Maximum Independent Set on Massive Graphs Supervisor Prof. Lu Special 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 bc a ∈ Label(b)a ∈ Label(c)

Thanks Q&A