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13

I strongly recommend the paper by Bixby, the "father" of CPLEX, that surveys not only on implementing aspects of the (revised) simplex algorithm: Robert E. Bixby, Solving Real-World Linear Programs: A Decade and More of Progress, Operations Research (50) 2002, 3-15.

8

A simple DFS+DP implementation was added to SAGE 4.8 last year: sage.graphs.graph_decompositions.vertex_separation.path_decomposition It's implemented in Cython (GNU GPL) here and here. Very simple and short if you ignore everything nonessential. $O(n\omega 2^n)$ time where $\omega = pw(G)$. It could be sped up with pruning rules, and particularly a ...

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

The answer is yes, check the following paper: SNARKs for C: Verifying Program Executions Succinctly and in Zero Knowledge Eli Ben-Sasson and Alessandro Chiesa and Daniel Genkin and Eran Tromer and Madars Virza http://eprint.iacr.org/2013/507 (also published at Crypto 2013)

3

sometimes with various CS optimization problems, the best available or most evolved implementations can be found in EE applications. in this case, consider Espresso, a logic minimizer. its open source and mainly written in C. it has a built in [exact] and also heuristic set cover as a subroutine after generating prime implicants for SAT. the exact covering ...

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 ...

3

Copy of my comment above (I suppose that the question can be accepted/closed): I think that the question is not research level, however perhaps this can help you: http://msl.cs.uiuc.edu/~lavalle/cs326a/rs.c (README: http://msl.cs.uiuc.edu/~lavalle/cs326a/README_RS). You can also take a look at Chapter 13 of the book "Planning algorithms".

2

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

2

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

2

There is no standard notion of "fundamentalness". It's not clear that what you are looking for is meaningful or makes any sense. What is "fundamental" is a matter of perspective; I don't see any reason to privilege insert as more fundamental than splice, or vice versa. So, if you need a concept of "fundamental" for some reason, you'll need to define for ...

2

Hisao Tamaki recently devised an exact algorithm for directed pathwidth (WG 2011). There he refers to some successful practical application of his approach (ISCIT 2010), so I guess he also has an implementation of the algorithm. Hisao Tamaki: A directed path-decomposition approach to exactly identifying attractors of boolean networks. International ...

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

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

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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