An Efficient Data Structure to Obtain Range Minima in Constant Time in Constructing Suffix Arrays
Heejin Park · Jeongbo gwahaghoe nonmunji. si'seu'tem mich i'lon · 2004
We present an efficient data structure to obtain the range minima in an away in constant time. Recently, suffix ways are extensively used to search DNA sequences fast in bioinformatics. In constructing suffix arrays, solving the range minima problem is necessary When we construct suffix arrays, we should solve the range minima problem not only in a time-efficient way but also in a space-efficient way. The reason is that DNA sequences consist of millions or billions of bases. Until now, the most efficient data structure to find the range minima in an way in constant time is based on the method that converts the range minima problem in an array into the LCA (Lowest Common Ancestor) problem in a Cartesian tree and then converts the LCA problem into the range minima problem in a specific array. This data structure occupies O( n) space and is constructed in O(n) time. However since this data structure includes intermediate data structures required to convert the range minima problem in an array into other problems, it requires large space (=13n) and much time. Our data structure is based on the method that directly solves the range minima problem. Thus, our data structure requires small space (=5n) and less time in practice. As a matter of course, our data structure requires O(n) time and space theoretically.