Compressing Dynamic Fully Indexable Dictionaries in Word-RAM
Gabriel Marques Domingues

TL;DR
This paper introduces a new dynamic fully indexable dictionary (FID) data structure in the Word-RAM model that uses space close to the theoretical minimum and supports efficient updates and queries, improving over previous methods.
Contribution
It presents the first deterministic dynamic FID in the Word-RAM model with near-optimal space and worst-case time bounds, based on a modified fusion-tree structure.
Findings
Achieves space close to the information-theoretic lower bound.
Supports rank, select, and update operations in worst-case time.
Reduces space redundancy to o(n√w) bits with optimal time.
Abstract
We study the problem of constructing a dynamic fully indexable dictionary (FID) in the Word-RAM model using space close to the information-theoretic lower bound. A FID is a data-structure that encodes a bit-vector of length and answers, for , and ( if empty). A dynamic FID supports updates that modify a single bit of , i.e., . We work in the Word-RAM model with -bit words, assuming . Integer multiplication takes time. Our memory model is , allowing access to a fixed precomputed table of words, which can be computed in time. In this paper, we show a dynamic FID based on the famous fusion-tree data-structure of…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAlgorithms and Data Compression · semigroups and automata theory · Computability, Logic, AI Algorithms
