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