Maximum Independent Set on Massive Graphs Supervisor Prof. Lu Special thanks to Hua.
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Transcript of Maximum Independent Set on Massive Graphs Supervisor Prof. Lu Special thanks to Hua.
![Page 1: Maximum Independent Set on Massive Graphs Supervisor Prof. Lu Special thanks to Hua.](https://reader035.fdocuments.in/reader035/viewer/2022070403/56649f2e5503460f94c483b3/html5/thumbnails/1.jpg)
Maximum Independent Set on Massive Graphs
Supervisor Prof. LuSpecial thanks to Hua
![Page 2: Maximum Independent Set on Massive Graphs Supervisor Prof. Lu Special thanks to Hua.](https://reader035.fdocuments.in/reader035/viewer/2022070403/56649f2e5503460f94c483b3/html5/thumbnails/2.jpg)
Problem Definition
• Independent Set(IS), Maximal IS, and Maximum IS
Easy! NP
![Page 3: Maximum Independent Set on Massive Graphs Supervisor Prof. Lu Special thanks to Hua.](https://reader035.fdocuments.in/reader035/viewer/2022070403/56649f2e5503460f94c483b3/html5/thumbnails/3.jpg)
Problem Definition
• Independent Set(IS), Maximal IS, and Maximum IS
• MIS on massive graphs?– In-memory algorithm?
![Page 4: Maximum Independent Set on Massive Graphs Supervisor Prof. Lu Special thanks to Hua.](https://reader035.fdocuments.in/reader035/viewer/2022070403/56649f2e5503460f94c483b3/html5/thumbnails/4.jpg)
Preliminaries
• Massive Graphs(Power Law Graphs)
![Page 5: Maximum Independent Set on Massive Graphs Supervisor Prof. Lu Special thanks to Hua.](https://reader035.fdocuments.in/reader035/viewer/2022070403/56649f2e5503460f94c483b3/html5/thumbnails/5.jpg)
Preliminaries
• Massive Graphs(Power Law Graphs)
• For a typical massive graph(i.e. social network graph),
α~14~10, β~2~3
|{v|d(v)=x}| = e^α/x^β
![Page 6: Maximum Independent Set on Massive Graphs Supervisor Prof. Lu Special thanks to Hua.](https://reader035.fdocuments.in/reader035/viewer/2022070403/56649f2e5503460f94c483b3/html5/thumbnails/6.jpg)
Preliminaries
• External & Semi-external graph algorithms– External graph algorithm
– Semi-external graph algorithm
M<|G.V|<|G.E|
|G.V|<M<|G.E|
![Page 7: Maximum Independent Set on Massive Graphs Supervisor Prof. Lu Special thanks to Hua.](https://reader035.fdocuments.in/reader035/viewer/2022070403/56649f2e5503460f94c483b3/html5/thumbnails/7.jpg)
Preliminaries
• Local Optimization Algorithms– Greedy Algorithm– Hill Climbing
• 1-k-swap
![Page 8: Maximum Independent Set on Massive Graphs Supervisor Prof. Lu Special thanks to Hua.](https://reader035.fdocuments.in/reader035/viewer/2022070403/56649f2e5503460f94c483b3/html5/thumbnails/8.jpg)
Intuitions
• “Compress” the graph?
• Load graph into memory block by block, then merge the results?
• Only load the “useful” part of the graph?
![Page 9: Maximum Independent Set on Massive Graphs Supervisor Prof. Lu Special thanks to Hua.](https://reader035.fdocuments.in/reader035/viewer/2022070403/56649f2e5503460f94c483b3/html5/thumbnails/9.jpg)
Our Algorithm: SemiExternalGreedy(SEG)
• For preprocessing
• Good performance on β>2 PLRGs!
![Page 10: Maximum Independent Set on Massive Graphs Supervisor Prof. Lu Special thanks to Hua.](https://reader035.fdocuments.in/reader035/viewer/2022070403/56649f2e5503460f94c483b3/html5/thumbnails/10.jpg)
Our Algorithm: OneKSwap
• Condition for 1-k-swap?
• “deadlock”
• Our in-memory data structure
![Page 11: Maximum Independent Set on Massive Graphs Supervisor Prof. Lu Special thanks to Hua.](https://reader035.fdocuments.in/reader035/viewer/2022070403/56649f2e5503460f94c483b3/html5/thumbnails/11.jpg)
TwoKSwap, C-Kswap?
![Page 12: Maximum Independent Set on Massive Graphs Supervisor Prof. Lu Special thanks to Hua.](https://reader035.fdocuments.in/reader035/viewer/2022070403/56649f2e5503460f94c483b3/html5/thumbnails/12.jpg)
The Hardness of TwoKSwap
• Hardness 1: Finding a 3-independent (sub)set externally
• Hardness 2: Conflict with others!
a
b c
a Label(∈ b) a Label(∈ c)
![Page 13: Maximum Independent Set on Massive Graphs Supervisor Prof. Lu Special thanks to Hua.](https://reader035.fdocuments.in/reader035/viewer/2022070403/56649f2e5503460f94c483b3/html5/thumbnails/13.jpg)
Thanks
Q&A