## Bar Chart: Accuracy vs. Length of Paths in SPARQL ### Overview The image is a bar chart comparing the accuracy of two methods, PoG and PoG-E, against the length of paths in SPARQL queries. The x-axis represents the length of paths, ranging from 1 to 8+, while the y-axis represents accuracy in percentage. ### Components/Axes * **X-axis:** Length of paths in SPARQL. Categories: 1, 2, 3, 4, 5, 6, 7, 8+ * **Y-axis:** Accuracy (%). Scale: 0 to 100, with tick marks at intervals of 20. * **Legend:** Located at the top-center of the chart. * PoG: Light blue bars with a black outline. * PoG-E: Dark gray bars with a black outline. ### Detailed Analysis Here's a breakdown of the accuracy for each path length, for both PoG and PoG-E: * **Path Length 1:** * PoG: No bar present, implying 0% accuracy. * PoG-E: No bar present, implying 0% accuracy. * **Path Length 2:** * PoG (Light Blue): Approximately 100% accuracy. * PoG-E (Dark Gray): Approximately 75% accuracy. * **Path Length 3:** * PoG (Light Blue): Approximately 82% accuracy. * PoG-E (Dark Gray): Approximately 80% accuracy. * **Path Length 4:** * PoG (Light Blue): Approximately 70% accuracy. * PoG-E (Dark Gray): Approximately 69% accuracy. * **Path Length 5:** * PoG (Light Blue): Approximately 57% accuracy. * PoG-E (Dark Gray): Approximately 55% accuracy. * **Path Length 6:** * PoG (Light Blue): Approximately 56% accuracy. * PoG-E (Dark Gray): Approximately 56% accuracy. * **Path Length 7:** * PoG (Light Blue): Approximately 51% accuracy. * PoG-E (Dark Gray): Approximately 47% accuracy. * **Path Length 8+:** * PoG (Light Blue): Approximately 63% accuracy. * PoG-E (Dark Gray): Approximately 50% accuracy. **Trends:** * **PoG:** Accuracy starts at 0% for path length 1, peaks at 100% for path length 2, then generally decreases until path length 7, before increasing again at path length 8+. * **PoG-E:** Accuracy starts at 0% for path length 1, peaks at 80% for path length 3, then generally decreases until path length 7, before increasing again at path length 8+. ### Key Observations * PoG generally outperforms PoG-E in terms of accuracy, except at path length 6 where they are approximately equal. * Both methods show a decrease in accuracy as the path length increases from 2 to 7. * Both methods show an increase in accuracy when the path length is 8+. * The most significant difference in accuracy between PoG and PoG-E is at path length 2. ### Interpretation The chart suggests that the accuracy of both PoG and PoG-E is affected by the length of paths in SPARQL queries. Shorter paths (length 2) result in higher accuracy, particularly for PoG. As the path length increases, the accuracy tends to decrease, possibly due to increased complexity or ambiguity in the queries. The increase in accuracy at path length 8+ could indicate a different behavior or characteristic of very long paths. The data implies that PoG is generally more accurate than PoG-E, especially for shorter paths.

## Bar Chart: Accuracy (%) vs. Length of paths in SPARQL ### Overview This image is a bar chart comparing the accuracy of two methods, "PoG" and "PoG-E", across different lengths of paths in SPARQL queries. The x-axis represents the length of paths in SPARQL queries, categorized from 1 to 8+. The y-axis represents the accuracy in percentage. ### Components/Axes * **Title:** Implicitly, the chart title is "Accuracy (%) vs. Length of paths in SPARQL". * **X-axis Label:** "Length of paths in SPARQL" * **X-axis Markers:** 1, 2, 3, 4, 5, 6, 7, 8+ * **Y-axis Label:** "Accuracy (%)" * **Y-axis Markers:** 0, 20, 40, 60, 80, 100 * **Legend:** Located at the top-center of the chart. * **"PoG"**: Represented by light blue bars. * **"PoG-E"**: Represented by dark gray bars. ### Detailed Analysis The chart displays paired bars for each category on the x-axis, representing the accuracy for "PoG" and "PoG-E". * **Path Length 1:** * PoG: No bar is visible, suggesting an accuracy of 0% or it's not applicable/measured. * PoG-E: No bar is visible, suggesting an accuracy