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This paper studies the near-duplicate text alignment problem under the constraint of Jaccard similarity. Specifically, given a collection of long texts and a short query text, this problem finds all thesubsequencesin each text whose Jaccard similarities to the query are no smaller than a given threshold. Near-duplicate text alignment is computationally intensive. This is because there are O(n2) subsequences in a text withntokens. To remedy this issue, a few recent studies propose to first generate the min-hash sketch of every subsequence in each text and then find all the subsequences whose min-hash sketches are similar to that of the query. They introduce the concept of compact windows and show that the O(n2k) min-hashes in a text withntokens can be losslessly compressed in compact windows using O(nk) space, wherekis the sketch size. However, the space cost O(nk) is still too high for long texts, especially when the sketch sizekis large. To address this issue, we propose to use One Permutation Hashing (OPH) to generate the min-hash sketch and introduce the concept of OPH compact windows. Although the size of each sketch remains the same, which is O(k), we prove that all the O(n2k) min-hashes generated by OPH in a text withntokens can be losslessly compressed in OPH compact windows using only O(n+k) space. Note the generation of OPH compact windows does not necessitate the enumeration of the O(n2k) min-hashes. Moreover, we develop an algorithm to find all the sketches in a text similar to that of the query directly from OPH compact windows, along with three optimizations.We conduct extensive experiments on three real-world datasets. Empirical results show our proposed algorithms significantly outperformed existing methods in terms of index cost and query latency and scaled well.
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This content will become publicly available on June 10, 2026
Membership Testing for Semantic Regular Expressions
This paper is about semantic regular expressions (SemREs). This is a concept that was recently proposed by Smore (Chen et al. 2023) in which classical regular expressions are extended with a primitive to query external oracles such as databases and large language models (LLMs). SemREs can be used to identify lines of text containing references to semantic concepts such as cities, celebrities, political entities, etc. The focus in their paper was on automatically synthesizing semantic regular expressions from positive and negative examples. In this paper, we study themembership testing problem. First, we present a two-pass NFA-based algorithm to determine whether a stringwmatches a SemRErinO(|r|2|w|2+ |r| |w|3) time, assuming the oracle responds to each query in unit time. In common situations, where oracle queries are not nested, we show that this procedure runs inO(|r|2|w|2) time. Experiments with a prototype implementation of this algorithm validate our theoretical analysis, and show that the procedure massively outperforms a dynamic programming-based baseline, and incurs a ≈ 2 × overhead over the time needed for interaction with the oracle. Second, we establish connections between SemRE membership testing and the triangle finding problem from graph theory, which suggest that developing algorithms which are simultaneously practical and asymptotically faster might be challenging. Furthermore, algorithms for classical regular expressions primarily aim to optimize their time and memory consumption. In contrast, an important consideration in our setting is to minimize the cost of invoking the oracle. We demonstrate an Ω(|w|2) lower bound on the number of oracle queries necessary to make this determination.
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- PAR ID:
- 10625805
- Publisher / Repository:
- ACM
- Date Published:
- Journal Name:
- Proceedings of the ACM on Programming Languages
- Volume:
- 9
- Issue:
- PLDI
- ISSN:
- 2475-1421
- Page Range / eLocation ID:
- 1245 to 1268
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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