacity: α | Helped |
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