Longest Common Extensions in Sublinear Space
Philip Bille, Inge Li G{\o}rtz, Mathias B{\ae}k Tejs Knudsen, Moshe, Lewenstein, Hjalte Wedel Vildh{\o}j

TL;DR
This paper presents a new data structure for the LCE problem that achieves a flexible trade-off between space and query time, significantly improving previous bounds and nearly matching the theoretical lower bound.
Contribution
It introduces a novel approach to solve the LCE problem with sublinear space, providing a tunable trade-off between space and query time that improves upon prior results.
Findings
Achieves $O(n/\tau)$ space and $O(\tau)$ query time for any $1 \leq \tau \leq n$
Significantly improves previous time-space trade-offs for the LCE problem
Nearly matches the known lower bound for the problem's time-space product
Abstract
The longest common extension problem (LCE problem) is to construct a data structure for an input string of length that supports LCE queries. Such a query returns the length of the longest common prefix of the suffixes starting at positions and in . This classic problem has a well-known solution that uses space and query time. In this paper we show that for any trade-off parameter , the problem can be solved in space and query time. This significantly improves the previously best known time-space trade-offs, and almost matches the best known time-space product lower bound.
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 · Network Packet Processing and Optimization · semigroups and automata theory
