Gapped String Indexing in Subquadratic Space and Sublinear Query Time
Philip Bille, Inge Li G{\o}rtz, Moshe Lewenstein, Solon P. Pissis, Eva, Rotenberg, Teresa Anna Steiner

TL;DR
This paper introduces new data structures for Gapped String Indexing that achieve subquadratic space and sublinear query time, advancing the efficiency of pattern matching with gaps in large texts.
Contribution
It presents the first polynomially subquadratic space and sublinear query time trade-offs for Gapped String Indexing, along with a novel reduction to the Shifted Set Intersection problem.
Findings
Achieved polynomially subquadratic space and sublinear query time for Gapped String Indexing.
Introduced the Shifted Set Intersection problem and proved its equivalence to 3SUM Indexing.
Improved data structures for 3SUM Indexing and Jumbled Indexing for constant-sized alphabets.
Abstract
In Gapped String Indexing, the goal is to compactly represent a string of length such that for any query consisting of two strings and , called patterns, and an integer interval , called gap range, we can quickly find occurrences of and in with distance in . Gapped String Indexing is a central problem in computational biology and text mining and has thus received significant research interest, including parameterized and heuristic approaches. Despite this interest, the best-known time-space trade-offs for Gapped String Indexing are the straightforward space and query time or space and query time. We break through this barrier obtaining the first interesting trade-offs with polynomially subquadratic space and polynomially sublinear query time. In…
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