We consider the dynamic dictionary problem for multisets. Given an upper bound $n$ on the total cardinality of the multiset (i.e., including multiplicities) at any point in time, the goal is to design a data structure that supports multiplicity queries and allows insertions and deletions to the multiset (i.e., the dynamic setting). The data structure must be space-efficient (the space is $1+o(1)$ times the information-theoretic lower bound) and support all operations in constant time with high probability.
In this paper, we present the first dynamic dictionary for multisets that achieves these performance guarantees. This answers an open problem of Arbitman, Naor and Segev (FOCS 2010). The previously best-known construction of Pagh, Pagh and Rao (SODA 2005) supports membership in constant time, multiplicity queries in $O(\log n)$ time in the worst case, and insertions and deletions in constant expected amortized time. The main technical component of our solution is a strategy for efficiently storing variable-length binary counters using weighted balls-into-bins experiments in which balls have logarithmic weights.
We also obtain a counting filter that approximates multiplicity queries with a one sided error, using the reduction of Carter et al. (STOC 1978). Counting filters have received significant attention over the years due to their applicability in practice.We present the first counting filter with constant time operations.
Online matching games in bipartite expanders: applications to bitprobes and dictionaries with non-adaptive probing
National Research University Higher School of Economics, Faculty of Computer Science（高等经济大学计算机学院）；Department of Computer and Information Sciences, Towson University（汤森大学计算机与信息科学系）
De-amortized Cuckoo Hashing: Provable Worst-Case Performance and Experimental Results
Cuckoo hashing是一个非常实用的动态字典：它提供了摊销常数插入时间，最坏情况下的常数删除时间和查找时间，以及良好的内存利用率。然而，在插入n个元素的过程中，有一个明显的概率，一些插入需要Ω（log n）时间。尽管这种分期保证可能适用于某些应用，但在其他应用（例如高性能路由）中，这是非常不可取的。最近，Kirsch和Mitzenmacher（Allerton '07）提出了一种使用各种保留其吸引人的特性的加密技术的cuckoo hashing的去摊销。Kirsch和Mitzenmacher通过实验结果证明了对布谷鸟散列的最坏情况性能的显着改善，但他们留下了构建具有可证明属性的方案的问题。在这项工作中，我们遵循Kirsch和Mitzenmacher，并提出了一个去摊销的布谷鸟散列，可证明保证恒定的最坏情况下的操作。具体地，对于多项式多个操作的任何序列，在初始化阶段的随机性上具有压倒性的概率，每个操作在恒定时间内执行。我们的理论分析和实验结果表明，该计划是非常有效的，并提供了一个实际的替代方案，只有其他已知的动态字典与这种最坏的情况下的保证，由于Dietzfelbinger和Meyer auf der Heide（ICALP '90）。
