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Many modern programming languages are shifting toward a functional style forcollection interfaces such as sets, maps, and sequences. Functional interfacesoffer many advantages, including being safe for parallelism and providingsimple and lightweight snapshots. However, existing high-performance functionalinterfaces such as PAM, which are based on balanced purely-functional trees,incur large space overheads for large-scale data analysis due to storing everyelement in a separate node in a tree.  This paper presents PaC-trees, a purely-functional data structure supportingfunctional interfaces for sets, maps, and sequences that provides a significantreduction in space over existing approaches. A PaC-tree is a balanced binarysearch tree which blocks the leaves and compresses the blocks using arrays. Weprovide novel techniques for compressing and uncompressing the blocks whichyield practical parallel functional algorithms for a broad set of operations onPaC-trees such as union, intersection, filter, reduction, and range querieswhich are both theoretically and practically efficient.  Using PaC-trees we designed CPAM, a C++ library that implements the fullfunctionality of PAM, while offering significant extra functionality forcompression. CPAM consistently matches or outperforms PAM on a set ofmicrobenchmarks on sets, maps, and sequences while using about a quarter of thespace. On applications including inverted indices, 2D range queries, and 1Dinterval queries, CPAM is competitive with or faster than PAM, while using2.1--7.8x less space. For static and streaming graph processing, CPAM offers1.6x faster batch updates while using 1.3--2.6x less space than thestate-of-the-art graph processing system Aspen.

PaC-trees: Supporting Parallel and Compressed Purely-Functional Collections