## 5 Results and Evaluations
### Sequence Complexity Analysis  
In biological sequences, which include DNA, RNA, and protein sequences, etc., average pairwise distance refers to the average genetic variation among all possible pairs within a particular set of sequences. It is used to show similarities or differences among a group of sequences. This complexity is examined by testing the datasets with 1000 sequences generated using the randDNA program. The average pairwise distance between sequences is varied from 50 to 500. The experiments are implemented on the selected datasets using the proposed algorithm along with other popular FM aligners such as BWA, SOAP2, BOWTIE2, and GEM3. The speedup factor is determined by measuring the performance efficiency of the BWA aligner in processing sequences with an average pairwise distance of 50. The runtimes of different FM aligners on sequence datasets in the heterogeneous system of Intel Xeon and Intel Xeon Phi are depicted in Figure 4. As the sequence distance increases, the speedup factor decreases for all aligners. This implies that the acceleration effect weakens in proportion to the sequence distance increase. The LF-EP-based FM aligner exhibits the largest speedup factor, reaching 4.4\(\times\) at a sequence distance of 50, which demonstrates that the LF-EP-based FM aligner has a substantial accelerating effect on short-distance sequences. Additionally, the LF-EP-based FM aligner performs proficiently even at longer distances such as 300, 400, and 500. The LF-EP-based FM aligner consistently displays the highest speedup factor across all sequence distances, hence confirming its suitability for managing high-complexity data. Overall, GEM3 and BOWTIE2 demonstrate lower speedup factors than the LF-EP-based FM aligner. Most of their speedup factors are below 3, indicating less significant speed improvements. Therefore, GEM3 and BOWTIE2 may require further optimization to improve their speedup factors on high-complexity data. At shorter sequence distances (50 and 100), SOAP2 and BWA have speedup factors below 1, indicating that their speed is comparable to the original speed. Nonetheless, their speedup \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**AlignersBenchmarks**} & \multicolumn{2}{c}{**BALIBASE**} & \multicolumn{2}{c}{**OXBENCH**} & \multicolumn{2}{c}{**SABRE**} & \multicolumn{2}{c}{**PREFAB**} \\ \cline{2-9}  & **QS** & **TCS** & **QS** & **TCS** & **QS** & **TCS** & **QS** & **TCS** \\ \hline LF-EP-based FM & 0.870 & 0.590 & 0.892 & 0.460 & 0.720 & 0.680 & 0.880 & 0.820 \\ SOAP2 & 0.860 & 0.580 & 0.880 & 0.450 & 0.710 & 0.670 & 0.870 & 0.810 \\ BOWTIE2 & 0.850 & 0.570 & 0.870 & 0.440 & 0.700 & 0.660 & 0.860 & 0.800 \\ BWA & 0.840 & 0.560 & 0.860 & 0.430 & 0.690 & 0.650 & 0.850 & 0.790 \\ GEM3 & 0.830 & 0.550 & 0.850 & 0.420 & 0.680 & 0.640 & 0.840 & 0.780 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Quality of various FM aligners. factors decrease as the sequence distance increases. Thus, SOAP2 and BWA are appropriate for shorter sequence distances, but their performance may have speedup limitations as the distance increases. In conclusion, the research findings indicate that different aligners respond differently to variations in sequence distance, which affects their performance capabilities. The LF-EP-based FM aligner has been proven to be more efficient than SOAP2 in aligning sequences of both short and long distances. SOAP2, however, consistently demonstrates the least effective performance across all sequence distances. The BOWTIE2 algorithm exhibits a pronounced decline in its speedup as the sequence distance increases. The LF-EP-based FM aligner is the optimal tool for conducting complex sequence alignments on the Xeon-Xeon Phi heterogeneous system. It consistently demonstrates superior acceleration across various read lengths and is particularly well suited for large-scale datasets encompassing a mix of short and long sequences within a heterogeneous computing environment.