feat: implement improved shortest path algorithm based on arXiv:2504.…

[wendelmax]

…17033

• Add improved_shortest_path: optimized Dijkstra with reduced sorting overhead
• Add bucket_shortest_path: O(E + V) algorithm for small integer weights
• Add adaptive_shortest_path: hybrid approach that chooses best algorithm
• Include comprehensive documentation with paper references
• Add 9 comprehensive tests covering various scenarios
• Update DIRECTORY.md to include new algorithm
• Export functions in graph module

This implementation demonstrates how to break the sorting barrier described in 'Breaking the Sorting Barrier for Directed Single-Source Shortest Paths' paper, providing significant performance improvements for graphs with small integer weights.

Pull Request Template

Description

Please include a summary of the change and which issue (if any) is fixed.
A brief description of the algorithm and your implementation method can be helpful too. If the implemented method/algorithm is not so
well-known, it would be helpful to add a link to an article explaining it with more details.

Type of change

Please delete options that are not relevant.

• Bug fix (non-breaking change which fixes an issue)
• New feature (non-breaking change which adds functionality)
• Breaking change (fix or feature that would cause existing functionality to not work as expected)

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.

Please make sure that if there is a test that takes too long to run ( > 300ms), you #[ignore] that or
try to optimize your code or make the test easier to run. We have this rule because we have hundreds of
tests to run; If each one of them took 300ms, we would have to wait for a long time.

[codecov-commenter]

Codecov Report

❌ Patch coverage is 99.75309% with 1 line in your changes missing coverage. Please review.
✅ Project coverage is 95.37%. Comparing base (aa3194f) to head (e44a006).
⚠️ Report is 3 commits behind head on master.

Files with missing lines	Patch %	Lines
src/graph/improved_shortest_path.rs	99.75%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master     #915      +/-   ##
==========================================
+ Coverage   95.33%   95.37%   +0.03%     
==========================================
  Files         319      320       +1     
  Lines       20890    21295     +405     
==========================================
+ Hits        19916    20310     +394     
- Misses        974      985      +11     

☔ View full report in Codecov by Sentry.
📢 Have feedback on the report? Share it here.

🚀 New features to boost your workflow:

• ❄️ Test Analytics: Detect flaky tests, report on failures, and find test suite problems.