Fast and Lean Immutable Multi-Maps on the JVM based on Heterogeneous \n Hash-Array Mapped Tries

Abstract

An immutable multi-map is a many-to-many thread-friendly map data structure \nwith expected fast insert and lookup operations. This data structure is used \nfor applications processing graphs or many-to-many relations as applied in \nstatic analysis of object-oriented systems. When processing such big data sets \nthe memory overhead of the data structure encoding itself is a memory usage \nbottleneck. Motivated by reuse and type-safety, libraries for Java, Scala and \nClojure typically implement immutable multi-maps by nesting sets as the values \nwith the keys of a trie map. Like this, based on our measurements the expected \nbyte overhead for a sparse multi-map per stored entry adds up to around 65B, \nwhich renders it unfeasible to compute with effectively on the JVM. \n In this paper we propose a general framework for Hash-Array Mapped Tries on \nthe JVM which can store type-heterogeneous keys and values: a Heterogeneous \nHash-Array Mapped Trie (HHAMT). Among other applications, this allows for a \nhighly efficient multi-map encoding by (a) not reserving space for empty value \nsets and (b) inlining the values of singleton sets while maintaining a (c) \ntype-safe API. \n We detail the necessary encoding and optimizations to mitigate the overhead \nof storing and retrieving heterogeneous data in a hash-trie. Furthermore, we \nevaluate HHAMT specifically for the application to multi-maps, comparing them \nto state-of-the-art encodings of multi-maps in Java, Scala and Clojure. We \nisolate key differences using microbenchmarks and validate the resulting \nconclusions on a real world case in static analysis. The new encoding brings \nthe per key-value storage overhead down to 30B: a 2x improvement. With \nadditional inlining of primitive values it reaches a 4x improvement