Breaking a Time-and-Space Barrier in Constructing Full-Text Indices

Suffix trees and suffix arrays are the most prominent full-text indices, and their construction algorithms are well studied. In the literature, the fastest algorithm runs in O(n) time, while it requires O(n log n)-bit working space, where n denotes the length of the text. On the other hand, the most space-efficient algorithm requires O(n)-bit working space while it runs in O(n log n) time. It was open whether these indices can be constructed in both o(n log n) time and o(n log n)-bit working space. This paper breaks the above time-and-space barrier under the unit-cost word RAM. We give an algorithm for constructing the suffix array which takes O(n) time and O(n)-bit working space, for texts with constant-size alphabets. Note that both the time and the space bounds are optimal. For constructing the suffix tree, our algorithm requires O(n log n) time and O(n)-bit working space for any 0 < 2 < 1. Apart from that, our algorithm can also be adopted to build other existing full-text indices, such as Compressed Suffix Tree, Compressed Suffix Arrays and FM-index. We also study the general case where the size of the alphabet Σ is not constant. Our algorithm can construct a suffix array and a suffix tree using optimal O(n log |Σ|)-bit working space while running in O(n log log |Σ|) time and O(n(log n + log |Σ|)) time, respectively. These are the first algorithms that achieve o(n log n) time with optimal working space. Moreover, for the special case where log |Σ| = O((log log n)1−2), we can speed up our suffix array construction algorithm to the optimal O(n).