Caring For Your Andersen Gliding Patio Door - Andersen Windows & Doors
Identifying local structure in large networks Reid Andersen Joint work with Fan Chung and Lincoln...
-
date post
22-Dec-2015 -
Category
Documents
-
view
217 -
download
3
Transcript of Identifying local structure in large networks Reid Andersen Joint work with Fan Chung and Lincoln...
Identifying local structure in large networks
Reid Andersen
Joint work with Fan Chung and Lincoln Lu
• Many small world models presume a trivial underlying geometry.
• We address the problem of identifying local structure in an arbitrary network.
• We introduce hybrid graphs, a random graph model with a power law
degree dist. and planted local structure represented by a local graph.
• Our algorithm Extract computes the largest local graph in a given network
with specified parameters.
• Existing clustering algorithms aren’t designed to identify local structure.• Existing performance guarantees are not suitable for this problem.
• We show that Extract approximately recovers planted local structure in
hybrid graphs• Improved approximation algorithm for max short flow.• New bounds for short versions of the max flow - min cut theorem.• Bounds on neighborhood growth in the hybrid graph model.
Also:
How can we identify local structure?
• We use short network flow to identify subgraphs with high local connectivity, which we call local graphs.
Outline:
Approximation algorithms for Max Short Flow
[Garg, Könemann 97]:• Algorithms for multicommodity flow, fractional packing.• Ratio
[Shahrokhi, Matula 89] and [Plotkin, Shmoys, Tardos 91]:• Introduced exponential length function technique for multi-flows
History:
[Fleischer, Skutella 02]:• Used Max Short Flow to approximate Quickest Multicommodity Flow.• Solve Max Short Flow using:
Ellipsoid method,Fractional packing.
• Adapted from multicommodity flow algorithm of [GK97].• Same approximation ratio.• Improved running time for testing local connectivity:
Our algorithm:
Recovery theorem:
and G(w) satisfies
then with probability
If L is an (f, )-local graph with bounded degree
(1)
(II)
Spectral drawings of a grid and random edges
Standard drawing
Drawing that ignores
edges removed by EXTRACT