I am in a bit of a situation. Basically, the research on which I was basing my PhD was carried out by a former post-doc in our group. After one year and a half not being able to replicate his results, I exploited my admin privileges on our cluster to download his codes. I discovered that the algorithms he used in his publication are different from the ones used in the experiments, as the ones he claims he is using are not really applicable and the ones he is using do not have the claimed complexity. He even went so far to provide made up (theoretical) timings to cover this up.
My supervisor knows about this issue from me and he also knows that the post-doc has stopped responding to my mails trying to replicated his work. My supervisor is very hands-off and I don't believe that he has any fault in this but his name is on the publication. Moreover, I feel he is disappointed in the post-doc and feels guilty. So, it seems to me that pressing the issue does no good for me and I have stopped mentioning the topic to my supervisor. (I am still quite angry about this issue as this has cost me about a year and a half of my PhD)
I have been able to salvage the original idea of the publication and come up with an algorithm which has the correct complexity and we are now writing the paper. To the reader these two publications might appear extremely similar and I would like to include a sentence in the introduction that the previous publication is not a working algorithm. What is a good, diplomatic way of doing this?