1. Note that "algorithms" cannot be patented (in the US) [A]. Application of an algorithm to solve a specific problem can however be patented.
2. I am assuming you have access to the said patent. With '1' above in mind, read through the said patent multiple times, paying attention to the "claims" and see if you are actually violating them. Ignore if you have already done this. Just know that the claims are the most important part. Unless what you are selling includes everything that is needed by the independent claims of the patent, you are not violating.
3. If you find that you would be violating the patent, things will be against you if a lawsuit happens, as this will be considered to be a case of willful infringement, since it is already clear that you are aware of the patent.
4. If you are adding some real value on the top of what is claimed by the competition's patent or product, you may consider filing a patent of your own invention, if any, and if patentable. I know HN crowd is generally against patenting, so that is your call. This will NOT help you overcome the competition's patent, but would come in the way of your competition copying those aspects of your invention that were not already there in their product or patent.
5. Last but not the least, you may consider working in association with them rather than competing. Patents and laws aside, there is often a better human-friendly way of doing things.
Having said that, at the end of the day, evaluate your risks and rewards for this and other projects you may have in mind, and pick your best bets.
One of the principal reasons frivolous patents are filed is to unjustly intimidate small operators like yourself.
That would invalidate the patent due to prior art...