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I'm an undergrad computer science student who has been working on a paper for the past few months, and quite recently I saw a similar paper already published by someone on IEEE.

Can I still publish the paper? Are there any ways in which I can prove that its an independent paper?

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If you have done your research independently, then proving that your work is not plagiarized from the other paper should be almost trivially easy. While some of the core ideas or themes may be the similar, there are so many possible choices in how to go about implementing and testing ideas that the details of your work will almost certainly be quite different --- certainly enough that there is no reason to fear accusations of plagiarism if you didn't plagiarize.

Now, as to whether you can publish or not: the key question here is whether you make any significant contribution in your paper that has not already been made by the other paper. Since you are aware of the other paper, you must certainly put it in your related work section and discuss how your work is similar or different. If you can explain a difference that you find to be genuinely significant, then there is a good chance that the reviewers will agree with you, and that your paper can be published.

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