Abstract

With the first human DNA being decoded into a sequence of about 2.8 billion characters, many biological research has been centered on analyzing this sequence. Theoretically speaking, it is now feasible to accommodate an index for human DNA in the main memory so that any pattern can be located efficiently. This is due to the recent breakthrough on compressed suffix arrays, which reduces the space requirement from O(n log n) bits to O(n) bits for indexing a text of n characters. However, constructing compressed suffix arrays is still not an easy task because we still have to compute suffix arrays first and need a working memory of O(n log n) bits (i.e., more than 13 Gigabytes for human DNA). This paper initiates the study of constructing compressed suffix arrays directly from the text. The main contribution is a construction algorithm that uses only O(n) bits of working memory, and the time complexity is O(n log n). Our construction algorithm is also time and space efficient for texts with large alphabets such as Chinese or Japanese. Precisely, when the alphabet size is |Σ|, the working space becomes O(n(H0 + 1)) bits, where H0 denotes the order-0 entropy of the text and it is at most log |Σ|; for the time complexity, it remains O(n log n) which is independent of |Σ|. 1

Citations