To answer your question: the only way to know whether your algorithm has been published before is doing a literature search. You will eventually have to do this, anyway. No paper with an empty references section will be published, unless it is a truly extraordinary paper defining a new field of science.
But, I may have some good news for you. The other accepted answer conveyed bad news that your algorithm most likely has been published already. I have invented in the last two years three algorithms for which my literature search has not found prior art. The algorithms were invented before knowing the literature of the field, and I only did the literature search later to find out if the algorithms were novel. Not only that, but all of the algorithms are practically as simple as or simpler than the prior art. Two of the algorithms are 10x faster than prior art; the remaining one of them 2x faster for sorted data but 2x slower for unsorted data. I intend to publish the first paper about one of the 10x faster algorithms in a conference the next summer.
So, I would not omit doing the literature search merely based on the bad news of the accepted answer that your work most likely has been published already (yes, I know the other answer encouraged you to do a literature search but on the other hand presented it as "bad news"). You should, however, avoid calling your algorithm "novel" if the literature search failed to find prior art, because there is always a possibility of somebody already knowing your algorithm. And, if the paper is only about that algorithm, then it is expected by the reader that the algorithm is novel, so why mention it explicitly?
In order to publish your paper, you must obviously have heavy supporting evidence for the performance of your algorithm in comparison to the prior art. How fast it is? Does it parallelize? If so, what is the performance as a function of the CPU core count? If the literature search finds prior art, perhaps you could anyway publish your performance measurement results. After all, a thorough analysis of the real-world performance of various already known algorithms might be something that has been missing. But, getting a performance comparison paper accepted without containing a novel algorithm is obviously harder than getting a paper about a novel algorithm accepted, so you should do the literature search as early as possible in order to know which direction to take.