Computational Complexity on mdbrnowski blog

Some papers I liked #3

Wed, 06 May 2026 17:00:00 +0200

In my two previous “some papers I liked” posts, I featured mostly preprints from arXiv because I liked (and still kind of like) to procrastinate by browsing through documents published there. I don’t do that often anymore because:

I’ve realized that my understanding of a large portion of those papers is too rudimentary to call it time well spent;
There is a surprising amount of absolute crap on arXiv (maybe not a lot but still, surprisingly much).

I will elaborate on the second point in the last section of this post, but before I do, I’d like to recommend some articles I’ve found interesting. This time (and from now on) I’m not restricting myself to computer science / discrete mathematics papers. Still, if I (a CS & Math student) found them interesting, maybe you will too, my dear reader.

RX3C is NP-complete

Sun, 05 Oct 2025 19:00:00 +0200

You may know a classic $\textsf{NP}$-complete problem known as X3C (exact cover by 3-sets). In this post, I’ll show that a restricted version of X3C (called RX3C) is also $\textsf{NP}$-complete.

I think it was first proven in Clustering to minimize the maximum intercluster distance by Teofilo F. Gonzalez (it’s often cited as such), but I see two problems with this paper:

The proof is overcomplicated,
The paper references Computers and Intractability by Garey and Johnson for an intermediate problem (between X3C and RX3C), in which they in turn refer to their own “unpublished results”.

Yeah, so I decided that it would be good to provide a proof of this result, so that one doesn’t need to go search for some “unpublished results” from 1979.

Some papers I liked #2

Tue, 09 Sep 2025 22:35:00 +0200

The previous “some papers I liked” blog was published at the end of April, so I figured it was time to share some new papers I found informative, well-written, and interesting. As before, I am sharing only those that are quite short and don’t require very extensive background in any particular field (they should be understandable to a CS/Math undergraduate student).

Computational complexity theory

Evolomino is NP-complete. Andrei V. Nikolaev, link (11 pages) — The author shows that the pencil-and-paper game Evolomino is NP-complete (and even #P-complete) using simple and elegant gadgets.

Some papers I liked

Tue, 29 Apr 2025 19:00:00 +0200

Over the past four months, I’ve collected a few papers that I want to share with you now. These papers (mostly preprints) are unlikely to be the most significant ones ever written. Instead, they often have nice pictures and are short or very well-written — which is exactly the sort of thing that might interest an undergraduate student like myself.

Computational complexity theory

Col is PSPACE-complete on Triangular Grids. Kyle Burke and Craig Tennenhouse, link (9 pages)
Slant/Gokigen Naname is NP-complete, and Some Variations are in P. Jayson Lynch and Jack Spalding-Jamieson, link (7 pages)
Solving Maker-Breaker Games on 5-uniform hypergraphs is PSPACE-complete. Finn Koepke, link (12 pages)
A Note on the Complexity of Defensive Domination. Steven Chaplick, Grzegorz Gutowski, Tomasz Krawczyk, link (11 pages)

Miscellaneous

Well-quasi-orderings on word languages. Nathan Lhote, Aliaume Lopez, Lia Schütze, link (26 pages)
Canonical for Automated Theorem Proving in Lean. Chase Norman and Jeremy Avigad, link (15 pages, but it’s more about the software)
Proof or Bluff? Evaluating LLMs on 2025 USA Math Olympiad. Ivo Petrov, Jasper Dekoninck, et al., link (12 pages, but it’s more about the cool website)

Other

And finally, two articles that are not from this year but that I came across recently.