# Technical Document Extraction: Line Graph Analysis ## Chart Overview The image depicts a line graph comparing the performance of three variants of the "AoT" algorithm across varying numbers of visited nodes. The graph illustrates the relationship between the number of visited nodes (x-axis) and the number of games processed (y-axis). --- ## Axis Labels and Markers - **X-Axis**: - Title: `# of Visited Nodes` - Range: `0` to `400` - Increment: `100` (grid lines at 0, 100, 200, 300, 400) - **Y-Axis**: - Title: `# of Games` - Range: `0` to `100` - Increment: `20` (grid lines at 0, 20, 40, 60, 80, 100) --- ## Legend and Line Correspondence - **Legend**: - **Blue Line**: `AoT (Short)` - **Green Line**: `AoT` (standard variant) - **Red Line**: `AoT (Long)` - **Line Behavior**: - All lines originate at `(0, 0)`. - **AoT (Short)** (blue): - Steady linear growth until ~300 nodes. - Plateaus at ~80 games after 300 nodes. - **AoT** (green): - Slightly outperforms `AoT (Short)` in early stages. - Reaches ~90 games at 300 nodes, then plateaus. - **AoT (Long)** (red): - Slow initial growth (lags behind others until ~300 nodes). - Sharp exponential increase after 300 nodes, surpassing all variants to reach ~100 games at 400 nodes. --- ## Key Trends and Data Points 1. **Early-Stage Performance (0–100 nodes)**: - All variants show rapid growth, with `AoT (Short)` and `AoT` outperforming `AoT (Long)`. - At 100 nodes: - `AoT (Short)`: ~60 games - `AoT`: ~50 games - `AoT (Long)`: ~30 games 2. **Mid-Stage Performance (100–300 nodes)**: - `AoT (Short)` and `AoT` maintain similar trajectories. - `AoT (Long)` remains the weakest performer until ~300 nodes. - At 200 nodes: - `AoT (Short)`: ~75 games - `AoT`: ~70 games - `AoT (Long)`: ~40 games 3. **Late-Stage Performance (300–400 nodes)**: - `AoT (Long)` exhibits a dramatic acceleration, overtaking all variants. - At 300 nodes: - `AoT (Short)`: ~80 games - `AoT`: ~90 games - `AoT (Long)`: ~50 games - At 400 nodes: - All variants converge near 100 games, with `AoT (Long)` achieving the highest value. --- ## Observations - **Scalability**: - `AoT (Long)` demonstrates superior scalability in high-node regimes (>300 nodes). - **Efficiency Trade-offs**: - `AoT (Short)` and `AoT` prioritize early-stage efficiency but plateau in later stages. - **Convergence**: - All variants approach 100 games by 400 nodes, suggesting asymptotic performance limits. --- ## Conclusion The graph highlights the trade-offs between algorithmic variants: - `AoT (Short)` and `AoT` excel in low-to-mid node regimes. - `AoT (Long)` sacrifices early performance for late-stage scalability. This data is critical for selecting the optimal variant based on the expected node density in deployment scenarios.