This paper introduces a new data-structural object that we call the tiny pointer. In many applications, traditional $\log n $-bit pointers can be replaced with $o (\log n )$-bit tiny pointers at the cost of only a constant-factor time overhead. We develop a comprehensive theory of tiny pointers, and give optimal constructions for both fixed-size tiny pointers (i.e., settings in which all of the tiny pointers must be the same size) and variable-size tiny pointers (i.e., settings in which the average tiny-pointer size must be small, but some tiny pointers can be larger). If a tiny pointer references an element in an array filled to load factor $1 - 1 / k$, then the optimal tiny-pointer size is $\Theta(\log \log \log n + \log k) $ bits in the fixed-size case, and $ \Theta (\log k) $ expected bits in the variable-size case. Our tiny-pointer constructions also require us to revisit several classic problems having to do with balls and bins; these results may be of independent interest. Using tiny pointers, we revisit five classic data-structure problems: the data-retrieval problem, succinct dynamic binary search trees, space-efficient stable dictionaries, space-efficient dictionaries with variable-size keys, and the internal-memory stash problem. These are all well-studied problems, and in each case tiny pointers allow for us to take a natural space-inefficient solution that uses pointers and make it space-efficient for free.

翻译：本文引入了一个我们称之为小指针的新的数据结构对象。 在许多应用中, 传统的 $\ log n $- bit 指针可以用 $o (\ log n) $- bit 指示器替换为 $( log n ) 美元 美元 美元 美元 美元 点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点点