Maximum Independent Set on Massive Graphs
Supervisor Prof. LuSpecial thanks to Hua
Problem Definition
• Independent Set(IS), Maximal IS, and Maximum IS
Easy! NP
Problem Definition
• Independent Set(IS), Maximal IS, and Maximum IS
• MIS on massive graphs?– In-memory algorithm?
Preliminaries
• Massive Graphs(Power Law Graphs)
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
Preliminaries
• External & Semi-external graph algorithms– External graph algorithm
– Semi-external graph algorithm
M<|G.V|<|G.E|
|G.V|<M<|G.E|
Preliminaries
• Local Optimization Algorithms– Greedy Algorithm– Hill Climbing
• 1-k-swap
Intuitions
• “Compress” the graph?
• Load graph into memory block by block, then merge the results?
• Only load the “useful” part of the graph?
Our Algorithm: SemiExternalGreedy(SEG)
• For preprocessing
• Good performance on β>2 PLRGs!
Our Algorithm: OneKSwap
• Condition for 1-k-swap?
• “deadlock”
• Our in-memory data structure
TwoKSwap, C-Kswap?
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)
Thanks
Q&A