Combined Data Structure for Previous- and Next-Smaller-Values

Details Combined Data Structure for Previous- and Next-Smaller-Values Combined Data Structure for Previous- and Next-Smaller-Values

2011-02-02

arxiv.org/abs/1102.0395v1

Computer Science

Data Structures and Algorithms

to appear in Theoretical Computer Science

Scientific paper

Let $A$ be a static array storing $n$ elements from a totally ordered set. We present a data structure of optimal size at most $n\log_2(3+2\sqrt{2})+o(n)$ bits that allows us to answer the following queries on $A$ in constant time, without accessing $A$: (1) previous smaller value queries, where given an index $i$, we wish to find the first index to the left of $i$ where $A$ is strictly smaller than at $i$, and (2) next smaller value queries, which search to the right of $i$. As an additional bonus, our data structure also allows to answer a third kind of query: given indices $i

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