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Henrik A. Friberg @hafriberg.bsky.social · 22d

Great article, and I do like that you address my initial thoughts immediately: "One canonical approach...". Is it common to only have an exam period of 6 days though? That 7 day schedule looks at lot more attractive.

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Henrik A. Friberg @hafriberg.bsky.social · Aug 29

That is a much harder question I think. Reminds me of the largest sofa that you can move around a corner problem.

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Henrik A. Friberg @hafriberg.bsky.social · Aug 12

Don't forget to ignore posts with foul language. That really removes a lot of junk.

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Henrik A. Friberg @hafriberg.bsky.social · Aug 8

If yes, I would try adding a supernode (connected to all) and require flow conservation, an inflow of at least one for the closed neighborhood (setminus supernode) of each node, and minimize the number of used edges. For n=8, this is still a rather small problem for MIP solvers.

Henrik A. Friberg @hafriberg.bsky.social · Aug 8

Is this just one more than the shortest snake needed to visit the closed neighborhood of each node at least once? 🤔

Randall Munroe @xkcd.com · Aug 8

Snake-in-the-Box Problem

xkcd.com/3125/

Comic. A snake slithers around a hypercube. No two non-consecutive parts of its coils can be on adjacent corners. [Three small 4-dimensional hypercubes showing disallowed options with one large cube with snake wrapped around it. Dimensions = 4. Max Length - 7.] Snake(N) = Longest snake that can fit in an n-dimensional hypercube. Snake(N=1, 2, 3…8) = 1, 2, 4, 7, 13, 26, 50, 98. Snake(N>8) = UNSOLVED. [caption] It turns out every scientific field has a key thought experiment that involves putting a cute animal in a weird box for no reason. So far, quantum mechanics and graph theory have found theirs, but most other fields are still working on it.

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Henrik A. Friberg @hafriberg.bsky.social · Aug 5

Oh, that’s so satisfying! I stopped at the 4-norm ball thinking I had the solution as it fits the hole like a pot lid (has a perfect circle as an intersection).

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Henrik A. Friberg @hafriberg.bsky.social · Aug 5

Consider contributing to epoch.ai/frontiermath. As no sizes are given, it is kinda implicitly assumed that "every p norm ball" also includes every size. And with this, you probably want to rule out infinite packings with gap approaching zero, let alone trivial covers of the hole.

FrontierMath

FrontierMath is a benchmark of hundreds of unpublished and extremely challenging math problems to help us to understand the limits of artificial intelligence.

epoch.ai

Henrik A. Friberg @hafriberg.bsky.social · Jun 24

Unfortunately, it seems there is quite a theoretical gap between circles and hula hoops: link.springer.com/article/10.1...

On Packing $$\mathbb {R}^3$$ R 3 with Thin Tori - Discrete & Computational Geometry

We show that $$\mathbb {R}^3$$ R 3 can be packed at a density of $$0.222\ldots $$ 0.222 … with tori whose minor radius goes to zero. Furthermore, we show that the same torus arrangement yields an asym...

link.springer.com

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Henrik A. Friberg @hafriberg.bsky.social · Jun 24

So I should be able to fill space with hula hoops without bending them out of shape -- thinner the hoops, better the cover? Sounds impressive.

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Henrik A. Friberg @hafriberg.bsky.social · Jun 19

I have only tried for small code snippets and can't say its making me more productive, but it's definitely interesting and stimulates another skill set.

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Henrik A. Friberg @hafriberg.bsky.social · Jun 19

Having a strong background in programming, I find that code generation is a great exercise for peer reviewing. It starts with the naive approach, and then you iteratively refine it by corner case handling, performance tuning and simplification. Not unlike how some educational books are written.

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Henrik A. Friberg @hafriberg.bsky.social · Jun 16

It seems to me they distribute from their strongest military positions to minimize operational risk, using small boxes (=frequent revisits) to get better tracking of where it goes.

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Henrik A. Friberg @hafriberg.bsky.social · Jun 11

Has anyone built enough intuition for Gomory Cuts to dare explain when they are excellent and when they are terrible in this game?

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Henrik A. Friberg @hafriberg.bsky.social · Jun 6

The quote “I would have written a shorter letter, but I did not have the time” comes to mind.

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Henrik A. Friberg @hafriberg.bsky.social · May 26

Nice goal. I may object that the floors and ceils are a bit hard to distinguish, or is it just me?
⌊|⌈⌉|⌋|⌊

Henrik A. Friberg @hafriberg.bsky.social · May 21

I haven’t tried it yet, but the new kid on the block is Typst with Hayagriva for citations. Categories seems to make sense:
github.com/typst/hayagr...

github.com

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Henrik A. Friberg @hafriberg.bsky.social · Apr 26

I like this. A 68% confidence interval around 10 is probably quite a good model for what people actually mean when they say 10 ± 1 and do the hand gesture.

Henrik A. Friberg @hafriberg.bsky.social · Apr 25

10 ± 1 is
(a) the boolean expression "9 or 11",
(b) the set {9, 11},
(c) the interval [9, 11],
(d) an ambiguous operation that can't be used without context?

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Henrik A. Friberg @hafriberg.bsky.social · Apr 10

Consider the LP problem min{cᵀx : Ax=b, x≥0} with dual
max{bᵀy : Aᵀy≤c}. Adding Gaussian noise with std σ to all of A and c, the problem can be solved by a dual simplex method in O( 1/sqrt(σ) n^2.75 log(m)^1.75 ) pivot steps following the shadow vertex pivot rule. See arxiv.org/abs/2504.041....

Optimal Smoothed Analysis of the Simplex Method

Smoothed analysis is a method for analyzing the performance of algorithms, used especially for those algorithms whose running time in practice is significantly better than what can be proven through w...

arxiv.org

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Henrik A. Friberg @hafriberg.bsky.social · Mar 20

Agreed, but it sparks an interesting question. What is the most difficult optimization problem which is simple to explain without math?

Reposted by Henrik A. Friberg

Sophie Huiberts @sophie.huiberts.me · Mar 12

In November 1979, the NYT (🤮) writes of the then-new ellipsoid method that "the discovery may be applicable in weather prediction"

Does anyone know how LP would be used in weather prediction?

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Henrik A. Friberg @hafriberg.bsky.social · Feb 21

When you are so deep into OR you start thinking about injective functions as 'codomain packing'.. 😅

Let f: X → Y and consider the sets {f(x)} for each element x∈X. The function is injective/surjective/bijective if and only if these sets forms a packing/covering/partitioning of Y.

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Henrik A. Friberg @hafriberg.bsky.social · Feb 14

In Denmark it’s called “100 meter skoven” (the hundred meter forrest). Sounds tiny in comparison, but I always thought of it as referring to a feature of the forrest rather than its extend.

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Reposted by Henrik A. Friberg

Mosek Team @mosek.com · Feb 7

Our latest blogpost is a little weekend treat for everybody interested in conic reformulations!

themosekblog.blogspot.com/2025/02/a-sm...

A small breakthrough in the modeling of polynomial denominators

The MOSEK ApS official blog: announcements, new releases, activities, optimization modeling hints and examples.

themosekblog.blogspot.com

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Henrik A. Friberg @hafriberg.bsky.social · Jan 27

Today's word: Neutrosophic Number. Used to represent performance indicators such as product quality, delivery time, and cost, in the form of survey answers. An example is a triple such as (satisfied, uncertain, unsatisfied) = (70%, 10%, 20%).

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