of 0% or it's not applicable/measured. * **Path Length 2:** * PoG (light blue): Slopes upward to approximately 100%. * PoG-E (dark gray): Slopes upward to approximately 75%. * **Path Length 3:** * PoG (light blue): Slopes upward to approximately 82%. * PoG-E (dark gray): Slopes upward to approximately 81%. * **Path Length 4:** * PoG (light blue): Slopes upward to approximately 68%. * PoG-E (dark gray): Slopes upward to approximately 69%. * **Path Length 5:** * PoG (light blue): Slopes upward to approximately 58%. * PoG-E (dark gray): Slopes upward to approximately 56%. * **Path Length 6:** * PoG (light blue): Slopes upward to approximately 57%. * PoG-E (dark gray): Slopes upward to approximately 57%. * **Path Length 7:** * PoG (light blue): Slopes upward to approximately 50%. * PoG-E (dark gray): Slopes upward to approximately 46%. * **Path Length 8+:** * PoG (light blue): Slopes upward to approximately 63%. * PoG-E (dark gray): Slopes upward to approximately 50%. ### Key Observations * **Path Length 2:** "PoG" achieves its highest accuracy at approximately 100%, significantly outperforming "PoG-E" which is around 75%. * **Path Length 3:** Both "PoG" and "PoG-E" show very similar accuracies, around 82% and 81% respectively. * **General Trend:** For path lengths 2 through 7, the accuracy for both methods generally decreases as the path length increases, with a slight dip and then a rise for "PoG" at path length 8+. * **Path Length 8+:** "PoG" shows a notable increase in accuracy to approximately 63%, while "PoG-E" drops to approximately 50%. * **Comparison:** "PoG" generally performs better or comparably to "PoG-E" across most path lengths, with the exception of path length 4 where "PoG-E" is slightly higher. "PoG" shows a more pronounced peak at path length 2 and a significant recovery at path length 8+. ### Interpretation This chart demonstrates the performance of two methods, "PoG" and "PoG-E", in terms of accuracy when dealing with SPARQL queries of varying path lengths. * **Method Performance:** "PoG" appears to be a more robust method, especially for shorter and longer path lengths. Its peak performance at path length 2 (near 100% accuracy) suggests it is highly effective for queries with a single hop or very simple structures. The significant increase in accuracy for path length 8+ compared to path length 7 indicates that "PoG" might be better at handling complex, multi-hop queries than "PoG-E". * **Impact of Path Length:** The general trend of decreasing accuracy with increasing path length (from 2 to 7) is a common observation in query processing, as longer paths can introduce more complexity, ambiguity, and potential for errors. However, the behavior at path length 8+ for "PoG" suggests that for very complex queries, its architecture might be more adaptable or it might be leveraging different strategies. * **"PoG-E" Behavior:** "PoG-E" shows a more consistent, albeit lower, performance compared to "PoG" for path lengths 2 through 7. Its accuracy is generally slightly lower than "PoG" in this range, and it does not show the same recovery at path length 8+. This could imply that "PoG-E" is more sensitive to the increasing complexity of longer paths. * **Relationship between Elements:** The x-axis categories (path lengths) directly influence the y-axis values (accuracy) for each of the two data series ("PoG" and "PoG-E"). The legend clearly distinguishes these two series, allowing for direct comparison at each path length. The visual representation as bars allows for quick identification of relative performance. * **Underlying Data:** The data suggests that while both methods struggle with increasing path complexity, "PoG" exhibits a more dynamic performance profile, excelling at both very short and very long path lengths, while "PoG-E" offers a more stable but generally lower accuracy across intermediate path lengths. The absence of data for path length 1 for both methods might indicate that such queries are not relevant or not handled by these methods.

