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Parallel construction of wavelet trees on multicore architectures

2016; Springer Science+Business Media; Volume: 51; Issue: 3 Linguagem: Inglês

10.1007/s10115-016-1000-6

0219-1377

José Fuentes‐Sepúlveda, Erick Elejalde, Leo Ferres, Diego Seco,

Advanced Steganography and Watermarking Techniques

The wavelet tree has become a very useful data structure to efficiently represent and query large volumes of data in many different domains, from bioinformatics to geographic information systems. One problem with wavelet trees is their construction time. In this paper, we introduce two algorithms that reduce the time complexity of a wavelet tree's construction by taking advantage of nowadays ubiquitous multicore machines. Our first algorithm constructs all the levels of the wavelet in parallel with O(n) time and $$O(n\lg \sigma + \sigma \lg n)$$ bits of working space, where n is the size of the input sequence and $$\sigma $$ is the size of the alphabet. Our second algorithm constructs the wavelet tree in a domain decomposition fashion, using our first algorithm in each segment, reaching $$O(\lg n)$$ time and $$O(n\lg \sigma + p\sigma \lg n/\lg \sigma )$$ bits of extra space, where p is the number of available cores. Both algorithms are practical and report good speedup for large real datasets.