Table 1 Solution accuracy in terms of wrongly colored edges (lower value is better) comparison of heuristic (Tabucol), learning-based approaches (GNN and PI-SAGE), Ising methods, and Vectorized framework
From: Efficient optimization accelerator framework for multi-state spin Ising problems
Problem | #nodes | #edges | #colors | #GNN33 | #PI-SAGE33 | #Tabucol | #Probabilistic Ising | #Simulated Bifurcation | #Vectorized GPU | #Vectorized FPGA | # Probabilistic Ising + Parallel Tempering GPU | #Vectorized+ Parallel Tempering GPU |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
anna | 138 | 493 | 11 | 1 | 0 | 0 | 12 | 44 | 0 | 0 | 2 | 0 |
david | 87 | 406 | 11 | NA | NA | 0 | 17 | 11 | 0 | 0 | 10 | 0 |
huck | 74 | 301 | 11 | NA | NA | 0 | 0 | 13 | 0 | 0 | 0 | 0 |
myciel3 | 11 | 20 | 4 | NA | NA | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
myciel4 | 23 | 71 | 5 | NA | NA | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
myciel5 | 47 | 236 | 6 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
myciel6 | 95 | 755 | 7 | 0 | 0 | 0 | 4 | 6 | 0 | 0 | 2 | 0 |
myciel7 | 191 | 2360 | 8 | NA | NA | 0 | 144 | 61 | 0 | 0 | 52 | 0 |
queen5_5 | 25 | 160 | 5 | 0 | 0 | 0 | 5 | 5 | 0 | 0 | 0 | 0 |
queen6_6 | 36 | 290 | 7 | 4 | 0 | 0 | 3 | 6 | 1 | 1 | 1 | 0 |
queen7_7 | 49 | 476 | 7 | 15 | 0 | 0 | 21 | 24 | 6 | 5 | 14 | 0 |
queen8_8 | 64 | 728 | 9 | 7 | 1 | 0 | 41 | 29 | 4 | 2 | 15 | 1 |
queen9_9 | 81 | 1056 | 10 | 13 | 1 | 0 | 36 | 47 | 5 | 4 | 18 | 2 |
queen8_12 | 96 | 1368 | 12 | 7 | 0 | 0 | 44 | 73 | 2 | 2 | 21 | 0 |
queen11_11 | 121 | 1980 | 11 | 33 | 17 | 15 | 87 | 111 | 20 | 18 | 41 | 14 |
queen13_13 | 169 | 3328 | 13 | 40 | 26 | 21 | 124 | 199 | 31 | 26 | 60 | 21 |
