JuliaGraphs / JuliaGraphs/Graphs.jl
Time complexity of Johnson's algorithm wrongly stated in documentation
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- Dominant language
- Julia
- Stars
- 538
- Forks
- 128
- Avg merge
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- Merged PRs (30d)
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Description
Description of bug
Describe the bug clearly and concisely.
The documentation to Johnson's all-pairs shortest path algorithm is stated as O(|V||E|). This cannot be true, in particular if Dijkstra's algorithm is finally called for weighted graphs. If Dijkstra's algorithm uses a Fibonacci heap (I didn't look if this is the case here), the runtime is O(|V|^2 log |V|+|V|⋅|E|), which is a big difference for sparse graphs.
Only in case of an unweighted graph, one can achieve time O(|V||E|) by calling breadth first search from each node.
Contributor guide
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Research direction
Locate the documentation for Johnson's all-pairs shortest path algorithm and read the referenced complexity statement alongside the algorithm's treatment of weighted and unweighted graphs. Verify the appropriate bounds for the implementation, then update the documentation to distinguish the weighted and unweighted cases and confirm the stated complexity is accurate.
Written by the indexing model from the issue text.
Assessment
- Tech stack
- julia
- Domain
- documentation
- Issue type
- Documentation
- Difficulty
- 2/5
- Estimated time
- 1-3 hours
- Activity status
- Stale
- Clarity
- Mostly clear
- Newbie friendliness
- 38/100