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Expander Flows, Geometric Embeddings and Graph Partitioning

Summary: Expander Flows, Geometric Embeddings and Graph
Sanjeev Arora # Satish Rao + Umesh Vazirani #
We give a O( # log n)­approximation algorithm for spars­
est cut, balanced separator, and graph conduc­
tance problems. This improves the O(log n)­approxi­
mation of Leighton and Rao (1988). We use a well­
known semidefinite relaxation with triangle inequality
constraints. Central to our analysis is a geometric the­
orem about projections of point sets in # d , whose proof
makes essential use of a phenomenon called measure
We also describe an interesting and natural ``certifi­
cate'' for a graph's expansion, by embedding an n­node
expander in it with appropriate dilation and congestion.
We call this an expander flow.
Categories and Subject Descriptors
F.2 [Theory of Computation]: Analysis of Algorithms
General Terms


Source: Arora, Sanjeev - Department of Computer Science, Princeton University
Vazirani, Umesh - Department of Electrical Engineering and Computer Sciences, University of California at Berkeley


Collections: Computer Technologies and Information Sciences