We consider space-bounded computations on a random-access machine, where the input is given on a read-only random-access medium, the output is to be produced to a write-only sequential-access medium, and the available workspace allows random reads and writes but is of limited capacity. The length of the input is N elements, the length of the output is limited by the computation, and the capacity of the workspace is O ( S ) bits for some predetermined parameter S ≥ lg N . We present a state-of-the-art priority queue—called an adjustable navigation pile —for this restricted model. This priority queue supports M inimum in O (1) time, C onstruct in O ( N ) time, and E xtract - min in O ( N / S + lg S ) time for any S ≥ lg N . The priority queue can be further augmented in O ( N ) time to deal with a batch of at most S elements in a specified range of values at a time, and allow to I nsert (activate) or E xtract (deactivate) an element among these elements, such that I nsert and E xtract take O ( N / S + lg S ) time for any S ≥ lg N . We show how to use our data structure to sort N elements and to compute the convex hull of N points in the Euclidean plane in O ( N 2 / S + N lg S ) time for any S ≥ lg N . Following a known lower bound for the space-time product of any branching program for finding unique elements, both our sorting and convex-hull algorithms are optimal. The adjustable navigation pile has turned out to be useful when designing other space-efficient algorithms, and we expect that it will find its way to yet other applications.

中文翻译：

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内存可调节导航桩，适用于分拣和凸面船体

我们考虑随机存取机器上的空间受限计算，其中输入在只读随机存取介质上给出，输出将生成到只写顺序存取介质，并且可用工作空间允许随机读写，但容量有限。输入的长度是ñ元素，输出的长度受计算限制，工作空间的容量为○(小号) 一些预定参数的位小号≥ lgñ. 我们提出了一个最先进的优先级队列——称为可调式导航桩——对于这个受限模型。这个优先级队列支持 M最低限度在○(1) 时间，C指导在○(ñ) 时间和 E提取物-分钟在○(ñ/小号+ 体重小号) 任何时间小号≥ lgñ. 优先级队列可以进一步增加○(ñ) 最多处理一批的时间小号一次指定值范围内的元素，并允许我插入（激活）或 E提取物（停用）这些元素中的一个元素，这样我插入和 E提取物拿○(ñ/小号+ 体重小号) 任何时间小号≥ lgñ. 我们展示了如何使用我们的数据结构进行排序ñ元素并计算凸包ñ欧几里得平面上的点○(ñ 2/小号+ñlg小号) 任何时间小号≥ lgñ. 遵循任何用于查找唯一元素的分支程序的时空乘积的已知下限，我们的排序和凸包算法都是最优的。事实证明，在设计其他节省空间的算法时，可调节导航堆很有用，我们希望它能够找到其他应用程序。