Minimizers in Semi-Dynamic Strings
Wiktor Zuba, Oded Lachish, Solon P. Pissis

TL;DR
This paper introduces a new data structure for efficiently maintaining minimizers in semi-dynamic strings, enabling faster updates and reduced space usage while preserving linear time complexity for computing minimizers.
Contribution
It presents the first semi-dynamic string data structure supporting constant-time minimizer queries and updates, with a novel sublinear space algorithm for minimizer set computation.
Findings
Supports minimizer queries in O(1) amortized time with semi-dynamic updates.
Achieves O(n) time and O(√w) space for computing minimizers of a string.
Demonstrates practical effectiveness through application and experimental evaluation.
Abstract
Minimizers sampling is one of the most widely-used mechanisms for sampling strings. Let be a string over an alphabet . In addition, let and be two integers and be a total order on . The minimizer of window is the smallest position in where the smallest length- substring of based on starts. The set of minimizers for all is the set of the minimizers of . The set can be computed in time. The folklore algorithm for this computation computes the minimizer of every window in amortized time using working space. It is thus natural to pose the following two questions: Question 1: Can we efficiently…
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Taxonomy
TopicsAlgorithms and Data Compression
