鲁棒自适应搜索
Robust and adaptive search
摘要：
二分搜索在具有最佳$\log n$查询数的排序数组中查找给定元素。然而，即使数组只是轻微无序或对其元素的访问容易出错，二分搜索也会失败。我们研究了最坏情况下的查询复杂性的搜索算法，是强大的不精确的查询，并适应扰动的元素的顺序。我们给（几乎）严格的结果，量化查询错误和测量阵列混乱的各种参数。特别是，我们展示的设置中的查询复杂性的$\log n + ck$，$(1+\varepsilon)\log n + ck$，和$\sqrt{cnk}+o(nk)$是最好的可能参数值$k$，任何$\varepsilon>0$，和常数$c$。
英文摘要：
Binary search finds a given element in a sorted array with an optimal number of $\log n$ queries. However, binary search fails even when the array is only slightly disordered or access to its elements is subject to errors. We study the worst-case query complexity of search algorithms that are robust to imprecise queries and that adapt to perturbations of the order of the elements. We give (almost) tight results for various parameters that quantify query errors and that measure array disorder. In particular, we exhibit settings where query complexities of $\log n + ck$, $(1+\varepsilon)\log n + ck$, and $\sqrt{cnk}+o(nk)$ are best-possible for parameter value $k$, any $\varepsilon>0$, and constant $c$.
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