We introduce the Random Access Zipper (RAZ), a simple, purely-functional data structure for editable sequences. A RAZ combines the structure of a zipper with that of a tree: like a zipper, edits at the cursor require constant time; by leveraging tree structure, relocating the edit cursor in the sequence requires logarithmic time. While existing data structures provide these time bounds, none do so with the same simplicity and brevity of code as the RAZ. The simplicity of the RAZ provides the opportunity for more programmers to extend the structure to their own needs, and we provide some suggestions for how to do so.
The -Vector @cite_2 uses a balanced tree to represent immutable vectors, focusing on practical issues such as parallel performance and cache locality. These performance considerations are outside the scope of our current work, but are interesting for future work.
@cite_2
2036610497 2116365500 2093788424 2512549881
State-of-the-art immutable collections have wildly differing performance characteristics across their operations, often forcing programmers to choose different collection implementations for each task. Thus, changes to the program can invalidate the choice of collections, making code evolution costly. It would be desirable to have a collection that performs well for a broad range of operations. To this end, we present the RRB-Vector, an immutable sequence collection that offers good performance across a large number of sequential and parallel operations. The underlying innovations are: (1) the Relaxed-Radix-Balanced (RRB) tree structure, which allows efficient structural reorganization, and (2) an optimization that exploits spatio-temporal locality on the RRB data structure in order to offset the cost of traversing the tree. In our benchmarks, the RRB-Vector speedup for parallel operations is lower bounded by 7x when executing on 4 CPUs of 8 cores each. The performance for discrete operations, such as appending on either end, or updating and removing elements, is consistently good and compares favorably to the most important immutable sequence collections in the literature and in use today. The memory footprint of RRB-Vector is on par with arrays and an order of magnitude less than competing collections. We consider the implementation of abstract data types for the static objects: binary tree, rooted ordered tree and balanced parenthesis expression. Our representations use an amount of space within a lower order term of the information theoretic minimum and support, in constant time, a richer set of navigational operations than has previously been considered in similar work. In the case of binary trees, for instance, we can move from a node to its left or right child or to the parent in constant time while retaining knowledge of the size of the subtree at which we are positioned. The approach is applied to produce succinct representation of planar graphs in which one can test adjacency in constant time. We consider the implementation of abstract data types for the static objects: binary tree, rooted ordered tree, and a balanced sequence of parentheses. Our representations use an amount of space within a lower order term of the information theoretic minimum and support, in constant time, a richer set of navigational operations than has previously been considered in similar work. In the case of binary trees, for instance, we can move from a node to its left or right child or to the parent in constant time while retaining knowledge of the size of the subtree at which we are positioned. The approach is applied to produce a succinct representation of planar graphs in which one can test adjacency in constant time. Low-dimensional vector representations are widely used as stand-ins for the text of words, sentences, and entire documents. These embeddings are used to identify similar words or make predictions about documents. In this work, we consider embeddings for social media users and demonstrate that these can be used to identify users who behave similarly or to predict attributes of users. In order to capture information from all aspects of a user’s online life, we take a multiview approach, applying a weighted variant of Generalized Canonical Correlation Analysis (GCCA) to a collection of over 100,000 Twitter users. We demonstrate the utility of these multiview embeddings on three downstream tasks: user engagement, friend selection, and demographic attribute prediction.