Space-Efficient Construction of Compressed Suffix Trees
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We show how to build several data structures of central importance to string processing, taking as input the Burrows-Wheeler transform (BWT) and using small extra working space. Let n be the text length and σ be the alphabet size. We first provide two algorithms that enumerate all LCP values and suffix tree intervals in O(nσ) time using just o(nσ) bits of working space on top of the input BWT. Using these algorithms as building blocks, for any parameter 0 < ϵ≤ 1 we show how to build the PLCP bitvector and the balanced parentheses representation of the suffix tree topology in O(n(σ + ϵ^-1· n)) time using at most nσ·(ϵ + o(1)) bits of working space on top of the input BWT and the output. In particular, this implies that we can build a compressed suffix tree from the BWT using just succinct working space (i.e. o(nσ) bits) and any time in Θ(nσ) + ω(n n). This improves the previous most space-efficient algorithms, which worked in O(n) bits and O(n n) time. We also consider the problem of merging BWTs of string collections, and provide a solution running in O(nσ) time and using just o(nσ) bits of working space. An efficient implementation of our LCP construction and BWT merge algorithms use (in RAM) as few as n bits on top of a packed representation of the input/output and process data as fast as 2.92 megabases per second.
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