In many real-world database systems, a large fraction of the data is represented by strings: sequences of letters over some alphabet. This is because strings can easily encode data arising from different sources. It is often crucial to represent such string datasets in a compact form but also to simultaneously enable fast pattern matching queries. This is the classic text indexing problem. The four absolute measures anyone should pay attention to when designing or implementing a text index are: (i) index space; (ii) query time; (iii) construction space; and (iv) construction time. Unfortunately, however, most (if not all) widely-used indexes (e.g., suffix tree, suffix array, or their compressed counterparts) are not optimized for all four measures simultaneously, as it is difficult to have the best of all four worlds. Here, we take an important step in this direction by showing that text indexing with sampling based on locally consistent anchors (lc-anchors) offers remarkably good performance in all four measures, when we have at hand a lower bound <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="778_2025_935_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="12" /> </InlineMediaObject> <EquationSource Format="TEX">$\ell $</EquationSource> <EquationSource Format="MATHML"><math> <mi>ℓ</mi> </math></EquationSource> </InlineEquation> on the length of the queried patterns — which is arguably a quite reasonable assumption in practical applications. Specifically, we improve on a recently proposed index that is based on bidirectional string anchors (bd-anchors), a new type of lc-anchors, by: (i) introducing a randomized counterpart of bd-anchors which outperforms bd-anchors; (ii) designing an average-case linear-time algorithm to compute (the randomized) bd-anchors; and (iii) developing a semi-external-memory implementation and an internal-memory implementation to construct the index in small space using near-optimal work. Our index offers average-case guarantees. In our experiments using real (benchmark) datasets of sizes up to 10GB, we show that it compares favorably based on the four measures to all classic indexes: (compressed) suffix tree; (compressed) suffix array; and the FM-index. We also present a counterpart of our index with worst-case guarantees based on the lc-anchors notion of partitioning sets. To the best of our knowledge, this is the first index achieving the best of all worlds in the regime where we have at hand a lower bound <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="778_2025_935_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="12" /> </InlineMediaObject> <EquationSource Format="TEX">$\ell $</EquationSource> <EquationSource Format="MATHML"><math> <mi>ℓ</mi> </math></EquationSource> </InlineEquation> on the length of the queried patterns.

Text indexing for long patterns using locally consistent anchors

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2025年7月15日

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Lorraine A. K. Ayad,
Grigorios Loukides,
Solon P. Pissis

摘要

In many real-world database systems, a large fraction of the data is represented by strings: sequences of letters over some alphabet. This is because strings can easily encode data arising from different sources. It is often crucial to represent such string datasets in a compact form but also to simultaneously enable fast pattern matching queries. This is the classic text indexing problem. The four absolute measures anyone should pay attention to when designing or implementing a text index are: (i) index space; (ii) query time; (iii) construction space; and (iv) construction time. Unfortunately, however, most (if not all) widely-used indexes (e.g., suffix tree, suffix array, or their compressed counterparts) are not optimized for all four measures simultaneously, as it is difficult to have the best of all four worlds. Here, we take an important step in this direction by showing that text indexing with sampling based on locally consistent anchors (lc-anchors) offers remarkably good performance in all four measures, when we have at hand a lower bound $\ell $ $ℓ$ on the length of the queried patterns — which is arguably a quite reasonable assumption in practical applications. Specifically, we improve on a recently proposed index that is based on bidirectional string anchors (bd-anchors), a new type of lc-anchors, by: (i) introducing a randomized counterpart of bd-anchors which outperforms bd-anchors; (ii) designing an average-case linear-time algorithm to compute (the randomized) bd-anchors; and (iii) developing a semi-external-memory implementation and an internal-memory implementation to construct the index in small space using near-optimal work. Our index offers average-case guarantees. In our experiments using real (benchmark) datasets of sizes up to 10GB, we show that it compares favorably based on the four measures to all classic indexes: (compressed) suffix tree; (compressed) suffix array; and the FM-index. We also present a counterpart of our index with worst-case guarantees based on the lc-anchors notion of partitioning sets. To the best of our knowledge, this is the first index achieving the best of all worlds in the regime where we have at hand a lower bound $\ell $ $ℓ$ on the length of the queried patterns.