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## Line Charts: Performance Comparison of Sorting Algorithms on Different GPUs
### Overview
The image presents six line charts comparing the performance of three sorting algorithms (WMS, BMS, and RB-Sort) on three different GPUs (Tesla K40c with ECC on/off, and GeForce GTX 1080) with varying numbers of buckets. The y-axis represents the average running time in milliseconds (ms), and the x-axis represents the number of buckets, ranging from 1 to 256. Each chart corresponds to a specific GPU and ECC setting.
### Components/Axes
* **X-axis Title:** "Number of buckets (m)"
* **Y-axis Title:** "Average running time (ms)"
* **Legend:**
* WMS (represented by circles - 'o')
* BMS (represented by triangles pointing upwards - '^')
* RB-Sort (represented by plus signs - '+')
* **Chart Titles:**
* (a) Key-only: K40c (ECC on)
* (b) Key-only: K40c (ECC off)
* (c) Key-only: GTX 1080
* (d) Key-value: K40c (ECC on)
* (e) Key-value: K40c (ECC off)
* (f) Key-value: GTX 1080
* **X-axis Markers:** 1, 2, 4, 8, 16, 32, 64, 128, 256
* **Y-axis Scale:** Approximately 0 to 12 ms (charts a & d), 0 to 10 ms (charts b & e), 0 to 15 ms (charts c & f).
### Detailed Analysis or Content Details
**Chart (a): Key-only: K40c (ECC on)**
* **WMS (o):** Starts at approximately 4.2 ms at 1 bucket, increases steadily to approximately 12.2 ms at 256 buckets. The line slopes upward.
* **BMS (^):** Starts at approximately 3.8 ms at 1 bucket, remains relatively flat until 64 buckets (around 4 ms), then increases to approximately 6.5 ms at 256 buckets.
* **RB-Sort (+):** Starts at approximately 3.6 ms at 1 bucket, remains relatively flat until 32 buckets (around 3.8 ms), then increases to approximately 5.5 ms at 256 buckets.
**Chart (b): Key-only: K40c (ECC off)**
* **WMS (o):** Starts at approximately 3.5 ms at 1 bucket, increases steadily to approximately 8.5 ms at 256 buckets. The line slopes upward.
* **BMS (^):** Starts at approximately 3.2 ms at 1 bucket, remains relatively flat until 64 buckets (around 3.3 ms), then increases to approximately 5.0 ms at 256 buckets.
* **RB-Sort (+):** Starts at approximately 3.1 ms at 1 bucket, remains relatively flat until 32 buckets (around 3.2 ms), then increases to approximately 4.5 ms at 256 buckets.
**Chart (c): Key-only: GTX 1080**
* **WMS (o):** Starts at approximately 2.0 ms at 1 bucket, increases steadily to approximately 5.5 ms at 256 buckets. The line slopes upward.
* **BMS (^):** Starts at approximately 1.8 ms at 1 bucket, remains relatively flat until 64 buckets (around 2.0 ms), then increases to approximately 3.5 ms at 256 buckets.
* **RB-Sort (+):** Starts at approximately 1.7 ms at 1 bucket, remains relatively flat until 32 buckets (around 1.8 ms), then increases to approximately 3.0 ms at 256 buckets.
**Chart (d): Key-value: K40c (ECC on)**
* **WMS (o):** Starts at approximately 7.5 ms at 1 bucket, increases steadily to approximately 12.5 ms at 256 buckets. The line slopes upward.
* **BMS (^):** Starts at approximately 6.5 ms at 1 bucket, remains relatively flat until 64 buckets (around 6.7 ms), then increases to approximately 9.5 ms at 256 buckets.
* **RB-Sort (+):** Starts at approximately 6.0 ms at 1 bucket, remains relatively flat until 32 buckets (around 6.2 ms), then increases to approximately 8.0 ms at 256 buckets.
**Chart (e): Key-value: K40c (ECC off)**
* **WMS (o):** Starts at approximately 6.0 ms at 1 bucket, increases steadily to approximately 10.5 ms at 256 buckets. The line slopes upward.
* **BMS (^):** Starts at approximately 5.0 ms at 1 bucket, remains relatively flat until 64 buckets (around 5.2 ms), then increases to approximately 8.0 ms at 256 buckets.
* **RB-Sort (+):** Starts at approximately 4.5 ms at 1 bucket, remains relatively flat until 32 buckets (around 4.7 ms), then increases to approximately 7.0 ms at 256 buckets.
**Chart (f): Key-value: GTX 1080**
* **WMS (o):** Starts at approximately 3.5 ms at 1 bucket, increases steadily to approximately 8.0 ms at 256 buckets. The line slopes upward.
* **BMS (^):** Starts at approximately 3.0 ms at 1 bucket, remains relatively flat until 64 buckets (around 3.2 ms), then increases to approximately 5.5 ms at 256 buckets.
* **RB-Sort (+):** Starts at approximately 2.5 ms at 1 bucket, remains relatively flat until 32 buckets (around 2.7 ms), then increases to approximately 4.5 ms at 256 buckets.
### Key Observations
* WMS consistently exhibits the highest running time across all GPUs and settings, especially as the number of buckets increases.
* BMS and RB-Sort generally have lower running times than WMS, with RB-Sort often being the fastest.
* The GTX 1080 consistently outperforms the Tesla K40c for all algorithms.
* Enabling ECC on the K40c generally results in slightly higher running times compared to ECC off.
* The performance difference between algorithms is more pronounced with a larger number of buckets.
### Interpretation
The data demonstrates the performance characteristics of different sorting algorithms on various GPUs. The GTX 1080 consistently outperforms the K40c, indicating its superior processing capabilities. WMS appears to be the least efficient algorithm, scaling poorly with an increasing number of buckets. BMS and RB-Sort are more efficient, particularly RB-Sort, which maintains lower running times across all scenarios. The slight performance penalty associated with ECC on the K40c suggests a trade-off between performance and data integrity. The "key-value" scenarios generally exhibit higher running times than the "key-only" scenarios, likely due to the additional overhead of handling values alongside keys. These results are valuable for selecting the most appropriate sorting algorithm and hardware configuration based on specific performance requirements and data characteristics. The consistent upward slope of the WMS lines suggests a potential algorithmic complexity issue that becomes more apparent with larger datasets.
