Paper-Review on CuriousCoding

Quotes from "The Evolution of Mathematical Software"

Sun, 18 Jan 2026 00:00:00 +0100

These are some nice quotes from “The Evolution of Mathematical Software”, Turing Lecture by the 2021 Turing Award winner Jack J. Dongarra, which talks about algorithm and software development in the context of ever improving hardware.

a large infrastructure of mathematical libraries […] that must be mainted, ported, and enhanced for many years to come if the value of the application codes that depend on it are to be preserved and extended. The software that encapsulates all this time, energy, and thought, routinely outlasts the hardware it was originally designed to run on.

Thoughts on "Static Retrieval Revisited"

Tue, 04 Nov 2025 00:00:00 +0100

Table of Contents

1 Problem definitions
2 Optimal solutions
3 Why an overhead is necessary
4 Augmented Retrieval

These are some summarizing notes and thoughts on “Static Retrieval Revisited: To Optimality and beyond” by Hu, Kuszmaul, Liang, Yu, Zhang, and Zhou.

1 Problem definitions Link to heading

Static Retrieval. Given $n$ keys $X\subseteq U$ and $n$ $v$-bit values $f(X) \in [2^v]$, encode $f: X\to [2^v]$. The goal is use a minimal number of bits on top of the trivial $nv$ lower bound, while allowing efficient queries.

Thoughts on Singletrack

Tue, 04 Nov 2025 00:00:00 +0100

This is a quick post summarizing the idea of “Singletrack: An Algorithm for Improving Memory Consumption and Performance of Gap-Affine Sequence Alignment” by López-Villellas, Iñiguez, Jiménez-Blanco, Aguado-Puig, Moretó, Alastruey-Benedé, Ibáñez, and Marco-Sola to reduce memory usage of affine-cost alignment by removing the need to store the affine layers of the DP matrix.

Affine-cost alignment uses a gap-open cost $o>0$, so that a gap of length $\ell$ has cost $o + \ell \cdot e$. The classic DP solution for this is Gotoh’s method (Gotoh 1982) that uses two additional DP matrices $I$ and $D$ (alongside the main $M$ matrix): one to store the best cost to get to state $(i,j)$ while ending in an insertion, and one that ends with a deletion.

Understanding GreedyMini

Sun, 27 Apr 2025 00:00:00 +0200

In this post, we will look at the minimizer schemes generated by the greedy minimizer (Golan et al. 2025).

Thoughts on Consensus MPHF and tiny pointers

Wed, 12 Feb 2025 00:00:00 +0100

Table of Contents

1 Consensus
- 1.1 Consensus-RecSplit
2 IDEA: Consensus-PtrHash
3 Tiny pointers and optimal open addressing hash tables

These are some thoughts on the Consensus-based MPHF presented in Lehmann et al. (2025), and how this could be applied to PtrHash:

Lehmann, Hans-Peter, Peter Sanders, Stefan Walzer, and Jonatan Ziegler. 2025. “Combined Search and Encoding for Seeds, with an Application to Minimal Perfect Hashing.” Arxiv. https://doi.org/10.48550/ARXIV.2502.05613.

Below are also some thoughts on the papers on tiny pointers, used to achieve hash tables with load factors very close to 1: Bender et al. (2021), Farach-Colton, Krapivin, and Kuszmaul (2024).

Comments on Brisk

Fri, 29 Nov 2024 00:00:00 +0100

Table of Contents

Overview
Detailed comments

These are some (biased) comments on Brisk, a dynamic k-mer dictionary (Smith et al. 2024).

Comments on GreedyMini

Mon, 04 Nov 2024 00:00:00 +0100

Table of Contents

Overview
Detailed comments
Comments on “Expected density of random minimizers”

These are some (biased) comments on “Greedymini: Generating Low-Density Dna Minimizers” (Golan et al. 2024), which introduces the GreedyMini minimizer scheme. (Meanwhile, this has been published as Golan et al. (2025).)

At the bottom, there are also some comment on Golan and Shur (2025).

Comments on 'When Less is More' minimizer review

Tue, 15 Oct 2024 00:00:00 +0200

Table of Contents

The importance of ordering
Asymptotically optimal minimizers

These are some (biased) comments on “When Less Is More: Sketching with Minimizers in Genomics” (Ndiaye et al. 2024).

The importance of ordering Link to heading

the interest lies in constructing a minimizer with a density within a constant factor, i.e., $O(1/w)$ for any $k$. With lexicographic ordering, minimizers can achieve such density, but with large $k$ values ($\geq \log_{|Σ|}(w)-c$ for a constant $c$), which might not be desirable (Zheng, Kingsford, and Marçais 2020). However, random ordering can result in a lower density than that of the lexicographic ordering. Thus, random ordering (implemented with pseudo-random hash functions) is usually used in practice.

