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: $\Theta(n\log^2 n)$. - Order and range queries with named keys or endpoints: $\Theta(n\log^3 n)$. - Select: $\Theta(n^2)$. 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.
— The global aviation industry is struggling with a growing pilot shortage and rising operational costs. For this reason, Single Pilot Operations (SPO) has become one of the most important directions for the future of commercial aviation. This paper focuses on an SPO system architecture that ensures high safety, reliability, and flight efficiency. After analyzing key requirements including air-ground coordination, human-machine task distribution, and full-process flight automation, this paper proposes a four-party collaborative framework that includes the single pilot, an onboard intelligent core system, distributed ground support stations, and a cloud AI decision-making system. This paper also provides detailed designs for the intelligent decision-making module and the distributed ground support system, and evaluates its advantages in safety, efficiency, and scalability. Results show that this architecture can significantly reduce pilot workload, support better global flight decisions, and offer a practical technical plan for real-world SPO applications. At the same time, this study identifies technical and regulatory challenges that may slow down SPO implementation and offers possible solutions.
Sichen Wang· International journal of eng...· 0 citations
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