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Fix error in implementation of Erdos-Gallai condition in isgraphical #415

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Merged
merged 5 commits into from
Feb 18, 2025
Merged

Fix error in implementation of Erdos-Gallai condition in isgraphical #415

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c378d9f
Fix error in implementation of Erdos-Gallai condition in isgraphical
Syuizen Jan 10, 2025
c5aca53
improve isgraphical from O(n^2) to O(n*log(n))
Syuizen Jan 21, 2025
a803d32
format
Feb 18, 2025
e715f10
format
Syuizen Feb 18, 2025
77d0827
Merge branch 'isgraphical_fix' of https://github.com/Syuizen/Graphs.j…
Syuizen Feb 18, 2025
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11 changes: 3 additions & 8 deletions src/connectivity.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -805,17 +805,12 @@ function isgraphical(degs::AbstractVector{<:Integer})
sorted_degs = sort(degs; rev=true)
# Compute the length of the degree sequence
cur_sum = zero(UInt64)
# Compute the minimum of each degree and the corresponding index
mindeg = Vector{UInt64}(undef, n)
@inbounds for i in 1:n
mindeg[i] = min(i, sorted_degs[i])
end
# Check if the degree sequence satisfies the Erdös-Gallai condition
cum_min = sum(mindeg)
@inbounds for r in 1:(n - 1)
cur_sum += sorted_degs[r]
cum_min -= mindeg[r]
cond = cur_sum <= (r * (r - 1) + cum_min)
# Calculate the sum of the minimum of r and the degrees of the vertices
mid_deg_sum = sum([min(r, sorted_degs[i]) for i in (r + 1):n])
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@simonschoelly simonschoelly Jan 15, 2025

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Doing it this way makes the algorithm run in O(n^2) time. I think we might be able to avoid this by using the fact that we only need to consider in each iteration those degrees that are smaller than r. And for the other m degrees we can just add m * r to the sum. Using the factor that the degrees are sorted we can slide from the right hand side.

And we should be able to avoid a vector for each iteration.

Do you feel up for it? Otherwise I will give it a try.

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@Syuizen Syuizen Jan 17, 2025

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Thanks for the comment, then we need a pointer to track the index. I will make a revision over the weekend, along with some benchmark results.

cond = cur_sum <= (r * (r - 1) + mid_deg_sum)
cond || return false
end
return true
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1 change: 1 addition & 0 deletions test/connectivity.jl
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Expand Up @@ -316,6 +316,7 @@
@test @inferred(isgraphical([2, 2, 2]))
@test @inferred(isgraphical(fill(3, 10)))
@test @inferred(isgraphical(Integer[]))
@test @inferred(!isgraphical([4, 2, 2, 2, 0]))
##@test !@inferred(isgraphical([2]))

# Test simple digraphicality
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