Pat Morin boosted

A counterexample to the Ringel circle problem: arxiv.org/abs/2112.05042, via gilkalai.wordpress.com/2021/12

Ringel asked whether systems of circles, tangent only in pairs, can be colored with O(1) colors so no two tangent circles have the same color. Five colors were known to be necessary but unknown to be sufficient; see the lead image of my old web page ics.uci.edu/~eppstein/junkyard

Now Davies, Keller, Kleist, Smorodinsky, and Walczak have found systems of circles requiring arbitrarily many colors.

Pat Morin boosted

TheoretiCS, a new diamond-open-access journal in all areas of theoretical computer science: theoretics.episciences.org/

It is being run as an overlay of arXiv, through the Episciences platform for such overlays, with Javier Esparza and Uri Zwick as editors-in-chief and a large and distinguished editorial board.

Just wrapping up my second week at the Banff International Research Station. This week's workshop is on Statistics and Machine Learning. The highlight, for an outsider like me, has definitely been Tselil Schramm's mini-course on the sum-of-squares algorithmic paradigm. A decade's worth of research nicely condensed into four one-hour lectures.

Reviewing my notes for my grad class on Pătrașcu's dynamic partial sums lower bound. It still makes me sad every time.

Five talks from CanaDAM 2021 introducing graph product structure theory and its applications:

youtu.be/8Sv_FaEN8zE

This is probably the best / quickest introdoctrination to the topic currently available.

Today I'm heading to the clinic to receive my first dose of the AstraZeneca vaccine. Ignoring the possibility that it might save me from death by covid, the worst case estimates suggest that this increases my odds of dying in the next 365 days from 1/444 to 1/442. I can live with that.

www150.statcan.gc.ca/t1/tbl1/e

An implementation of the Product Structure Theorem for planar graphs, in Python:

github.com/patmorin/lhp

Not exactly industrial-strength, and leans towards simplicity over performance. Still, it can decompose 100k-vertex triangulations in a few seconds. I'm open to feature requests.

Good to see that the pandemic hasn't affected every aspect of our lives. SoDA is still charging exorbitant registration fees:

Tip: When you "attend" an online conference, book everything off: teaching, meetings, etc. I'm currently "attending" a conference and have only gotten to see one live session since I've been in meetings or teaching the rest of the time.

Pat Morin boosted

New blog post, Hex, books, and queues: 11011110.github.io/blog/2020/1

And new arXiv preprint, Stack-number is not bounded by queue-number (with Vida Dujmović, Robert Hickingbotham, Pat Morin, and David R. Wood), arxiv.org/abs/2011.04195

Banff Alberta, Election Day, 2016, Alan Frieze and Luc Devroye watching election results arrive.

How many integer colours are sufficient to colour an \(n\)-vertex planar graph so that the maximum colour encountered along any path of length at most 2 occurs only once along that path? It turns out that the correct answer is \(\Theta(\log n/\log\log\log n)\). The triple-log comes from the fact every planar graph is contained in the strong product of a planar 3-tree and a very simple graph.

arxiv.org/abs/2007.06455

Pat Morin boosted

Congratulations to my (now former) student, Luís Fernando Schulz Xavier da Silveira, who successfully defended his PhD thesis titled Turán Triangles, Cell Covers, Road Placement and Train Scheduling on Monday.

This is the first thesis defense I've taken part in where no two participants were in the same room.

Here's an option, Elsevier: Open up your catalogues for the duration of the crisis (at least):

Today the was the first day of three weeks (at least) of home school. This morning was intro to algebra for my nine year-old. Addition, subtraction, and number-recognition for my 5 year old. This afternoon was bicycling and stump-jumping. :)

Online investment site today: "We're currently experiencing a display issue. Your account earnings may appear incorrectly. We're working on a fix and everything will be back to normal shortly."

No, I don't think that's a display issue...

Congratulations to our student (cosupervised with Vida Dujmović) Céline Yelle who just masterfully defended her Master's thesis titled Stack Number, Track Number, and Layered Pathwidth.

The thesis contains two results:

1. \(\mathrm{sn}(G) \le 4\mathrm{lpw}(G) \)
2. \(\mathrm{tn}(G)\le 3\) implies \(\mathrm{lpw}(G)\le 4\).

Planar graphs (and related families of graphs) have \((1+o(1))\log n\)-bit adjacency labelling schemes. Equivalently, there is a graph with \(n^{1+o(1)}\) vertices that contains every \(n\)-vertex planar graph as an induced subgraph.

arxiv.org/abs/2003.04280

The proof combines our year-old product structure theorem with binary search trees!

Rolf explains fragile complexity with a concrete example.

Show older
Mathstodon

The social network of the future: No ads, no corporate surveillance, ethical design, and decentralization! Own your data with Mastodon!