Intereting Posts

Centre of the circle
Proving The Average Value of a Function with Infinite Length
Difference between the Laurent and Taylor Series.
Find a constant that minimizes $\int_0^1 |e^x – c| \ dx$
limit as $x$ approaches infinity of $\frac{1}{x}$
If $AB = I$ then $BA = I$
Infinite derivative
Intuition behind negative combinations
Proving inequality $(a+\frac{1}{a})^2 + (b+\frac{1}{b})^2 \geq \frac{25}{2}$ for $a+b=1$
Show that $(1+\frac{x}{n})^n \rightarrow e^x$ uniformly on any bounded interval of the real line.
The probability that two vectors are linearly independent.
What is the residue of this essential singularity?
$(a^{n},b^{n})=(a,b)^{n}$ and $=^{n}$?
I would like to show that all reflections in a finite reflection group $W :=\langle t_1, \ldots , t_n\rangle$ are of the form $wt_iw^{-1}.$
Nice proof for étale of degree 1 implies isomorphism.

The graph canonical labelling package nauty is widely regarded as one of the best (if not *the* best) around. Unfortunately, it’s quite a large package, and making a GPU version seems to be a highly nontrivial task.

In my research into algorithms for network motif detection, we often require an effective solution to the problem of, what I like to call, “canonically labelling a billion smalls graphs”. This should be a highly parallelisible problem, and therefore be suitable for the GPU architecture (although, there are issues of data transfer, memory usage, SIMD, etc., which I’m sweeping under the carpet).

This leads to the questions:

- Is “A New Kind of Science” a new kind of science?
- Proving $\pi^3 \gt 31$
- A valid floor function trick?
- Calculate the components of a unit vector that lies in the xy-plane and makes equal angles with the positive directions of the x- and y-axes
- How to solve this equation for $x$ with XOR involved?
- An elliptic curve for the multigrade $\sum^8 a_n^k = \sum^8 b_n^k$ for $k=1,2,3,4,5,9$?

What other algorithms/packages are around that can perform graph canonical labelling?

For my purposes, it should ideally be lightweight and parallelisible, although, academic curiosity makes me interested in any alternatives. Note that these alternatives do not necessarily need to be faster than nauty.

Nauty has been well-established since well before I started in mathematics, so I’m not at all familiar with what people did before nauty came along.

- Any equivalent to the Four color theorem for non-planar graphs?
- Graph with 10 nodes and 26 edges must have at least 5 triangles
- Assigning alternate crossings to closed curves
- When does a biregular graph for the free product 2∗(2×2) have a 4 cycle?
- Converting Integers from One Base to Another Digit by Digit
- How to find a linear extension of a poset
- In how many ways we can place $N$ mutually non-attacking knights on an $M \times M$ chessboard?
- Efficient computation of $\sum_{k=1}^n \lfloor \frac{n}{k}\rfloor$
- How many cycles, $C_{4}$, does the graph $Q_{n}$ contain?
- Prove that the tesseract graph is non-planar

There are a number of alternatives:

- Bliss – similar to nauty
- ConAuto – better search tree pruning
- GI-Ext – already parallelized
- Nishe – avoids some pathological slowness in nauty
- Saucy – specializes in sparse
*output* - Traces – small addition to nauty to help with pathologies

- Constructing a Galois extension field with Galois group $S_n$
- Show the inverse of a bijective function is bijective
- Calculate determinant of Vandermonde using specified steps.
- A linear operator commuting with all such operators is a scalar multiple of the identity.
- k-regular simple graph without 1-factor
- Example of a closed subspace of a Banach space which is not complemented?
- Certain products of mostly diagonal matrices are nonzero
- What is $f(f^{-1}(A))$?
- Is my proof that $U_{pq}$ is not cyclic if $p$ and $q$ are distinct odd primes correct?
- Continuous function $f:\mathbb{R}\to\mathbb{R}$ such that $f(f(x)) = -x$?
- What can we learn from prime generating polynomials?
- Constructing self-complementary regular graphs
- The strong topology on $U(\mathcal H)$ is metrisable
- If a cyclotomic integer has (rational) prime norm, is it a prime element?
- Minimal polynomial of the operator $T:V\oplus W\to V\oplus W$