Hard Problems and How To Figure Them Out

Explained using only the ten hundred words people use most often.

What is a good way of figuring out a problem?

First: it must be so simple and clear that we can explain it to a computer. (Or a Human. That’s not so different.)

Second: it must be fast enough so that it is done before lunch. (Or before the sun burns out. that’s not so different.)

Since people started using computers, lots of people get paid to think about ways to figure out problems. that’s what i’m doing.  Today we understand that some problems are hard, and others are pretty easy.

I want to help us becoming better at talking about what makes a problem hard.

So far, most of the people who think about this stuff look only at the size of the problem.

But some of us feel that you can think more clearly about problems when you not only look at their size, but at some other things as well. Sometimes, this way of thinking even helps us to come up with better ways to figure out problems!




Two other people and myself have come up with a way to finish the game for all five-letter words — as long as you are forced to visit only around ten words. Or maybe twenty. So we found out that the number of words all-in-all was not so important. instead, what makes the problem hard is how many you are forced to visit. We can even find the shortest such path!


Read more here: Another man, myself, and a woman, ‘Shortest path through stuff you didn’t choose’, place where people who care about this kind of question meet each year (the name sounds like a soft drink),  year twenty-hundred and ten and two.


The above is a summary of a poster I made for a research sharing day at ITU.

hard-problems-poster (draft) in pdf (designed for printing in A0)

I loathe poster sessions, partly because of the unclear concept of who the audience is, and mainly because the social interaction exhausts me.

But to motivate me I gave myself the challenge to design a poster in the style of  Randall Munroe’s Up-Goer Five: Use only the 1000 most used words of English, be concrete, whimsical, accessible, and informative. Munroe has since made a whole book in this style: Thing Explainer, which is quite lovely.

I did the whole thing in Omnigraffle Professional 5, which is hard pressed to handle a document with almost 6000 elements. Drawings are free-hand in Keynote (basically because I don’t have a good way of digitising my free-hand drawings — I am a competent artist, but Munroe’s style is sufficiently simple.) The font is xkcd-font from the iPython project, licensed under CCANC 3.0.

As a starting point I used a 2012 paper of Andreas, Nina, and myself that presents an efficient FPT-algorithm for shortest Steiner cycle. That’s as accessible a result as I have. The big drawing at the end shows a path from TEARS to SMILE passing through seven intervening emotions (WORRY, SPITE, etc.) This is a highly nontrivial result and a cute story that I’m insanely happy with, I haven’t found a good way of expressing this fact in only 1000 words.

Andreas Björklund, Thore Husfeldt, and Nina Taslaman, Shortest cycle through specified elements, Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms (SODA 2012),  January 17–19, 2012, Kyoto, Japan, SIAM, pages 1747-1753. [PDF].

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