Dominating Set

[SohamTamba]

Greedy heuristics for Dominating Set.

We really should consider changing the organisation of these heuristics for NP-Complete optimisation problems (vertex_cover, independent_set, dominating_set).

cc: @somil55 @sbromberger

[sbromberger]

We really should consider changing the organisation of these heuristics for NP-Complete optimisation problems.

What do you have in mind?

[SohamTamba]

I have a few ideas but they all have flaws. Maybe we can make a combination of them

1. Optimisation: Too broad, shortest paths also comes under this category
2. Vertex Set: Too broad
3. NP-Hard/Heuristic: Not very pleasant

How about Optimal Vertex Set?

[codecov]

Codecov Report

Merging #1039 into master will increase coverage by <.01%.
The diff coverage is 100%.

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##           master    #1039      +/-   ##
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+ Coverage   99.82%   99.82%   +<.01%     
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  Files          86       89       +3     
  Lines        2821     2847      +26     
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+ Hits         2816     2842      +26     
  Misses          5        5

[simonschoelly]

What about calling it "Combinatorics" ?
If you call it NP-Hard/Heuristic, you always must find a proof for that before you can put your problem there :)

[SohamTamba]

@sbromberger what do you think?

[sbromberger]

@sbromberger what do you think?

I don't have a well-formed opinion on the naming, but if this PR is ready for review, I'm game :) I'll probably want @jpfairbanks or @simonschoelly to review as well.

[simonschoelly]

What is DegreeDominatingSet? I think this should be explained somewhere.
Do these algorithms give some approximation guarantee such as outcome <= 2 * OPT ? Then you could mention that in the documentation.

[jpfairbanks]

I agree with @simonschoelly's comments.

[SohamTamba]

@simonschoelly there aren't approximation factors for these algos that I'm aware of

[sbromberger]

I'm ok with it being part of this PR, but it should probably go into utils.jl.

[SohamTamba]

@sbromberger I think Travis must be restarted.

Please take a look

[SohamTamba]

I think this is ready

[simonschoelly]

Isn't your algorithm the one described here: http://ac.informatik.uni-freiburg.de/teaching/ss_12/netalg/lectures/chapter7.pdf ? Then it has an approximation factor.

[SohamTamba]

Yeah you're right, the approximation factor is ln(maximum(degree(g)))+2