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. It has been open for a long time whether these indices can be constructed in both 0(n log n) time and 0(n log n)-bit working space, where n denotes the length of the text. In the literature, the fastest algorithm runs in O(n) time, while it requires 0(n log n)-bit working space.On the other hand, the most space-efficient algorithm requires 0(n)-bit working space while it runs in 0(n log n) time.This paper breaks the long-standing time-and-space barrier under the unit-cost word RAM. We give an algorithm for constructing the suffix array which takes 0(n) time and 0(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 0(nlog2n) time and 0(n)-bit working space for any 0 < < 1. Apart from that, our algorithm can also be adopted to build other existing full-text indices, such asCompressed Suffix Tree, Compressed Suffix Arrays and FM-index.We also study the general case where the size of the alphabet A is not constant. Our algorithm can construct a suffix array and a suffix tree using optimal 0(n log |A|)-bit working space while running in 0(n log log |A|) time and 0(n log n) time, respectively. These are the first algorithms that achieve 0(n log n) time with optimal working space, under a reasonable assumption that log |A| = 0(log n).