added a decremental connectivity data structure

[Miraksi]

Decremental Connectivity Query in Rust

Description

A data structure that, given a forest, allows dynamic-connectivity queries. Meaning deletion of an edge (u,v) and checking whether two vertecies are still connected. This implementation of an algorithm developed by Shimon Even and Yossi Shiloach, has a precomputiation phase with complexity O(n) (n being the number of verticies), a deletion complexity of O(log n) and a connectivity-query complexity of O(1).

New feature

• New feature (non-breaking change which adds functionality)

Checklist:

• I ran bellow commands using the latest version of rust nightly.
• I ran cargo clippy --all -- -D warnings just before my last commit and fixed any issue that was found.
• I ran cargo fmt just before my last commit.
• I ran cargo test just before my last commit and all tests passed.
• I added my algorithm to the corresponding mod.rs file within its own folder, and in any parent folder(s).
• I added my algorithm to DIRECTORY.md with the correct link.
• I checked COUNTRIBUTING.md and my code follows its guidelines.

[codecov-commenter]

Codecov Report

Attention: Patch coverage is 97.89474% with 4 lines in your changes are missing coverage. Please review.

Project coverage is 94.76%. Comparing base (10c986d) to head (1a656ee).
Report is 15 commits behind head on master.

Files	Patch %	Lines
src/graph/decremental_connectivity.rs	97.89%	4 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master     #684      +/-   ##
==========================================
+ Coverage   94.70%   94.76%   +0.06%     
==========================================
  Files         292      297       +5     
  Lines       23292    22148    -1144     
==========================================
- Hits        22058    20989    -1069     
+ Misses       1234     1159      -75     

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[vil02]

@Miraksi could you please share some reliable source about this data structure?

[Miraksi]

@Miraksi could you please share some reliable source about this data structure?

Shimon Even and Yossi Shiloach,
An On-Line Edge Deletion Problem,
SIAM Journal on Computing, 1972

This also is the paper took as reference, which was also referenced in the wikipedia entry on decremental connectivity
(I dont know if im allowed to share the whole paper for copyright reasons, which is why I only posted the relevant section)

[vil02]

@Miraksi your implementation works only for forests (connected list of trees), but the it is possible to (mis)use it for any graph. Do you see some reasonable way to avoid that?

By the way: feel free to rebase.

[Miraksi]

@Miraksi your implementation works only for forests (connected list of trees), but the it is possible to (mis)use it for any graph. Do you see some reasonable way to avoid that?

By the way: feel free to rebase.

Good Idea! I've added a function that checks whether the given graph is acyclic (ignoring cycles of lenght one). This check runs in O(n) time, so its basically for free.
Should the constructor panic, or return a result type?

[vil02]

Looks good enough, thanks!