[RFC] Possible idea for GSoC 2020

[Jakub Narebski <jnareb@gmail.com>]

Hello,

Here below is a possible proposal for a more difficult Google Summer of
Code 2020 project.

A few questions:
- is it too late to propose a new project idea for GSoC 2020?
- is it too difficult of a project for GSoC?

Best,

  Jakub Narębski

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### Graph labelling for speeding up git commands

 - Language: C
 - Difficulty: hard / difficult
 - Possible mentors: Jakub Narębski

Git uses various clever methods for making operations on very large
repositories faster, from bitmap indices for git-fetch[1], to generation
numbers (also known as topological levels) in the commit-graph file for
commit graph traversal operations like `git log --graph`[2].

One possible improvement that can make Git even faster is using min-post
intervals labelling.  The basis of this labelling is post-visit order of
a depth-first search traversal tree of a commit graph, let's call it
'post(v)'.

If for each commit 'v' we would compute and store in the commit-graph
file two numbers: 'post(v)' and the minimum of 'post(u)' for all commits
reachable from 'v', let's call the latter 'min_graph(v)', then the
following condition is true:

  if 'v' can reach 'u', then min_graph(v) <= post(u) <= post(v)

If for each commit 'v' we would compute and store in the commit-graph
file two numbers: 'post(v)' and the minimum of 'post(u)' for commits
that were visited during the part of depth-first search that started
from 'v' (which is the minimum of post-order number for subtree of a
spanning tree that starts at 'v').  Let's call the later 'min_tree(v)'.
Then the following condition is true:

  if min_tree(v) <= post(u) <= post(v), then 'v' can reach 'u'

The task would be to implement computing such labelling (or a more
involved variant of it[3][4]), storing it in commit-graph file, and
using it for speeding up git commands (starting from a single chosen
command) such as:

 - git merge-base --is-ancestor A B
 - git branch --contains A
 - git tag --contains A
 - git branch --merged A
 - git tag --merged A
 - git merge-base --all A B
 - git log --topo-sort

References:

1. <http://githubengineering.com/counting-objects/>
2. <https://devblogs.microsoft.com/devops/supercharging-the-git-commit-graph-iii-generations/>
3. <https://arxiv.org/abs/1404.4465>
4. <https://github.com/steps/Ferrari>

See also discussion in:

<https://public-inbox.org/git/86tvl0zhos.fsf@gmail.com/t/>