We present a linearizable, non-blocking @math -ary search tree ( @math -ST) that supports fast searches and range queries. Our algorithm uses single-word compare-and-swap (CAS) operations, and tolerates any number of crash failures. Performance experiments show that, for workloads containing small range queries, our @math -ST significantly outperforms other algorithms which support these operations, and rivals the performance of a leading concurrent skip-list, which provides range queries that cannot always be linearized.
Persistent data structures @cite_6 offer another approach. The nodes in a persistent data structure are immutable, so updates create new nodes, rather than modifying existing ones. In the case of a persistent tree, a change to one node involves recreating the entire path from the root to that node. After the change, the data structure has a new root, and the old version of the data structure remains accessible (via the old root). Hence, it is trivial to implement range queries in a persistent tree. However, significant downsides include contention at the root, and the duplication of many nodes during updates.
@cite_6
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When a C programmer needs an efficient data structure for a particular problem, he or she can often simply look one up in any of a number of good textbooks or handbooks. Unfortunately, programmers in functional languages such as Standard ML or Haskell do not have this luxury. Although some data structures designed for imperative languages such as C can be quite easily adapted to a functional setting, most cannot, usually because they depend in crucial ways on assignments, which are disallowed, or at least discouraged, in functional languages. To address this imbalance, we describe several techniques for designing functional data structures, and numerous original data structures based on these techniques, including multiple variations of lists, queues, double-ended queues, and heaps, many supporting more exotic features such as random access or efficient catenation. In addition, we expose the fundamental role of lazy evaluation in amortized functional data structures. Traditional methods of amortization break down when old versions of a data structure, not just the most recent, are available for further processing. This property is known as persistence, and is taken for granted in functional languages. On the surface, persistence and amortization appear to be incompatible, but we show how lazy evaluation can be used to resolve this conflict, yielding amortized data structures that are efficient even when used persistently. Turning this relationship between lazy evaluation and amortization around, the notion of amortization also provides the first practical techniques for analyzing the time requirements of non-trivial lazy programs. Finally, our data structures offer numerous hints to programming language designers, illustrating the utility of combining strict and lazy evaluation in a single language, and providing non-trivial examples using polymorphic recursion and higher-order, recursive modules.