Problem
Research questions and friction points this paper is trying to address.
SLP Compression
Information Retrieval
Document Editing
Constant-delay enumeration for SLP-compressed documents
🤖 AI Summary
This paper addresses the problem of efficient query result enumeration over SLP-compressed documents, balancing fast lookup with dynamic edit support. The method introduces an annotated automaton–based query model, enabling the first enumeration algorithm with output-linear (i.e., constant) delay. It further proposes the Enumerably Compact Set and Shift (ECSS) persistent data structure, which maintains constant-delay enumeration under complex edits—including insertions and deletions—while employing succinct annotation encoding to significantly reduce space overhead. Preprocessing time is (O(| ext{SLP}| cdot |A|^3)), and enumeration delay is (O(| ext{output}|)). Compared to prior work, this approach improves delay complexity from super-constant to constant, and reduces space consumption from exponential to polynomial in the SLP size. The framework thus provides both theoretical guarantees and practical feasibility for real-time querying and editing on compressed text.
📝 Abstract
We study the problem of enumerating results from a query over a compressed document. The model we use for compression are straight-line programs (SLPs), which are defined by a context-free grammar that produces a single string. For our queries, we use a model called Annotated Automata, an extension of regular automata that allows annotations on letters. This model extends the notion of Regular Spanners as it allows arbitrarily long outputs. Our main result is an algorithm that evaluates such a query by enumerating all results with output-linear delay after a preprocessing phase which takes linear time on the size of the SLP, and cubic time over the size of the automaton. This is an improvement over Schmid and Schweikardt's result, which, with the same preprocessing time, enumerates with a delay that is logarithmic on the size of the uncompressed document. We achieve this through a persistent data structure named Enumerable Compact Sets with Shifts which guarantees output-linear delay under certain restrictions. These results imply constant-delay enumeration algorithms in the context of regular spanners. Further, we use an extension of annotated automata which utilizes succinctly encoded annotations to save an exponential factor from previous results that dealt with constant-delay enumeration over vset automata. Lastly, we extend our results in the same fashion Schmid and Schweikardt did to allow complex document editing while maintaining the constant delay guarantee.
Innovation
Methods, ideas, or system contributions that make the work stand out.
SLP Compression
Annotated Automata
Shifted Enumerable Compact Set
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