Minimizers on CuriousCodinghttps://curiouscoding.nl/tags/minimizers/Recent content in Minimizers on CuriousCodingHugoenFri, 12 Jul 2024 00:00:00 +0200Computing random minimizers, fasthttps://curiouscoding.nl/posts/fast-minimizers/Fri, 12 Jul 2024 00:00:00 +0200https://curiouscoding.nl/posts/fast-minimizers/Table of Contents 1 Introduction 1.1 Results 2 Random minimizers 3 Algorithms 3.1 Problem statement Problem A: Only the set of minimizers Problem B: The minimizer of each window Problem C: Super-k-mers Which problem to solve Canonical k-mers 3.2 The naive algorithm Performance characteristics 3.3 Rephrasing as sliding window minimum 3.4 The queue Performance characteristics 3.5 Jumping: Away with the queue Performance characteristics 3.6 Re-scan Performance characteristics 3.7 Split windows Performance characteristics 4 Analysing what we have so far 4.A near-tight lower bound on minimizer densityhttps://curiouscoding.nl/posts/minimizer-lower-bound/Tue, 25 Jun 2024 00:00:00 +0200https://curiouscoding.nl/posts/minimizer-lower-bound/Table of Contents Succinct background Definitions Lower bounds A new lower bound Discussion Post scriptum Acknowledgement In this post I will prove a new lower bound on the density of any minimizer or forward sampling scheme: \[ d(f) \geq \frac{\lceil\frac{w+k}{w}\rceil}{w+k} = \frac{\lceil\frac{\ell+1}{w}\rceil}{\ell+1}. \]
In particular, this implies that when \(k=1\), any forward sampling scheme has density at least \(2/(w+1)\), and thus that random minimizers are optimal in this case.Mod-minimizers and other minimizershttps://curiouscoding.nl/posts/mod-minimizers/Thu, 18 Jan 2024 00:00:00 +0100https://curiouscoding.nl/posts/mod-minimizers/Table of Contents Applications Background Minimizers Density bounds Robust minimizers PASHA Miniception Closed syncmers Bd-anchors New: Mod-minimizers Experiments Conclusion Small k experiments Search methods Directed minimizer \(k=1\), \(w=2\) \(k=1\), \(w=4\) \(k=1\), \(w=5\) \(k=2\), \(w=2\) \(k=2\), \(w=4\) Notes Reading list \[ \newcommand{\d}{\mathrm{d}} \newcommand{\L}{\mathcal{L}} \]
This post introduces some background for minimizers and some experiments for a new minimizer variant. That new variant is now called the mod-minimizer and available as a preprint at bioRxiv (Groot Koerkamp and Pibiri 2024).Notes on bidirectional anchorshttps://curiouscoding.nl/posts/bd-anchors/Mon, 15 Jan 2024 00:00:00 +0100https://curiouscoding.nl/posts/bd-anchors/Table of Contents Paper overview Remarks on the paper Thoughts \[ \newcommand{\A}{\mathcal{A}_\ell} \newcommand{\T}{\mathcal{T}_\ell} \]
These are some notes on Bidirectional String Anchors (Loukides, Pissis, and Sweering 2023), also called bd-anchors.
Resources:
Loukides and Pissis (2021): preceding conference paper with subset of content. Loukides, Pissis, and Sweering (2023): The paper discussed here. Ayad, Loukides, and Pissis (2023): follow-up/second paper containing a faster average-case \(O(n)\) construction algorithm; a more memory efficient construction algorithms for the index.