## Bar Chart: Accuracy vs. Path Length in SPARQL ### Overview This bar chart compares the accuracy of two methods, PoG and PoG-E, across different lengths of paths in SPARQL queries. The x-axis represents the length of the paths, and the y-axis represents the accuracy in percentage. Each path length has two bars, one for PoG and one for PoG-E. ### Components/Axes * **X-axis Title:** "Length of paths in SPARQL" * Markers: 1, 2, 3, 4, 5, 6, 7, 8+ * **Y-axis Title:** "Accuracy (%)" * Scale: 0 to 100, with increments of 20. * **Legend:** Located at the top-center of the chart. * PoG: Light blue * PoG-E: Dark gray ### Detailed Analysis The chart consists of eight groups of bars, each representing a different path length. * **Path Length 1:** * PoG: Approximately 95% accuracy. * PoG-E: Approximately 75% accuracy. * **Path Length 2:** * PoG: Approximately 98% accuracy. * PoG-E: Approximately 78% accuracy. * **Path Length 3:** * PoG: Approximately 82% accuracy. * PoG-E: Approximately 80% accuracy. * **Path Length 4:** * PoG: Approximately 68% accuracy. * PoG-E: Approximately 65% accuracy. * **Path Length 5:** * PoG: Approximately 58% accuracy. * PoG-E: Approximately 52% accuracy. * **Path Length 6:** * PoG: Approximately 54% accuracy. * PoG-E: Approximately 50% accuracy. * **Path Length 7:** * PoG: Approximately 52% accuracy. * PoG-E: Approximately 46% accuracy. * **Path Length 8+:** * PoG: Approximately 57% accuracy. * PoG-E: Approximately 59% accuracy. **Trends:** * **PoG:** The accuracy of PoG generally decreases as the path length increases from 1 to 7, then slightly increases for 8+. The initial drop is significant, from approximately 98% at length 2 to around 52% at length 7. * **PoG-E:** The accuracy of PoG-E also generally decreases as the path length increases, but the decrease is less pronounced than for PoG. It starts at approximately 75% at length 1 and reaches around 46% at length 7, then increases to 59% at 8+. ### Key Observations * PoG consistently outperforms PoG-E for path lengths 1, 2, 3, and 4. * For path lengths 5, 6, and 7, the performance difference between PoG and PoG-E is smaller. * At path length 8+, PoG-E slightly outperforms PoG. * Both methods exhibit a decline in accuracy as path length increases, suggesting a challenge in maintaining accuracy with longer SPARQL paths. ### Interpretation The data suggests that both PoG and PoG-E methods are effective for short SPARQL paths (length 1 and 2), achieving high accuracy. However, as the path length increases, the accuracy of both methods decreases. This could be due to the increased complexity of reasoning over longer paths, leading to more potential errors. The initial superior performance of PoG suggests it may be better suited for simpler queries. However, PoG-E's relative stability and slight outperformance at path length 8+ indicate it might be more robust for complex queries involving longer paths. The crossover point where PoG-E becomes competitive is around path length 5. The slight increase in accuracy for both methods at path length 8+ could be due to a variety of factors, such as the nature of the queries used for evaluation or the limitations of the evaluation dataset. Further investigation would be needed to understand this trend. The data highlights a trade-off between simplicity and robustness in SPARQL query processing.

## Grouped Bar Chart: Accuracy of PoG vs. PoG-E by SPARQL Path Length ### Overview The image is a grouped bar chart comparing the accuracy (in percentage) of two methods, labeled "PoG" and "PoG-E," across different lengths of paths in SPARQL queries. The chart demonstrates how the performance of each method changes as the complexity (path length) of the query increases. ### Components/Axes * **Chart Type:** Grouped (clustered) bar chart. * **X-Axis:** Labeled **"Length of paths in SPARQL"**. It has categorical tick marks for path lengths: **1, 2, 3, 4, 5, 6, 7, and 8+**. * **Y-Axis:** Labeled **"Accuracy (%)"**. It is a linear scale ranging from 0 to 100, with major tick marks at intervals of 20 (0, 20, 40, 60, 80, 100). * **Legend:** Positioned at the **top center** of the chart area. * **PoG:** Represented by a light blue (periwinkle) bar. * **PoG-E:** Represented by a dark gray bar. * **Data Series:** Two series of bars, one for each method, grouped together for each x-axis category. ### Detailed Analysis The following table reconstructs the approximate accuracy values for each method at each path length. Values are estimated from the bar heights relative to the y-axis. | Length of paths in SPARQL | PoG Accuracy (Approx. %) | PoG-E Accuracy (Approx. %) | | :--- | :--- | :--- | | 1 | No data plotted | No data plotted | | 2 | 100 | ~75 | | 3 | ~82 | ~80 | | 4 | ~70 | ~69 | | 5 | ~58 | ~55 | | 6 | ~57 | ~56 | | 7 | ~50 | ~46 | | 8+ | ~62 | ~49 | **Trend Verification:** * **PoG (Light Blue):** The trend line slopes downward from a peak at path length 2 (100%) to a low at length 7 (~50%), with a notable upward rebound at length 8+ (~62%). * **PoG-E (Dark Gray):** The trend line shows a consistent, gradual downward slope from its highest point at length 2 (~75%) to its lowest at length 7 (~46%), with a very slight increase at length 8+ (~49%). ### Key Observations 1. **Performance Gap:** PoG consistently achieves higher accuracy than PoG-E across all reported path lengths where data is present (2 through 8+). 