Linear Time Construction Of Compressed Text Indices In Compact Space

We show that the compressed suffix array and the compressed suffix tree for a string of length n over an integer alphabet of size a < n can both be built in 0(n) (randomized) time using only 0(n log o-) bits of working space. The previously fastest construction algorithms that used 0 (n log a) bits of space took times 0(n log logo-) and 0(n log' n) respectively (where E is any positive constant smaller than 1).