Abstract:The move structure represents a permutation $\pi$ of $[0,n)$ by partitioning the domain into $O(r)$ disjoint, contiguously permuted intervals, with $r$ being the minimum number of such intervals. This data structure occupies $O(r)$ words of space and enables $O(1)$-time computation of $\pi(i)$ given the interval that contains $i$. For permutations where $r \ll n$, this provides an efficient, compressed representation for navigation. While existing best $O(r)$-space construction approaches require $O(r\log r)$-time, we present an optimal $O(r)$-time and space construction algorithm. This is achieved by replacing balanced search trees with pointer-based lists by introducing a bidirectional strategy that synchronizes construction of the structures for $\pi$ and its inverse $\pi^{-1}$ in a single, unified pass. By applying this algorithm, we achieve the first optimal $O(n)$-time construction of the longest common prefix (LCP) array from a run-length-encoded Burrows-Wheeler transform (RLBWT) of $r$ runs in $O(r)$ working space. Empirical evaluation on pangenome-scale data confirms that our move structure construction algorithm is consistently faster than the previous best, achieving speedups of up to $\sim 2\times$ with comparable memory usage.
From: Nathaniel K. Brown [view email]
[v1]
Mon, 23 Mar 2026 16:12:19 UTC (37 KB)
[v2]
Fri, 24 Apr 2026 03:50:39 UTC (288 KB)
[v3]
Tue, 21 Jul 2026 04:25:14 UTC (341 KB)
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