Reproduce “Theory Meets Practice for Bit Vectors Supporting Rank and Select” on OpenResearch
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About this paper
Florian Kurpicz, Niccolò Rigi-Luperti, Peter Sanders
Researchers from Karlsruhe Institute of Technology developed `3*`, a bit vector data structure that provides worst-case constant-time rank and select operations. This structure achieves a 0.78% space overhead, consuming 4.5x to 64.1x less memory than previous designs while maintaining competitive query performance.
Key insights
- A systematic combination of summary and sample trees, coupled with bit-compression and hardware-aware optimizations, can effectively bridge the theory-practice gap for rank and select data structures.
- It is possible to achieve worst-case constant-time performance for both rank and select operations with an extremely low space overhead, making them practically viable.
- Careful parameter tuning, informed by both asymptotic analysis and experimental validation, is essential for deriving highly efficient and robust space-time trade-offs in real-world scenarios.
Summary by alphaXiv.
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