2. **Peak Performance:** Both methods achieve their highest accuracy at the shortest measured path length (2). PoG reaches a perfect 100% here. 3. **General Decline:** There is a clear general trend of decreasing accuracy for both methods as the SPARQL path length increases from 2 to 7. 4. **Anomaly at 8+:** The expected downward trend is broken at the "8+" category. PoG shows a significant recovery in accuracy (~62%), while PoG-E shows only a marginal increase (~49%). This suggests PoG may handle very long paths better than the general trend would predict. 5. **Convergence Points:** The performance of the two methods is closest at path lengths 3, 4, and 6, where the difference in bar heights is minimal (within ~2-3 percentage points). 6. **Missing Data:** No accuracy data is plotted for a path length of 1. ### Interpretation The data suggests that the **PoG method is generally more accurate than PoG-E** for generating or answering SPARQL queries of varying path complexities. The strong performance of PoG at length 2 (100%) indicates it is highly reliable for simpler queries. The **inverse relationship between path length and accuracy** for both methods (from length 2 to 7) demonstrates that increasing query complexity—measured by the number of hops or relationships in the path—poses a significant challenge, leading to a drop in performance. This is a common pattern in knowledge graph and semantic web tasks. The **notable outlier is the "8+" category for PoG**. Its accuracy rebound suggests one of two possibilities: 1) The "8+" bin may contain a different distribution of query types that PoG is better suited for, or 2) The method has a specific architectural advantage for handling very long-range dependencies that does not scale linearly with intermediate lengths. This anomaly would be a critical point for further investigation in a technical paper. The **relatively small performance gap at lengths 3, 4, and 6** indicates that for mid-complexity queries, the choice between PoG and PoG-E may depend on other factors like computational cost or recall, as their accuracy is nearly equivalent. The widening gap at lengths 2, 7, and 8+ highlights the scenarios where PoG's advantage is most pronounced.

## Bar Chart: Accuracy (%) vs. Length of Paths in SPARQL ### Overview The chart compares the accuracy of two systems, **PoG** (blue) and **PoG-E** (gray), across varying lengths of SPARQL query paths. Accuracy is measured in percentage, with path lengths categorized as 1, 2, 3, 4, 5, 6, 7, and "8+". The legend is positioned at the top, with PoG in blue and PoG-E in gray. ### Components/Axes - **Y-axis**: Accuracy (%) ranging from 0 to 100% in 20% increments. - **X-axis**: Path lengths labeled as 1, 2, 3, 4, 5, 6, 7, and "8+". - **Legend**: Located at the top, associating blue with PoG and gray with PoG-E. ### Detailed Analysis - **Path Length 1**: No data (0% accuracy for both systems). - **Path Length 2**: - PoG: ~100% accuracy. - PoG-E: ~75% accuracy. - **Path Length 3**: - PoG: ~80% accuracy. - PoG-E: ~80% accuracy. - **Path Length 4**: - PoG: ~70% accuracy. - PoG-E: ~70% accuracy. - **Path Length 5**: - PoG: ~55% accuracy. - PoG-E: ~50% accuracy. - **Path Length 6**: - PoG: ~55% accuracy. - PoG-E: ~55% accuracy. - **Path Length 7**: - PoG: ~50% accuracy. - PoG-E: ~45% accuracy. - **Path Length 8+**: - PoG: ~60% accuracy. - PoG-E: ~50% accuracy. ### Key Observations 1. **PoG Dominates Shorter Paths**: PoG achieves near-perfect accuracy (100%) for path length 2, while PoG-E lags at ~75%. 2. **Convergence at Medium Paths**: At path lengths 3 and 4, both systems show similar accuracy (~70-80%). 3. **Decline in Longer Paths**: Accuracy drops for both systems as path length increases beyond 4, with PoG-E consistently underperforming PoG. 4. **Slight Uptick at 8+**: PoG shows a modest recovery (~60%) for very long paths, while PoG-E remains lower (~50%). ### Interpretation The data suggests that **PoG** is more effective than **PoG-E** in handling shorter SPARQL query paths, achieving near-perfect accuracy for path length 2. Both systems degrade in performance as path length increases, but PoG-E consistently underperforms, indicating potential limitations in handling complex or longer queries. The slight improvement in PoG’s accuracy for path length "8+" may imply better scalability for extremely long paths, though this trend is less pronounced. The convergence at medium path lengths (3-4) suggests both systems are similarly capable in moderately complex scenarios. PoG-E’s lower accuracy across most categories highlights a need for optimization in longer-path processing.