Thoughts on POASTA

Tue, 28 May 2024 00:00:00 +0200

Table of Contents

Summary
Background
Review comments

Here are some thoughts on POASTA (van Dijk et al. 2024), a recent affine-cost sequence-to-DAG (POA) aligner inspired by WFA and using A*.

Summary Link to heading

Take a query and a directed acyclic graph (DAG).
Align the query to the full DAG. It’s like global alignment for graphs.
- In fact I think the graph doesn’t actually have to be acyclic, as long as it has a start and end. (When there is a cycle, the maximum remaining path length is simply $\infty$.)
Do greedy extension of matches, similar to WFA and A*PA.
- Note that this is not as strong as full diagonal transition as done by WFA and gWFA (graph WFA for unit costs only), which only consider farthest reaching states.
In fact, this is the first implementation of affine-cost WFA!
It also uses A* with the classic gap-cost heuristic extended to graphs.
- For each point in the graph the minimal and maximal remaining distance is computed, and if the remaining query length is outside this range, the difference to get into the range is a lowerbound on number of indels.
Greedy extension is applied (although this is inherent when using WFA).
Suboptimal states in superbubbles are pruned using additional logic.

Background Link to heading

Daniel: why is nobody doing exact banded alignment, i.e., simple band doubling, for exact DP-based alignment. We are still not convinced that A*/WFA is faster than DP, especially when divergence is not super low ($<1\%$).

Review comments Link to heading

Fig 1 confuses me: (partly Daniel)

Review of refined minimizes

Fri, 26 Jan 2024 00:00:00 +0100

Table of Contents

Summary
Main issues
1. Introduction
2. Methods
- 2.3 heuristic
3. Results
Discussion
Code

These are my review-like notes on refined minimizers, introduced in Pan and Reinert (2024).

Summary Link to heading

The paper introduces refined minimizers, a new scheme for sampling canonical minimizers that is less biased than the usual scheme.

Instead of taking the minimum of the minimizer of the forward and reverse strand, the minimizer of the strand with the higher GT density is chosen.
The less bias towards small minimizers causes a more equal distribution of frequency of selected kmers.

Main issues Link to heading

The methods contain a number of mistakes in the math and proofs.
The limit to $|s|$ needs to be made much more precise. In fact it is a $k\to\infty$ limit (rather than a $w\to\infty$ limit), which seems not as useful in practice.
A comparison to NtHash2 should be made, for both kmer frequency distribution and speed.
The provided code (github:xp3i4/mini_benchmark) segfaults and is undocumented.

1. Introduction Link to heading

the minimizer concept is a data structure: to me, minimizers by themselves are not a data structure.
$w>k$: not needed. $w\geq 1$ is sufficient.
In many places, \citep citations like (Pan and Reinert 2024) would have been more appropriate then \citet ones like Pan and Reinert (2024).
of a predefined ordering scheme: the minimum of/over some set with respect to some ordering scheme.
nitpicky imprecision: $X$ is the set of positions of kmers, not simply the set of kmer strings themselves. (Or I suppose $X$ could be a list of kmers.) (Otherwise we have $|X| \leq 4^k$ and $|S|\to\infty$ so that $\rho\to 0$.)
a k-mer $X = x$ => Why not just $x$? The notation is confusing.
$n(x)/|S|$ is not really an average (there is only one string $S$); rather it’s a density.
The definition of $V$ is not clear to me. What is random? What is counted?
3. Its density converges => For $w\to \infty$ or $k\to\infty$ or both?
CMP (branch conditions) can be one of the slowest instructions on modern hardware. Branch misses in an inner loop for minimizer computation can severely affect performance.
Simple operations and L1 accesses can be pipelined and latency can be hidden, making them take 2-4x time less in practice. This makes branch-misses up to 4 times as bad, relatively.
Are lexicographic minimizers used much in practice?

2. Methods Link to heading

There are a number of mistaken in the math here here and some unclarities that could use fixing.

Loukides, Pissis, Thankachan, Zuba :: Suffix-Prefix Queries on a Dictionary

Fri, 07 Jul 2023 00:00:00 +0200

Table of Contents

Comments
A small rant on $τ$-micro-macro trees
Ideas for simplification
Closing thoughts

\[\newcommand{\dol}{\$}\]

These are some comments and new ideas on the paper by Loukides, Pissis, Thankachan, and Zuba (2023).