Efficiently aligning a lot of reads on the same small reference sequence The context: I have a DNA-sequence coding for a protein, about 1500 bp in length. Using NGS, a lot of reads of (mutants of) this same sequence were acquired. All of these reads need to be aligned to the reference. We're talking about a lot of reads (100,000 - 1,000,000) of not too short length (120 - 300 bp). All of these reads can belong to different mutants of the template sequence, so the alignment is necessary to determine the exact sequence of every single mutant.

Currently, I'm just using Smith-Waterman-based local alignment to align every single read to the reference one by one. Yet I can't help but feel there might be a more computationally/time-efficient solution to this specific problem. 

Maybe there exists an algorithm that's not very efficient for most alignment problems, but that becomes very worthwile if it has to map a ton of reads to the same place over and over again. For example, it might do some time-consuming operations on the short template that make it fast to align reads to it, but these operations aren't worth it if only aligning a couple of reads. That's just an idea, I don't know all the different techniques that are out there.

So, to recap: I want to align a lot (100,000 - 1,000,000) of 120-300 bp reads to the same short 1500 bp reference sequence. If anyone has any suggestions about an algorithm, or just a specific workflow, that is particularly suited to do this, it would be appreciated. I work in R so I can implement some things myself, it doesn't have to be a ready-to-use software package or anything like that. Thanks in advance!
I would suggest using a whole genome aligner like BWA or BOWTIE2 and swapping out the whole genome reference with your specific reference.  

These alignment algorithms are designed to align large numbers of NGS reads against a single reference.  They can be used with any reference including short ones like your example or small viruses.