# Construction of Suffix Array in External Memory - Follow Up

Many short-read alignment programs (BWA, Bowtie, SOAP2) use suffix arrays to hold indexed reference genome, because suffix arrays provide savings in memory. In case of human genome, BWT-indexed genome can be loaded with less than 4 GB RAM. However, construction of suffix arrays is not so memory efficient and can take lot more than 4GB of RAM for human genome. Few weeks back, we covered the state-of-the-art algorithm from Timo Bergmann and colleagues on constructing suffix arrays and LCP arrays in external memory. Although Dr. Bergmann’s website provides excellent information on his algorithm with paper, slides and code, we did not understand few parts of the implementation. We sent an email to Dr. Bergmann with our questions and he graciously replied with helpful comments. We are sharing the response for our readers in case they get stuck where we did.

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Question:

_Getting back to you algorithm, I understand SA-IS very well and am trying to figure out the difference in your implementation. Let us say, you have a massive file in the hard-disk that you want to construct Suffix array of. SA- IS goes through the array in memory, and finds locations of S. Instead, you are reading chunks of it from end to beginning, and creating pointers to locations of S, right?

Q1. How are you storing those pointers? In disk? In memory?

Q2. In the next step, I presume you are running some kind of radix sort on the sub-words beginning from S* elements. Are you rearranging the pointers in memory based on reading the letters in disk? Does that need many rounds of random disk access for every S* and every radix position? SA-IS algorithm did not use this sorting step and instead placed S* elements in their respective buckets._

Dr. Bergmann:

*Answers to Q1+2: Goal of the the first part it just to order all S-substrings globally. Thus we read a portion of them into memory, sort them, write them to EM. Repeat until done. Then merge them, (reading Theta(M/B) sorted streams,) yielding a stream of sorted S-substrings. No pointers are involved; pointers dont work in EM. In the code there are the classes “Substring” and “SubstringPtr”. The Ptr class is used to sort all S-substring within the currently loaded portion of the input.

Only remaining problem are “long” (> B) S*-strings. These, however, can be split basically arbitrarily.

SA-IS does not explicity sort the S-substrings, that is true. It does however, sorting them implicitly in it’s first step: by putting the S-substrings into the buckets in string order and performing the two inducing sweeps, it implicitly sorts S*-substrings. Actually that’s the only purpose of the first pair of sweeps.

SA-DS does explicit radix sorting. That is similar to was we do.**

Question:

_Q3. If you have suffix arrays or Burrows Wheeler transform constructed for two very large files, do you know any easy way to merge them?

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Dr. Bergmann:

**No I don’t think it can be done efficiently. The best ideas about merging are already used in bwtdisk.

I remember that to merge SA_1 and SA_2 of T_1 and T_2 efficiently in RAM you have to search for the position of each longer suffix “s + T_2” in the SA_2 with s being a suffix of T_1 (the search can be done incrementally using backwards search). I cant remember where I read that idea atm.**

Written by M. //