# Tag Info

22

The cycle cover problem (CC) is the problem of finding a spanning set of cycles in a given directed or undirected input graph. If all the cycles in the cover must consist of at least $k$ edges/arcs, the resulting restriction of the problem is denoted $k$-UCC (in undirected graphs) and $k$-DCC (in directed graphs). The complexity of the directed version is ...

8

I don't have an answer to your question of whether the theory of Conway games has been used in building game-playing programs, but still you might be interested in the Combinatorial Game Suite, "an open-source program to aid research in combinatorial game theory" (which I first learned about here). It includes an implementation of various standard ...

7

It is implemented in Maxima (http://maxima.sourceforge.net/docs/manual/de/maxima_77.html#SEC400), to which Sage has interface. A few dozens of examples (ranging from very easy to very difficult) I tested today work in the exact same way as in Maple.

5

NAUTY can be used as a library to help you build a hashtable for the entire poset of graph minors for small $n$. The key would be the cannonial form given by NAUTY and the value would be a concatenation in sorted order of the cannonical forms of it's direct minors.

4

A slow brute-force implementation of the graph crossing number was added to Sage in Sage Trac ticket 24216: Add crossing number of a graph which was closed 2018-01-05, and merged in Sage 8.2.beta3.

3

on some search there do not seem to be much published general implementations of surreal numbers. heres an implementation of surreal numbers in coq. Surreal numbers in coq / Mamane, TYPES'04 Proceedings of the 2004 international conference on Types for Proofs and Programs Surreal Numbers form a totally ordered (commutative) Field, containing copies of ...

3

By the definition in the linked paper on page 5, the statement is wrong. Binary space partition (BSP) trees have been used for decades on computer graphics to speed up spatial queries, as have quadtrees and octrees. K-d trees are used extensively in machine learning to speed up nearest-neighbor searches. If you squint just a little, decision trees also fit ...

2

Here is an implementation of Surreal Numbers in a relatively new language, Julia. https://github.com/mroughan/SurrealNumbers.jl Described at https://www.sciencedirect.com/science/article/pii/S2352711018302152

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He keeps the source code on his web page : http://graphics.ucmerced.edu/software/tripath/index.html

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If you want an implementation, Sage has one. With a LP, as usual ;-) http://www.sagemath.org/doc/reference/graphs/sage/graphs/generic_graph.html#sage.graphs.generic_graph.GenericGraph.disjoint_routed_paths Nathann

1

Disclaimer: This is based on generic information theory knowledge only. Too long for a comment. Summary: The pointwise product of your two plots should go to some limit, as the relevant blocklengths and sequence lengths increase. I don't know if this applies to DNA but in theory if your sequence is ergodic (stationary, and time averages are the same as ...

1

Perfect hash construction (https://en.wikipedia.org/wiki/Perfect_hash_function#Construction) would apply to any use-case with static or infrequently-changing keys (e.g. top level domain names on routers, keywords in compilers, or function names in standard libraries) but the last time I looked I couldn't find any implementations. Parametric search can solve ...

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