可合并字典
Mergeable Dictionaries
摘要：
本文提出了一种可合并字典抽象数据类型的数据结构，它支持对不相交的全序数据集的集合的下列操作：前序搜索、分裂和合并。虽然Predecessor-Search和Split以正常方式工作，但新操作是Merge。虽然在典型的可合并字典（例如2-4树）中，合并操作只能在键空间中跨越不相交区间的集合上执行，但这里的结构没有这样的限制，并且允许合并任意交织的集合。Tarjan和Brown提出了一种数据结构，它可以在O（log n）摊销时间内处理任意的合并操作，如果操作集被限制为不包括拆分操作。在存在拆分操作的情况下，其结构的摊销时间复杂度变为Ω（n）。Farach和Thorup给出了一种数据结构，它同时支持Split和Merge操作，每次操作的平均时间为O（log^2 n）。相比之下，我们的数据结构支持所有的操作，包括拆分和合并，在O（log n）摊销时间，从而表明，交错合并操作可以支持在没有额外的成本相对于一个不相交的合并操作。
英文摘要：
A data structure is presented for the Mergeable Dictionary abstract data type, which supports the following operations on a collection of disjoint sets of totally ordered data: Predecessor-Search, Split and Merge. While Predecessor-Search and Split work in the normal way, the novel operation is Merge. While in a typical mergeable dictionary (e.g. 2-4 Trees), the Merge operation can only be performed on sets that span disjoint intervals in keyspace, the structure here has no such limitation, and permits the merging of arbitrarily interleaved sets. Tarjan and Brown present a data structure which can handle arbitrary Merge operations in O(log n) amortized time per operation if the set of operations is restricted to exclude the Split operation. In the presence of Split operations, the amortized time complexity of their structure becomes Ω(n). A data structure which supports both Split and Merge operations in O(log^2 n) amortized time per operation was given by Farach and Thorup. In contrast, our data structure supports all operations, including Split and Merge, in O(log n) amortized time, thus showing that interleaved Merge operations can be supported at no additional cost vis-a-vis disjoint Merge operations.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
