AI 中文总结
该研究针对对数方法的读写乘积，在强物化合并栈模型下，得出不同查询类型的读写乘积界，明确了精确顺序等查询的访问模型障碍与选择查询的二次障碍。
AI 中文摘要
对数方法是一种经典的静态转动态变换：它将一个动态有序集合存储为多个不可变的静态组件，并通过合并操作对这些组件进行重建。这种相同的组件-合并规则是写优化有序索引的基础，在这类索引中，必须平衡廉价插入操作与精确有序查询的需求。本文研究在n次插入后仅插入的版本，针对抽象键，采用强物化合并栈模型，该模型包含顺序组件合并，且每次查询对活跃组件进行一次正向扫描。我们对n次插入期间写入的总数据量与单次查询最坏情况下读取的数据量的乘积（即读写乘积）进行了界定，最优界如下：成员查询与本地证书查询：Θ(n log² n)；带命名键或端点的顺序查询与范围查询：Θ(n log³ n)；选择查询：Θ(n²)。因此，对数方法并未施加通用的动态开销：在物化单向访问下，最优值取决于查询在扫描开始前揭示的信息。这明确了精确顺序查询和范围查询额外对数因子背后的访问模型障碍，以及选择查询的二次障碍。
英文摘要
The logarithmic method is a classical static-to-dynamic transformation: it stores one dynamic ordered set as several immutable static components and rebuilds them by merges. The same component-and-merge discipline underlies write-optimized ordered indexes, where cheap insertions must be reconciled with exact ordered queries. In this paper, we study the insertion-only version after $n$ insertions, over abstract keys, in a strongly materialized merge-stack model with sequential component merges and one forward scan of the live components per query. We bound the product between the total amount of data written during the $n$ insertions and the worst-case amount of data read by a single query, known as the write-read product. The optimal bounds are as follows: - Membership and local certificates: $Θ(n\log^2 n)$. - Order and range queries with named keys or endpoints: $Θ(n\log^3 n)$. - Select: $Θ(n^2)$. Thus, the logarithmic method does not impose a universal dynamic overhead: under materialized one-way access, the optimum depends on what information the query reveals before the scan starts. This pinpoints the access-model obstruction behind the extra logarithm for exact order and range queries, and the quadratic barrier for select.
