对平均移动结构查询进行边界限制以实现更快和更小的RLBWT排列
Bounding the Average Move Structure Query for Faster and Smaller RLBWT Permutations
AI总结：
本文提出通过截断长区间来简化分裂方法，从而在保持最优查询时间的同时提升构造时间，并在理论和实践中展示出空间压缩和查询效率的改进。
摘要：
移动结构通过压缩空间表示具有长连续置换区间的排列，并以最优查询时间实现。它们已成为使用与Burrows-Wheeler变换（BWT）运行数成比例的空间压缩文本索引的重要特征，常用于基因组学。这不仅得益于对过去方法的理论改进，还因实际中的高缓存效率和平均查询时间。即使不使用原始结果的区间分裂平衡提供的最坏情况保证，这一结论也成立。本文证明了一种更简单的分裂类型，即通过截断长区间来限制平均移动结构查询时间，同时获得比传统方法更优的构造时间。这也证明了在单个循环排列的任意起始位置的完整遍历中，查询时间是常数。此类方案在理论和实践中都有意想不到的好处。对于具有r个运行的移动结构，我们用O(r log n)位组件替换所有，从而将整体表示减少O(r log r)位。最坏情况下的查询时间也改进到O(log(n/r))，无需平衡。O(r)时间O(r)空间的构造使我们能够将该方法应用于运行长度编码BWT（RLBWT）排列，如LF和φ，从而在O(r)额外工作空间内获得最优时间的BWT反向和后缀数组（SA）枚举算法。最后，我们引入了Orbit库来支持移动结构，并使用它评估我们的分裂方法。实验发现，长度截断构造比平衡更快且内存使用更少，查询也更快。我们还发现实际中的空间压缩，对于LF来说，在大规模重复基因组集合中至少减少了约40%的磁盘大小。
英文摘要：
The move structure represents permutations with long contiguously permuted intervals in compressed space with optimal query time. They have become an important feature of compressed text indexes using space proportional to the number of Burrows-Wheeler Transform (BWT) runs, often applied in genomics. This is in thanks not only to theoretical improvements over past approaches, but great cache efficiency and average case query time in practice. This is true even without using the worst case guarantees provided by the interval splitting balancing of the original result. In this paper, we show that an even simpler type of splitting, length capping by truncating long intervals, bounds the average move structure query time to optimal whilst obtaining a superior construction time than the traditional approach. This also proves constant query time when amortized over a full traversal of a single cycle permutation from an arbitrary starting position. Such a scheme has surprising benefits both in theory and practice. For a move structure with $r$ runs over a domain $n$, we replace all $O(r \log n)$-bit components to reduce the overall representation by $O(r \log r)$-bits. The worst case query time is also improved to $O(\log \frac{n}{r})$ without balancing. An $O(r)$-time and $O(r)$-space construction lets us apply the method to run-length encoded BWT (RLBWT) permutations such as LF and $ϕ$ to obtain optimal-time algorithms for BWT inversion and suffix array (SA) enumeration in $O(r)$ additional working space. Finally, we introduce the Orbit library for move structure support, and use it to evaluate our splitting approach. Experiments find length capping construction is faster and uses less memory than balancing, with faster queries. We also see a space reduction in practice, with at least a $\sim 40\%$ disk size decrease for LF across large repetitive genomic collections.
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