Konsep Inti
The authors present a space-time trade-off for the Internal Pattern Matching (IPM) problem, where the goal is to construct a data structure over a string S that allows efficiently answering queries about occurrences of a fragment P of S inside another fragment T of S, provided that |T| < 2|P|.
Abstrak
The authors consider the Internal Pattern Matching (IPM) problem in the read-only setting, where the goal is to bound the space usage on top of storing the input strings. Their main contribution is a space-time trade-off for IPM queries.
For any integer τ = O(n/ log^2 n), the authors present a data structure that can be built using O(n log(n/τ) + (n/τ) log^4 n log log n) time and O((n/τ) log n (log log n)^3) extra space, and can answer IPM queries in O(τ + log n log^3 log n) time. This data structure is nearly optimal in the sense that the product of the query time and space is optimal up to polylogarithmic factors.
The authors achieve this result by utilizing the concept of τ-partitioning sets as anchor points for identifying pattern occurrences, and employing sparse suffix trees and a three-dimensional range searching structure. For patterns that do not avoid a specific periodic structure, they leverage the periodic structure to construct the necessary anchor points.
The authors further showcase the applicability of their IPM data structure by using it to obtain space-time trade-offs for the longest common substring and circular pattern matching problems in the asymmetric streaming setting.