You would use a colon or semi-colon when joining 2 independent clauses. But in your example, the second clause  
>as necessity of additional time for rectifying the algorithms, lengthy literature survey than expected and etc.  

refers to the reasons for *summarizing* mentioned in the first clause. Also the first clause is not independent (able to stand by itself). So you should use a comma instead.
>Here, I would like to summarize the reasons for my extension request, **due to the** necessity of additional time for rectifying the algorithms, lengthy literature survey than expected and etc.  

I used *due to* because the second clause is explaining or expanding on the first clause.